{"id":217,"date":"2020-08-21T19:43:14","date_gmt":"2020-08-21T23:43:14","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/add-and-subtract-integers\/"},"modified":"2021-03-24T10:52:03","modified_gmt":"2021-03-24T14:52:03","slug":"add-and-subtract-integers","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/add-and-subtract-integers\/","title":{"raw":"1.4 Add and Subtract Integers","rendered":"1.4 Add and Subtract Integers"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Use negatives and opposites<\/li>\n \t<li>Simplify: expressions with absolute value<\/li>\n \t<li>Add integers<\/li>\n \t<li>Subtract integers<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Use Negatives and Opposites<\/h1>\n<p id=\"fs-id1170655222181\">Our work so far has only included the counting numbers and the whole numbers. But if you have ever experienced a temperature below zero or accidentally overdrawn your checking account, you are already familiar with negative numbers. <strong data-effect=\"bold\">Negative numbers<\/strong> are numbers less than \\(0\\). The <span class=\"no-emphasis\" data-type=\"term\">negative numbers<\/span> are to the left of zero on the number line. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_03_001_new\">Figure 1<\/a>.<\/p>\n\n\n[caption id=\"\" align=\"aligncenter\" width=\"389\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_01_03_001_new.jpg\" alt=\"A number line extends from negative 4 to 4. A bracket is under the values \u201cnegative 4\u201d to \u201c0\u201d and is labeled \u201cNegative numbers\u201d. Another bracket is under the values 0 to 4 and labeled \u201cpositive numbers\u201d. There is an arrow in between both brackets pointing upward to zero.\" width=\"389\" height=\"113\" data-media-type=\"image\/jpeg\"> Figure 1 The number line shows the location of positive and negative numbers.[\/caption]\n\nThe arrows on the ends of the number line indicate that the numbers keep going forever. There is no biggest positive number, and there is no smallest negative number.\n<p id=\"fs-id1170655007025\">Is zero a positive or a negative number? Numbers larger than zero are positive, and numbers smaller than zero are negative. Zero is neither positive nor negative.<\/p>\nConsider how numbers are ordered on the number line. Going from left to right, the numbers increase in value. Going from right to left, the numbers decrease in value. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_03_002_new\">Figure 2<\/a>.\n<div id=\"CNX_ElemAlg_Figure_01_03_002_new\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"440\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_002_new.jpg\" alt=\"A number line ranges from negative 4 to 4. An arrow above the number line extends from negative 1 towards 4 and is labeled \u201clarger\u201d. An arrow below the number line extends from 1 towards negative 4 and is labeled \u201csmaller\u201d.\" width=\"440\" height=\"102\" data-media-type=\"image\/jpeg\"> Figure 2 The numbers on a number line increase in value going from left to right and decrease in value going from right to left.[\/caption]\n\n<\/div>\n<div class=\"textbox shaded\">\n\nRemember that we use the notation:\n<p id=\"fs-id1170654965355\"><em data-effect=\"italics\">a<\/em> &lt; <em data-effect=\"italics\">b<\/em> (read \u201ca is less than b\u201d) when a is to the left of b on the number line.<\/p>\n<p id=\"fs-id1170654901053\"><em data-effect=\"italics\">a<\/em> &gt; <em data-effect=\"italics\">b<\/em> (read \u201c<em data-effect=\"italics\">a<\/em> is greater than <em data-effect=\"italics\">b<\/em>\u201d) when <em data-effect=\"italics\">a<\/em> is to the right of <em data-effect=\"italics\">b<\/em> on the number line.<\/p>\n\n<\/div>\n<p id=\"fs-id1170654965087\">Now we need to extend the number line which showed the whole numbers to include negative numbers, too. The numbers marked by points in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_03_003_new\">Figure 3<\/a> are called the integers. The integers are the numbers \\(\\text{\u2026}-3,-2,-1,0,1,2,3\\text{\u2026}\\)<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_01_03_003_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\"><\/div>\n\n[caption id=\"\" align=\"aligncenter\" width=\"401\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_003_new.jpg\" alt=\"A number line extends from negative four to four. Points are plotted at negative four, negative three, negative two, negative one, zero, one, two, 3, and four.\" width=\"401\" height=\"44\" data-media-type=\"image\/jpeg\"> Figure 3 All the marked numbers are called integers.[\/caption]\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655160945\" data-type=\"problem\">\n<p id=\"fs-id1170654952892\">Order each of the following pairs of numbers, using &lt; or &gt;: a) \\(14\\)___\\(6\\) b) \\(-1\\)___\\(9\\) c) \\(-1\\)___\\(-4\\) d) \\(2\\)___\\(-20\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655177826\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170655192048\">It may be helpful to refer to the number line shown.<\/p>\n<span id=\"fs-id1170655201463\" data-type=\"media\" data-alt=\"A number line ranges from negative twenty to fifteen with ticks marks between numbers. Every fifth tick mark is labeled a number. Points are plotted at points negative twenty, negative 4, negative 1, 2, 6, 9 and 14.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_004_img_new.jpg\" alt=\"A number line ranges from negative twenty to fifteen with ticks marks between numbers. Every fifth tick mark is labeled a number. Points are plotted at points negative twenty, negative 4, negative 1, 2, 6, 9 and 14.\" data-media-type=\"image\/jpeg\"><\/span>\n<table id=\"eip-672\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a) 14 is to the right of 6 on the number line.<\/td>\n<td>\\(14\\)___\\(6\\)\u00a0 \\(14\\) &gt; \\(6\\)<\/td>\n<\/tr>\n<tr>\n<td>b) \u22121 is to the left of 9 on the number line.<\/td>\n<td>\\(-1\\)___\\(9\\)\u00a0 \\(-1&lt;9\\)<\/td>\n<\/tr>\n<tr>\n<td>c) \u22121 is to the right of \u22124 on the number line.<\/td>\n<td>\\(-1\\)___\\(-4\\)<\/td>\n<\/tr>\n<tr>\n<td>d) 2 is to the right of \u221220 on the number line.<\/td>\n<td>\\(2\\)___\\(-20\\) \\(2\\) &gt; \\(-20\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655162060\" data-type=\"problem\">\n<p id=\"fs-id1170654967573\">Order each of the following pairs of numbers, using &lt; or &gt; \\(\\text{:}\\) a) \\(15\\)___\\(7\\) b) \\(-2\\)___\\(5\\) c) \\(-3\\)___\\(-7\\)\nd) \\(5\\)___\\(-17\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654978104\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654967500\">a) &gt; b) &lt; c) &gt; d) &gt;<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655162421\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170655203196\" data-type=\"exercise\">\n<div id=\"fs-id1170655162060\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654880201\" data-type=\"problem\">\n<p id=\"fs-id1170654981845\">Order each of the following pairs of numbers, using &lt; or &gt; \\(\\text{:}\\) a) \\(8\\)___\\(13\\) b) \\(3\\)___\\(-4\\) c) \\(-5\\)___\\(-2\\)\nd) \\(9\\)___\\(-21\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654902746\">a) &lt; b) &gt; c) &lt; d) &gt;<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655114791\">You may have noticed that, on the <span class=\"no-emphasis\" data-type=\"term\">number line<\/span>, the negative numbers are a mirror image of the positive numbers, with zero in the middle. Because the numbers 2 and \\(-2\\) are the same distance from zero, they are called opposite<strong data-effect=\"bold\">s<\/strong>. The opposite of 2 is \\(-2\\), and the opposite of \\(-2\\) is 2<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Opposite<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nThe <strong data-effect=\"bold\">opposite<\/strong> of a number is the number that is the same distance from zero on the number line but on the opposite side of zero.\n\n<\/div>\n<\/div>\n<p id=\"fs-id1170654959734\"><a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_03_005_new\">(Figure 4)<\/a> illustrates the definition.<\/p>\nThe opposite of 3 is \\(-3\\).\n<div id=\"CNX_ElemAlg_Figure_01_03_005_new\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"440\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_005_new.jpg\" alt=\"A number line ranges from negative 4 to 4. There are two brackets above the number line. The bracket on the left spans from negative three to 0. The bracket on the right spans from zero to three. Points are plotted on both negative three and three.\" width=\"440\" height=\"81\" data-media-type=\"image\/jpeg\"> Figure 4[\/caption]\n\n<\/div>\n<p id=\"fs-id1170655163898\">Sometimes in algebra the same symbol has different meanings. Just like some words in English, the specific meaning becomes clear by looking at how it is used. You have seen the symbol \u201c\u2212\u201d used in three different ways.<\/p>\n\\(\\begin{array}{cccc}10-4\\hfill &amp; &amp; &amp; \\text{Between two numbers, it indicates the operation of}\\phantom{\\rule{0.2em}{0ex}}\\mathit{\\text{subtraction}}.\\hfill \\\\ &amp; &amp; &amp; \\text{We read}\\phantom{\\rule{0.2em}{0ex}}10-4\\phantom{\\rule{0.2em}{0ex}}\\text{as}\\phantom{\\rule{0.2em}{0ex}}\\text{\u201c}10\\phantom{\\rule{0.2em}{0ex}}\\text{minus}\\phantom{\\rule{0.2em}{0ex}}4.\\text{\u201d}\\hfill \\\\ -8\\hfill &amp; &amp; &amp; \\text{In front of a number, it indicates a}\\phantom{\\rule{0.2em}{0ex}}\\mathit{\\text{negative}}\\phantom{\\rule{0.2em}{0ex}}\\text{number.}\\hfill \\\\ &amp; &amp; &amp; \\text{We read}\\phantom{\\rule{0.2em}{0ex}}-8\\phantom{\\rule{0.2em}{0ex}}\\text{as \u201cnegative eight.\u201d}\\hfill \\\\ -x\\hfill &amp; &amp; &amp; \\text{In front of a variable, it indicates the}\\phantom{\\rule{0.2em}{0ex}}\\mathit{\\text{opposite}}.\\phantom{\\rule{0.2em}{0ex}}\\text{We read}\\phantom{\\rule{0.2em}{0ex}}-x\\phantom{\\rule{0.2em}{0ex}}\\text{as \u201cthe opposite of}\\phantom{\\rule{0.2em}{0ex}}x.\\text{\u201d}\\hfill \\\\ -\\left(-2\\right)\\hfill &amp; &amp; &amp; \\text{Here there are two}\\phantom{\\rule{0.2em}{0ex}}\\text{\u201c}-\\text{\u201d}\\phantom{\\rule{0.2em}{0ex}}\\text{signs. The one in the parentheses tells us the number is}\\hfill \\\\ &amp; &amp; &amp; \\text{negative}\\phantom{\\rule{0.2em}{0ex}}2.\\phantom{\\rule{0.2em}{0ex}}\\text{The one outside the parentheses tells us to take the}\\phantom{\\rule{0.2em}{0ex}}\\mathit{\\text{opposite}}\\phantom{\\rule{0.2em}{0ex}}\\text{of}\\phantom{\\rule{0.2em}{0ex}}-2.\\hfill \\\\ &amp; &amp; &amp; \\text{We read}\\phantom{\\rule{0.2em}{0ex}}-\\left(-2\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{as \u201cthe opposite of negative two.\u201d}\\hfill \\end{array}\\)\n<table id=\"eip-36\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 316.705px;\">\\(10-4\\)<\/td>\n<td style=\"width: 857.614px;\">Between two numbers, it indicates the operation of <em data-effect=\"italics\">subtraction<\/em>.\nWe read \\(10-4\\) as \"10 minus 4.\"<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 316.705px;\">\\(-8\\)<\/td>\n<td style=\"width: 857.614px;\">In front of a number, it indicates a <em data-effect=\"italics\">negative<\/em> number.\nWe read \u22128 as \"negative eight.\"<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 316.705px;\">\\(-x\\)<\/td>\n<td style=\"width: 857.614px;\">In front of a variable, it indicates the <em data-effect=\"italics\">opposite<\/em>. We read \\(-x\\) as \"the opposite of \\(x\\).\"<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 316.705px;\">\\(-\\left(-2\\right)\\)<\/td>\n<td style=\"width: 857.614px;\">Here there are two \"\u2212\" signs. The one in the parentheses tells us the number is negative 2. The one outside the parentheses tells us to take the <em data-effect=\"italics\">opposite<\/em> of \u22122.\nWe read \\(-\\left(-2\\right)\\) as \"the opposite of negative two.\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1170655189167\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Opposite Notation<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170655174724\">\\(-a\\) means the opposite of the number <em data-effect=\"italics\">a<\/em>.<\/p>\n<p id=\"fs-id1170655160739\">The notation \\(-a\\) is read as \u201cthe opposite of <em data-effect=\"italics\">a<\/em>.\u201d<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654943981\" data-type=\"problem\">\n<p id=\"fs-id1170655120989\">Find: a) the opposite of 7 b) the opposite of \\(-10\\) c) \\(-\\left(-6\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654978387\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169750893702\" style=\"width: 100%;\" summary=\"This figure has three parts: a , b, and c. Each part has text on the left and a corresponding number line on the right. The text for part \u201ca\u201d reads \u201cnegative seven is the same distance from zero as seven, but on the opposite side of zero.\u201d To the right is a number line ranging from negative seven to seven. There are two brackets above the number line. The first bracket is from negative 7 to zero. Above this bracket reads \u201c10\u201d. The second bracket is from 0 to seven. Above this bracket reads \u201c10\u201d. Under the number line it reads \u201cThe opposite of seven is negative seven\u201d. Points are plotted on negative seven and seven. The text for part \u201cb\u201d reads \u201cten is the same distance from zero as negative 10, but on the opposite side of zero.\u201d To the right is is a number line ranging from negative ten to ten. There are two brackets above the number line. The first bracket is from negative 10 to zero. Above this bracket reads \u201c10\u201d. The second bracket is from 0 to ten. Above this bracket reads \u201c10\u201d. Under the number line it reads \u201cThe opposite of negative ten is ten\u201d. Points are plotted on negative 10 and 10. The text for part \u201cc\u201d is an algebraic term: negative sign, open parenthesis, negative 6, close parenthesis. To the right is a number line ranging from negative six to six. There are two brackets above the number line. The first bracket is from negative 6 to zero. Above this bracket reads \u201c6\u201d. The second bracket is from 0 to 6. Above this bracket reads \u201csix\u201d. Under the number line it reads \u201cThe opposite of negative 6 is six\u201d. Points are plotted on negative 6 and 6.\" data-label=\"\">\n<tbody>\n<tr>\n<td>a) \u22127 is the same distance from 0 as 7, but on the opposite side of 0.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169750893747\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span>\nThe opposite of 7 is \u22127.<\/td>\n<\/tr>\n<tr>\n<td>b) 10 is the same distance from 0 as \u221210, but on the opposite side of 0.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169750893770\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span>\nThe opposite of \u221210 is 10.<\/td>\n<\/tr>\n<tr>\n<td>c) \u2212(\u22126)<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169746122554\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span>\nThe opposite of \u2212(\u22126) is \u22126.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655219776\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170655004578\" data-type=\"exercise\">\n<div id=\"fs-id1170654916783\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655020985\" data-type=\"problem\">\n<p id=\"fs-id1170655026818\">Find: a) the opposite of 4 b) the opposite of \\(-3\\) c) \\(-\\left(-1\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654916783\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654952585\">a)\\(-4\\) b) 3 c) 1<\/p>\n\n<\/details><\/div>\n&nbsp;\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655105370\" data-type=\"problem\">\n<p id=\"fs-id1170655229618\">Find: a) the opposite of 8 b) the opposite of \\(-5\\) c) \\(-\\left(-5\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655113221\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655155259\">a)\\(-8\\) b) 5 c) 5<\/p>\n\n<\/details><\/div>\n&nbsp;\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654920902\">Our work with opposites gives us a way to define the integers.The whole numbers and their opposites are called the integers. The integers are the numbers \\(\\text{\u2026}-3,-2,-1,0,1,2,3\\text{\u2026}\\)<\/p>\n\n<div id=\"fs-id1170655134778\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Integers<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170654954489\">The whole numbers and their opposites are called the <strong data-effect=\"bold\">integers<\/strong>.<\/p>\n<p id=\"fs-id1170654878555\">The integers are the numbers<\/p>\n\n<div id=\"fs-id1170655114692\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\text{\u2026}-3,-2,-1,0,1,2,3\\text{\u2026}\\)<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654999979\">When evaluating the opposite of a <span class=\"no-emphasis\" data-type=\"term\">variable<\/span>, we must be very careful. Without knowing whether the variable represents a positive or negative number, we don\u2019t know whether \\(-x\\) is positive or negative. We can see this in <a class=\"autogenerated-content\" href=\"#fs-id1170655134821\">Example 3<\/a>.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655134821\" data-type=\"problem\">\n<p id=\"fs-id1170655353645\">Evaluate a) \\(-x\\), when \\(x=8\\) b) \\(-x\\), when \\(x=-8\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654982628\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<ol id=\"fs-id1166422695391\" class=\"circled\" type=\"a\">\n \t<li>\n<table id=\"eip-id1169754061868\" class=\"unnumbered unstyled\" summary=\"This is an image of a solution in two columns, with text in the left column and math in the right column. In the first row of the first column, the text reads, \u201cTo evaluate when x equals 8 means to substitute 8 for x,\u201d where the number 8 is written in red. The next line down in the right column is negative x. The second line down in the left column, the text reads, \u201cSubstitute 8 for x.\u201d Next to this in the right column is the term negative sign, open parenthesis, 8, close parenthesis, where the number 8 is written in red. The next line down in the left column, the text reads \u201cWrite the opposite of 8.\u201d Next to this in the right column is negative 8.\" data-label=\"\">\n<tbody>\n<tr>\n<td><span id=\"eip-id1169754061885\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">\u2212<em data-effect=\"italics\">x<\/em><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169752188793\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752188805\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the opposite of 8.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752188824\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_007d_img.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n&nbsp;<\/li>\n \t<li>\n<table id=\"eip-id1169754029691\" class=\"unnumbered unstyled\" summary=\"This is an image of a solution in two columns, with text in the left column and math in the right column. In the first row of the first column, the text reads, \u201cTo evaluate when x equals negative 8 means to substitute negative 8 for x,\u201d where the number negative 8 is written in red. The next line down in the right column is negative x. The second line down in the left column, the text reads, \u201cSubstitute negative 8 for x.\u201d Next to this in the right column is the term negative sign, open parenthesis, negative 8, close parenthesis, where the number negative 8 is written in red. The next line down in the left column, the text reads \u201cWrite the opposite of negative 8.\u201d Next to this in the right column is the number 8.\" data-label=\"\">\n<tbody>\n<tr>\n<td><span id=\"fs-id1169754375291\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">\u2212<em data-effect=\"italics\">x<\/em><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169754029738\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169751926699\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the opposite of \u22128.<\/td>\n<td data-align=\"center\">8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654985194\" data-type=\"problem\">\n<p id=\"fs-id1170654964972\">Evaluate \\(-n\\), when a) \\(n=4\\) b) \\(n=-4\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655022421\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655022423\">a)\\(-4\\) b) 4<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654984479\" data-type=\"problem\">\n<p id=\"fs-id1170654984481\">Evaluate \\(-m\\), when a) \\(m=11\\) b) \\(m=-11\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654966628\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654943547\">a)\\(-11\\) b) 11<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Simplify: Expressions with Absolute Value<\/h1>\nWe saw that numbers such as \\(2\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}-2\\) are opposites because they are the same distance from 0 on the number line. They are both two units from 0. The distance between 0 and any number on the number line is called the <strong data-effect=\"bold\">absolute value<\/strong> of that number.\n<div id=\"fs-id1170655195725\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Absolute Value<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170655354299\">The absolute value of a number is its distance from 0 on the number line.<\/p>\n<p id=\"fs-id1170654982157\">The absolute value of a number <em data-effect=\"italics\">n<\/em> is written as \\(|n|\\).<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655160915\">For example,<\/p>\n\n<ul id=\"fs-id1166424918316\" data-bullet-style=\"bullet\">\n \t<li>\\(-5\\phantom{\\rule{0.2em}{0ex}}\\text{is}\\phantom{\\rule{0.2em}{0ex}}5\\) units away from \\(0\\), so \\(|-5|=5\\).<\/li>\n \t<li>\\(\\phantom{\\rule{0.65em}{0ex}}5\\phantom{\\rule{0.2em}{0ex}}\\text{is}\\phantom{\\rule{0.2em}{0ex}}5\\) units away from \\(0\\), so \\(|5|=5\\).<\/li>\n<\/ul>\n<p id=\"fs-id1170655134144\"><a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_03_009_new\">Figure 5<\/a> illustrates this idea.<\/p>\nThe integers \\(5\\phantom{\\rule{0.2em}{0ex}}\\text{and are}\\phantom{\\rule{0.2em}{0ex}}5\\) units away from \\(0\\).\n<div id=\"CNX_ElemAlg_Figure_01_03_009_new\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"385\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_009_new.jpg\" alt=\"A number line is shown ranging from negative 5 to 5. A bracket labeled \u201c5 units\u201d lies above the points negative 5 to 0. An arrow labeled \u201cnegative 5 is 5 units from 0, so absolute value of negative 5 equals 5.\u201d is written above the labeled bracket. A bracket labeled \u201c5 units\u201d lies above the points \u201c0\u201d to \u201c5\u201d. An arrow labeled \u201c5 is 5 units from 0, so absolute value of 5 equals 5.\u201d and is written above the labeled bracket.\" width=\"385\" height=\"130\" data-media-type=\"image\/jpeg\"> Figure 5[\/caption]\n\n<\/div>\n<p id=\"fs-id1170654957170\">The absolute value of a number is never negative (because distance cannot be negative). The only number with absolute value equal to zero is the number zero itself, because the distance from \\(0\\phantom{\\rule{0.2em}{0ex}}\\text{to}\\phantom{\\rule{0.2em}{0ex}}0\\) on the number line is zero units.<\/p>\n\n<div id=\"fs-id1170654997376\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Property of Absolute Value<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170654916082\">\\(|n|\\ge 0\\) for all numbers<\/p>\n<p id=\"fs-id1170655074945\">Absolute values are always greater than or equal to zero!<\/p>\n&nbsp;\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655150245\">Mathematicians say it more precisely, \u201cabsolute values are always non-negative.\u201d Non-negative means greater than or equal to zero.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655164890\" data-type=\"problem\">\n<p id=\"fs-id1170655164892\">Simplify:\u00a0a)\u00a0\\(|3|\\)\u00a0b)\u00a0\\(|-44|\\)\u00a0c)\u00a0\\(|0|\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655213327\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170654944089\">The absolute value of a number is the distance between the number and zero. Distance is never negative, so the absolute value is never negative.<\/p>\n<p id=\"fs-id1166424887501\">a) \\(|3|\\)\n\\(\\phantom{\\rule{1.2em}{0ex}}3\\)<\/p>\nb) \\(|-44|\\)\n\\(\\phantom{\\rule{1.5em}{0ex}}44\\)\n\nc) \\(|0|\\)\n\\(0\\phantom{\\rule{1.5em}{0ex}}\\)\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655074703\" data-type=\"problem\">\n<p id=\"fs-id1170655178086\">Simplify:\u00a0a)\u00a0\\(|4|\\)\u00a0b)\u00a0\\(|-28|\\)\u00a0c)\u00a0\\(|0|\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655161378\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655161380\">a)\u00a04\u00a0b)\u00a028\u00a0c)\u00a00<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655160962\" data-type=\"problem\">\n<p id=\"fs-id1170655000504\">Simplify:\u00a0a)\u00a0\\(|-13|\\)\u00a0b)\u00a0\\(|47|\\)\u00a0c)\u00a0\\(|0|\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655026795\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655026797\">a)\u00a013\u00a0b)\u00a047\u00a0c) 0<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654887750\">In the next example, we\u2019ll order expressions with absolute values. Remember, positive numbers are always greater than negative numbers!<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1170654953584\">Fill in &lt;, &gt;, \\(\\phantom{\\rule{0.2em}{0ex}}\\text{or}\\phantom{\\rule{0.2em}{0ex}}=\\) for each of the following pairs of numbers:<\/p>\n<p id=\"fs-id1170654916476\">a) \\(|-5|\\)___\\(-|-5|\\) b) \\(8\\)___\\(-|-8|\\)c) \\(-9\\)___\\(-|-9|\\) d) -\\(-16\\)___\\(-|-16|\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1170655106909\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%; height: 184px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td>\\(|-5|\\)___ -\\(|-5|\\)<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td>a) Simplify.\nOrder.<\/td>\n<td>5 ___ -5<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td>5\u00a0 &gt; -5<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td>\\(|-5|\\)\u00a0 &gt; -\\(|-5|\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td>b) Simplify.\nOrder.<\/td>\n<td>\\(8\\) ___ -\\(|-8|\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td>8 ___ -8<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td>8 &gt; -8<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td>8 &gt; -\\(|-8|\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td>c) Simplify.\nOrder.<\/td>\n<td>9 ___ -\\(|-9|\\)\n\n-9 ___ -9\n\n-9 = -9\n\n-9 = -\\(|-9|\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td>d) Simplify.\nOrder.<\/td>\n<td>-\\((-16)\\) ___ -\\(|-16|\\)\n\n16 ____ -16\n\n16 &gt; -16\n\n-\\((-16)\\) &gt; -\\(|-16|\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655121090\" data-type=\"problem\">\n<p id=\"fs-id1170655099637\">Fill in &lt;, &gt;, or \\(=\\) for each of the following pairs of numbers:\u00a0a) \\(|-9|\\)___-\\(|-9|\\) b) \\(2\\)___-\\(|-2|\\) c) \\(-8\\)___\\(|-8|\\)\nd) \\(\\-(-9\\)___\\(-|-9|\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655228722\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655352028\">a)\u00a0&gt;\u00a0b)\u00a0&gt;\u00a0c)\u00a0&lt;\u00a0d)\u00a0&gt;<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655083336\" data-type=\"problem\">\n<p id=\"fs-id1170655065401\">Fill in &lt;, &gt;, or \\(=\\) for each of the following pairs of numbers:\u00a0a) \\(7\\)___-\\(|-7|\\) b) \\(\\-(-10\\)___-\\(|-10|\\)\nc) \\(|-4|\\)___\\(-|-4|\\) d) \\(-1\\)___\\(|-1|\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655003444\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655157651\">a)\u00a0&gt;\u00a0b)\u00a0&gt;\u00a0c)\u00a0&gt;\u00a0d) &lt;<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655060167\">We now add absolute value bars to our list of grouping symbols. When we use the order of operations, first we simplify inside the absolute value bars as much as possible, then we take the <span class=\"no-emphasis\" data-type=\"term\">absolute value<\/span> of the resulting number.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\"><caption>Grouping Symbols<\/caption>\n<tbody>\n<tr>\n<td style=\"width: 50%;\">Parentheses<\/td>\n<td style=\"width: 50%;\">( )<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Brackets<\/td>\n<td style=\"width: 50%;\">[ ]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Braces<\/td>\n<td style=\"width: 50%;\">{ }<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Absolute value<\/td>\n<td style=\"width: 50%;\">| |<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655103794\">In the next example, we simplify the expressions inside absolute value bars first, just like we do with parentheses.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655218379\" data-type=\"problem\">\n<p id=\"fs-id1170655000668\">Simplify: \\(24-|19-3\\left(6-2\\right)|\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654968392\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-46\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(24-|19-3\\left(6-2\\right)|\\)<\/td>\n<\/tr>\n<tr>\n<td>Work inside parentheses first: subtract 2 from 6.<\/td>\n<td>\\(24-|19-3\\left(4\\right)|\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply 3(4).<\/td>\n<td>\\(24-|19-12|\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract inside the absolute value bars.<\/td>\n<td>\\(24-|7|\\)<\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td>\\(24-7\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>\\(17\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655222089\" data-type=\"problem\">\n<p id=\"fs-id1170655222091\">Simplify: \\(19-|11-4\\left(3-1\\right)|\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654963377\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654963379\">16<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654931969\" data-type=\"problem\">\n<p id=\"fs-id1170654931971\">Simplify: \\(9-|8-4\\left(7-5\\right)|\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655150934\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655269907\">9<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655194444\" data-type=\"problem\">\n<p id=\"fs-id1170655218370\">Evaluate: a) \\(|x|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=-35\\) b) \\(|-y|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}y=-20\\) c) \\(-|u|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}u=12\\) d) \\(-|p|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}p=-14\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655030077\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1166425224104\">a)\\(|x|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=-35\\)<\/p>\n\n<table id=\"eip-id1169747671487\" class=\"unnumbered unstyled\" summary=\"This image shows a solution in two columns. In the right column is the term \u201cabsolute value of x.\u201d One row down, the text in the left column reads \u201cSubstitute negative 35 for x.\u201d Next to this in the right column is the term \u201cabsolute value of negative 35\u201d, where negative 35 is written in red. One row down, the text in the left column reads \u201cTake the absolute value.\u201d Next to this in the right column is 35.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\">\\(|x|\\)<\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169747671518\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td data-align=\"right\"><span id=\"eip-id1169747671530\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td data-align=\"right\">35<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nb)\\(|-y|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}y=-20\\)\n<table id=\"eip-id1169752110168\" class=\"unnumbered unstyled\" summary=\"This image shows a solution in two columns. In the right column is the term \u201cabsolute value of negative y\u201d . One row down, the text in the left column reads \u201cSubstitute negative 20 for y.\u201d Next to this in the right column is the term \u201cabsolute value of negative sign, partenthesis, negative 20, close parenthesis.\u201d Negative 20 is written in red. One row down, the text in the left column row reads \u201cSimplify.\u201dNext to this in the right column is the term \u201cabsolute value of 20\u201d. One row down, the text in the left column reads \u201cTake the absolute value.\u201d Next to this in the right column is 20.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\">\\(|-y|\\)<\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169749467086\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_011a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td data-align=\"right\"><span id=\"eip-id1169749467098\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_011b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"right\">\\(|20|\\)<\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td data-align=\"right\">20<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nc)\\(-|u|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}u=12\\)\n<table id=\"eip-id1169750879718\" class=\"unnumbered unstyled\" summary=\"This image shows a solution in two columns. In the right column is the term \u201cnegative sign, absolute value of u\u201d. One row down, the text in the left column reads \u201cSubstitute 12 for u.\u201d Next to this in the right column is the term \u201cnegative sign, absolute value of 12\u201d, where 12 is written in red. One row down, the text in the left column reads \u201cTake the absolute value.\u201d Next to this in the right column is negative 12.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\">\\(-|u|\\)<\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169753237141\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_012a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td data-align=\"right\"><span id=\"eip-id1169753237153\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_012b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td data-align=\"right\">\\(-12\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nd)\\(-|p|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}p=-14\\)\n<table id=\"eip-id1169754142438\" class=\"unnumbered unstyled\" summary=\"This image shows a solution in two columns. In the right column is the term \u201cnegative sign, absolute value of p\u201d. One row down, the text in the left column reads \u201cSubstitute negative 14 for p.\u201d Next to this in the right column is the term \u201cnegative sign, absolute value of negative 14\u201d, where negative 14 is written in red. One row down, the text in the left column reads \u201cTake the absolute value.\u201d Next to this in the right column is negative 14.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\">\\(-|p|\\)<\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169754142474\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td data-align=\"right\"><span id=\"eip-id1169754130713\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td data-align=\"right\">\\(-14\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655193881\" data-type=\"problem\">\n<p id=\"fs-id1170655193884\">Evaluate: a) \\(|x|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=-17\\) b) \\(|-y|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}y=-39\\) c) \\(-|m|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}m=22\\) d) \\(-|p|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}p=-11\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655129135\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655129137\">a) \\(17\\) b) \\(39\\) c) \\(-22\\) d) \\(-11\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655355508\" data-type=\"problem\">\n\nEvaluate: a) \\(|y|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}y=-23\\) b) \\(|-y|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}y=-21\\) c) \\(-|n|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}n=37\\) d) \\(-|q|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}q=-49\\).\n\n<\/div>\n<div id=\"fs-id1170654902359\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655098975\">a) \\(23\\) b) \\(21\\) c) \\(-37\\) d) \\(-49\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Add Integers<\/h1>\n<p id=\"fs-id1170654942147\">Most students are comfortable with the addition and subtraction facts for positive numbers. But doing addition or subtraction with both positive and negative numbers may be more challenging.<\/p>\n<p id=\"fs-id1170654982815\">We will use two colour counters to model addition and subtraction of negatives so that you can visualize the procedures instead of memorizing the rules.<\/p>\n<p id=\"fs-id1170654940836\">We let one colour (blue) represent positive. The other colour (red) will represent the negatives. If we have one positive counter and one negative counter, the value of the pair is zero. They form a neutral pair. The value of this neutral pair is zero.<\/p>\n<span id=\"fs-id1170654940841\" data-type=\"media\" data-alt=\"In this image we have a blue counter above a red counter with a circle around both. The equation to the right is 1 plus negative 1 equals 0.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_014_img_new.jpg\" alt=\"In this image we have a blue counter above a red counter with a circle around both. The equation to the right is 1 plus negative 1 equals 0.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1170654925278\">We will use the counters to show how to add the four addition facts using the numbers \\(5,-5\\) and \\(3,-3\\).<\/p>\n\\(\\begin{array}{cccccccccc}\\hfill 5+3\\hfill &amp; &amp; &amp; \\hfill -5+\\left(-3\\right)\\hfill &amp; &amp; &amp; \\hfill -5+3\\hfill &amp; &amp; &amp; \\hfill 5+\\left(-3\\right)\\hfill \\end{array}\\)\n<p id=\"fs-id1170654942111\">To add \\(5+3\\), we realize that \\(5+3\\) means the sum of 5 and 3<\/p>\n\n<table id=\"eip-id1169751875448\" style=\"width: 100%;\" summary=\"In this figure, there are two columns and three rows. The left column, first row reads \u201cwe start with 5 positives.\u201d Next to this in the right column are 5 positive counters with the number 5 underneath. In the next row, it reads, \u201cAnd then we add 3 positives. Next to this is a group of 5 positive counters, separated by a space and then 3 positive counters. The next row down reads, \u201cWe now have eight positives. The sum of 5 and 3 is 8.\u201d Next to this are eight positive counters. with the label \u201c8 positives\u201d written underneath.\" data-label=\"\">\n<tbody>\n<tr>\n<td>We start with 5 positives.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169754176959\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_015a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>And then we add 3 positives.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169754176978\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_015b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We now have 8 positives. The sum of 5 and 3 is 8.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169753253870\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_015c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654940990\">Now we will add \\(-5+\\left(-3\\right)\\). Watch for similarities to the last example \\(5+3=8\\).<\/p>\n<p id=\"fs-id1170655170230\">To add \\(-5+\\left(-3\\right)\\), we realize this means the sum of \\(-5\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}-3\\).<\/p>\n\n<table id=\"eip-id1169751926722\" style=\"width: 100%;\" summary=\"In this figure, there are two columns and three rows. The left column, first row reads \u201cwe start with 5 negatives.\u201d Next to this in the right column are 5 negative counters with the numeral negative 5 underneath. In the next row, it reads, \u201cAnd then we add 3 negatives. Next to this is a group of 5 negative counters, separated by a space and then 3 negative counters. The next row down reads, \u201cWe now have eight negatives. The sum of negative 5 and negative 3 is negative 8.\u201d Next to this are eight negative counters. with the label \u201c8 negatives\u201d written underneath.\" data-label=\"\">\n<tbody>\n<tr>\n<td>We start with 5 negatives.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169751926744\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_018a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>And then we add 3 negatives.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169754029689\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_018b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We now have 8 negatives. The sum of \u22125 and \u22123 is \u22128.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169754029708\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_018c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654905072\">In what ways were these first two examples similar?<\/p>\n\n<ul id=\"fs-id1166424896444\" data-bullet-style=\"bullet\">\n \t<li>The first example adds 5 positives and 3 positives\u2014both positives.<\/li>\n \t<li>The second example adds 5 negatives and 3 negatives\u2014both negatives.<\/li>\n<\/ul>\n<p id=\"fs-id1170654905046\">In each case we got 8\u2014either 8 positives or 8 negatives.<\/p>\n<p id=\"fs-id1170654905109\">When the signs were the same, the counters were all the same color, and so we added them.<\/p>\n<span id=\"fs-id1170655040356\" data-type=\"media\" data-alt=\"This figure is divided into two columns. In the left column there are eight blue counters in a horizontal row. Under them is the text \u201c8 positives.\u201d Centred under this is the equation 5 plus 3 equals 8. In the right column are eight red counters in a horizontal row which are labled below with the phrase \u201c8 negatives\u201d. Centred under this is the equation negative 5 plus negative 3 equals negative 8, where negative 3 is in parentheses.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_021_img_new.jpg\" alt=\"This figure is divided into two columns. In the left column there are eight blue counters in a horizontal row. Under them is the text \u201c8 positives.\u201d Centred under this is the equation 5 plus 3 equals 8. In the right column are eight red counters in a horizontal row which are labled below with the phrase \u201c8 negatives\u201d. Centred under this is the equation negative 5 plus negative 3 equals negative 8, where negative 3 is in parentheses.\" data-media-type=\"image\/jpeg\"><\/span>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655040352\" data-type=\"problem\">\n<p id=\"fs-id1170655030146\">Add:\u00a0a)\u00a0\\(1+4\\)\u00a0b)\u00a0\\(-1+\\left(-4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655030382\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\na)\n\n[caption id=\"\" align=\"alignnone\" width=\"270\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_022_img_new.jpg\" alt=\".\" width=\"270\" height=\"75\" data-media-type=\"image\/jpeg\"> 1 positive plus 4 positives is 5 positives.[\/caption]\n\n&nbsp;\n<p id=\"fs-id1169145731676\">b)<\/p>\n\n\n[caption id=\"\" align=\"alignnone\" width=\"285\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_023_img_new.jpg\" alt=\".\" width=\"285\" height=\"72\" data-media-type=\"image\/jpeg\"> 1 negative plus 4 negatives is 5 negatives.[\/caption]\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655040471\" data-type=\"problem\">\n<p id=\"fs-id1170655040473\">Add:\u00a0a)\u00a0\\(2+4\\)\u00a0b)\u00a0\\(-2+\\left(-4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655040605\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655040607\">a)\u00a06\u00a0b)\u00a0\\(-6\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655040652\" data-type=\"problem\">\n<p id=\"fs-id1170655040655\">Add:\u00a0a)\u00a0\\(2+5\\)\u00a0b)\u00a0\\(-2+\\left(-5\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655040708\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655040710\">a)\u00a07\u00a0b) \\(-7\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655030242\">So what happens when the signs are different? Let\u2019s add \\(-5+3\\). We realize this means the sum of \\(-5\\) and 3. When the counters were the same color, we put them in a row. When the counters are a different color, we line them up under each other.<\/p>\n\n<table id=\"eip-id1169750997833\" style=\"width: 100%;\" summary=\"This figure is divided into two columns. Text at the top of the image in the right column reads \u201cnegative 5 plus 3 means the sum of negative 5 and 3.\u201d One line down in the left column, the text reads \u201cWe start with 5 negatives.\u201d In the right column are five red counters. One line down in the left column, the text reads \u201cAnd then we add 3 positives\u201d. Next to this in the right column is a horizontal row of five red counters drawn above three blue counters. One line down, the text in the left column reads \u201cWe remove any neutral pairs.\u201d Next to this in the right column are three pairs of one red counter and one blue counter, each pair circled. There are two remaining red counters to the right of the paired counters. One line down, the text in the left column reads \u201cWe have 2 negatives left.\u201d Next to this in the right column are two red counters labeled \u201c2 negatives\u201d. In the last row, the text in the left column reads \u201cThe sum of negative 5 and 3 is negative 2.\u201d Next to this in the right column is the equation negative 5 plus 3 equals negative 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\u22125 + 3 means the sum of \u22125 and 3.<\/td>\n<\/tr>\n<tr>\n<td>We start with 5 negatives.<\/td>\n<td><span id=\"eip-id1169750997858\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_024a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>And then we add 3 positives.<\/td>\n<td><span id=\"eip-id1169750997874\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_024b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We remove any neutral pairs.<\/td>\n<td><span id=\"eip-id1169747671495\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_024c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We have 2 negatives left.<\/td>\n<td><span id=\"eip-id1169747671512\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_024d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>The sum of \u22125 and 3 is \u22122.<\/td>\n<td>\u22125 + 3 = \u22122<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654936878\">Notice that there were more negatives than positives, so the result was negative.<\/p>\nLet\u2019s now add the last combination, \\(5+\\left(-3\\right)\\).\n<table id=\"eip-id1169754030168\" style=\"width: 100%;\" summary=\"This figure is divided into two columns. Text at the top of the image in the right column reads \u201c5 plus negative 3 means the sum of negative 5 and 3.\u201d One line down in the left column, the text reads \u201cWe start with 5 positives.\u201d In the right column are five blue counters. One line down in the left column, the text reads \u201cAnd then we add 3 negatives\u201d. Next to this in the right column is a horizontal row of five blue counters drawn above three red counters. One line down, the text in the left column reads \u201cWe remove any neutral pairs.\u201d Next to this in the right column are three pairs of one blue counter and one red counter, each pair circled. There are two remaining blue counters to the right of the paired counters. One line down, the text in the left column reads \u201cWe have 2 positives left.\u201d Next to this in the right column are two blue counters labeled \u201c2 positives\u201d. In the last row, the text in the left column reads \u201cThe sum of 5 and negative 3 is 2.\u201d Next to this in the right column is the equation 5 plus negative 3 equals 2, where negative 3 is in parentheses.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>5 + (\u22123) means the sum of 5 and \u22123.<\/td>\n<\/tr>\n<tr>\n<td>We start with 5 positives.<\/td>\n<td><span id=\"eip-id1169754030192\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_025a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>And then we add 3 negatives.<\/td>\n<td><span id=\"eip-id1169754030208\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_025b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We remove any neutral pairs.<\/td>\n<td><span id=\"eip-id1169754030225\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_025c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We have 2 positives left.<\/td>\n<td><span id=\"eip-id1169748875617\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_025d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>The sum of 5 and \u22123 is 2.<\/td>\n<td>5 + (\u22123) = 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655057773\">When we use counters to model addition of positive and negative integers, it is easy to see whether there are more positive or more negative counters. So we know whether the sum will be positive or negative.<\/p>\n<span id=\"fs-id1170655058518\" data-type=\"media\" data-alt=\"Two images are shown and labeled. The left image shows five red counters in a horizontal row drawn above three blue counters in a horizontal row, where the first three pairs of red and blue counters are circled. Above this diagram is written \u201cnegative 5 plus 3\u201d and below is written \u201cMore negatives \u2013 the sum is negative.\u201d The right image shows five blue counters in a horizontal row drawn above three red counters in a horizontal row, where the first three pairs of red and blue counters are circled. Above this diagram is written \u201c5 plus negative 3\u201d and below is written \u201cMore positives \u2013 the sum is positive.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_026_img_new.jpg\" alt=\"Two images are shown and labeled. The left image shows five red counters in a horizontal row drawn above three blue counters in a horizontal row, where the first three pairs of red and blue counters are circled. Above this diagram is written \u201cnegative 5 plus 3\u201d and below is written \u201cMore negatives \u2013 the sum is negative.\u201d The right image shows five blue counters in a horizontal row drawn above three red counters in a horizontal row, where the first three pairs of red and blue counters are circled. Above this diagram is written \u201c5 plus negative 3\u201d and below is written \u201cMore positives \u2013 the sum is positive.\u201d\" data-media-type=\"image\/jpeg\"><\/span>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655058550\" data-type=\"problem\">\n<p id=\"fs-id1170655058552\">Add: a) \\(-1+5\\) b) \\(1+\\left(-5\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655029787\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1166422829183\">a)<\/p>\n\n<table id=\"eip-id1169754360753\" class=\"unnumbered unstyled\" summary=\"In this image we have two columns. The top of the right column has the equation \u201cnegative 1 plus 5.\u201d The next line down in the left column reads, \u201cThere are more positives, so the sum is positive.\u201d Next to this in the right column are five blue counters. Under this, one red counter. The first blue counter and the single red counter are circled. Under this in the same column it says \u201c4.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\">\u22121 + 5<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169749528166\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_027_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>There are more positives, so the sum is positive.<\/td>\n<td data-align=\"center\">4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nb)\n<table id=\"eip-id1169750608265\" class=\"unnumbered unstyled can-break\" summary=\"In this image we have two columns. The top of the right column has the equation \u201c1 plus negative 5.\u201d The next line down in the left column reads, \u201cThere are more negatives, so the sum is negative.\u201d Next to this in the right column is one blue counter. Under this, five red counters. The single blue counter and the first of the five red counters is circled. Under this in the same column it says \u201cnegative 4.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\">1 + (\u22125)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169750608293\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_028_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>There are more negatives, so the sum is negative.<\/td>\n<td data-align=\"center\">\u22124<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654904893\" data-type=\"problem\">\n<p id=\"fs-id1170654904895\">Add:\u00a0a)\u00a0\\(-2+4\\)\u00a0b)\u00a0\\(2+\\left(-4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655066666\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655066668\">a)\u00a02\u00a0b)\u00a0\\(-2\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655066631\" data-type=\"problem\">\n<p id=\"fs-id1170655066633\">Add:\u00a0a)\u00a0\\(-2+5\\)\u00a0b)\u00a0\\(2+\\left(-5\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655066149\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655066151\">a)\u00a03\u00a0b) \\(-3\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655066171\">Now that we have added small positive and negative integers with a model, we can visualize the model in our minds to simplify problems with any numbers.<\/p>\n<p id=\"fs-id1170655067182\">When you need to add numbers such as \\(37+\\left(-53\\right)\\), you really don\u2019t want to have to count out 37 blue counters and 53 red counters. With the model in your mind, can you visualize what you would do to solve the problem?<\/p>\n<p id=\"fs-id1170655067203\">Picture 37 blue counters with 53 red counters lined up underneath. Since there would be more red (negative) counters than blue (positive) counters, the sum would be <em data-effect=\"italics\">negative<\/em>. How many more red counters would there be? Because \\(53-37=16\\), there are 16 more red counters.<\/p>\n<p id=\"fs-id1170655067279\">Therefore, the sum of \\(37+\\left(-53\\right)\\) is \\(-16\\).<\/p>\n\n<div id=\"fs-id1170655067436\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(37+\\left(-53\\right)=-16\\)<\/div>\n<p id=\"fs-id1170655069654\">Let\u2019s try another one. We\u2019ll add \\(-74+\\left(-27\\right)\\). Again, imagine 74 red counters and 27 more red counters, so we\u2019d have 101 red counters. This means the sum is \\(-101\\).<\/p>\n\\(-74+\\left(-27\\right)=-101\\)\n<p id=\"fs-id1170655069404\">Let\u2019s look again at the results of adding the different combinations of \\(5,-5\\) and \\(3,-3\\).<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Addition of Positive and Negative Integers<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655069465\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill 5+3\\hfill &amp; &amp; &amp; \\hfill -5+\\left(-3\\right)\\hfill \\\\ \\hfill 8\\hfill &amp; &amp; &amp; \\hfill -8\\hfill \\\\ \\hfill \\text{both positive, sum positive}\\hfill &amp; &amp; &amp; \\hfill \\text{both negative, sum negative}\\hfill \\end{array}\\)<\/div>\n<p id=\"fs-id1170655072721\">When the signs are the same, the counters would be all the same color, so add them.<\/p>\n\\(\\begin{array}{cccc}\\hfill -5+3\\hfill &amp; &amp; &amp; \\hfill 5+\\left(-3\\right)\\hfill \\\\ \\hfill -2\\hfill &amp; &amp; &amp; \\hfill 2\\hfill \\\\ \\hfill \\text{different signs, more negatives, sum negative}\\hfill &amp; &amp; &amp; \\hfill \\text{different signs, more positives, sum positive}\\hfill \\end{array}\\)\n<p id=\"fs-id1170655163407\">When the signs are different, some of the counters would make neutral pairs, so subtract to see how many are left.<\/p>\n\n<\/div>\n<\/div>\n<p id=\"fs-id1170654942464\">Visualize the model as you simplify the expressions in the following examples.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654932186\" data-type=\"problem\">\n<p id=\"fs-id1170654932188\">Simplify:\u00a0a)\u00a0\\(19+\\left(-47\\right)\\)\u00a0b)\u00a0\\(-14+\\left(-36\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654942539\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<ol id=\"fs-id1166422639606\" class=\"circled\" type=\"a\">\n \t<li>\u00a0Since the signs are different, we subtract \\(\\text{19 from 47}\\text{.}\\) The answer will be negative because there are more negatives than positives.\n\\(\\begin{array}{cccc}&amp; &amp; &amp; \\hfill \\phantom{\\rule{0.3em}{0ex}}19+\\left(-47\\right)\\hfill \\\\ \\text{Add.}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{0.3em}{0ex}}-28\\hfill \\end{array}\\)<\/li>\n \t<li>\u00a0Since the signs are the same, we add. The answer will be negative because there are only negatives.\n\\(\\begin{array}{cccc}&amp; &amp; &amp; \\hfill -14+\\left(-36\\right)\\hfill \\\\ \\text{Add.}\\hfill &amp; &amp; &amp; \\hfill -50\\hfill \\end{array}\\)<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654941250\" data-type=\"problem\">\n<p id=\"fs-id1170654941252\">Simplify:\u00a0a)\u00a0\\(-31+\\left(-19\\right)\\)\u00a0b)\u00a0\\(15+\\left(-32\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654941827\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655215496\">a)\\(-50\\) b)\\(-17\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655226063\" data-type=\"problem\">\n<p id=\"fs-id1170655226065\">Simplify:\u00a0a)\u00a0\\(-42+\\left(-28\\right)\\)\u00a0b)\u00a0\\(25+\\left(-61\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655165460\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170655165462\">a)\\(-70\\) b)\\(-36\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654944039\">The techniques used up to now extend to more complicated problems, like the ones we\u2019ve seen before. Remember to follow the order of operations!<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654929156\" data-type=\"problem\">\n<p id=\"fs-id1170654929159\">Simplify: \\(-5+3\\left(-2+7\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654934976\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-256\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(-5+3\\left(-2+7\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify inside the parentheses.<\/td>\n<td>\\(-5+3\\left(5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>\\(-5+15\\)<\/td>\n<\/tr>\n<tr>\n<td>Add left to right.<\/td>\n<td>\\(10\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654936188\" data-type=\"problem\">\n<p id=\"fs-id1170654936190\">Simplify: \\(-2+5\\left(-4+7\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654944107\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654944110\">13<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div>\n<p id=\"fs-id1170655111076\">Simplify: \\(-4+2\\left(-3+5\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654944573\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1170654944575\">0<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Subtract Integers<\/h1>\n<p id=\"fs-id1170654921208\">We will continue to use counters to model the subtraction. Remember, the blue counters represent positive numbers and the red counters represent negative numbers.<\/p>\n<p id=\"fs-id1170654921213\">Perhaps when you were younger, you read \\(\\text{\u201c}5-3\\text{\u201d}\\) as \\(\\text{\u201c}5\\) take away \\(3.\\text{\u201d}\\) When you use counters, you can think of subtraction the same way!<\/p>\n<p id=\"fs-id1170654932154\">We will model the four subtraction facts using the numbers \\(5\\) and \\(3\\).<\/p>\n\n<div id=\"fs-id1170654936672\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccccccccc}\\hfill 5-3\\hfill &amp; &amp; &amp; \\hfill -5-\\left(-3\\right)\\hfill &amp; &amp; &amp; \\hfill -5-3\\hfill &amp; &amp; &amp; \\hfill 5-\\left(-3\\right)\\hfill \\end{array}\\)<\/div>\n<p id=\"fs-id1170654939339\">To subtract \\(5-3\\), we restate the problem as \\(\\text{\u201c}5\\) take away \\(3.\\text{\u201d}\\)<\/p>\n\n<table id=\"eip-id1169750607921\" style=\"width: 100%;\" summary=\"In this image, we have two columns and four rows. The first row, left column reads, \u201cWe start with 5 positives.\u201d Next to this is a horizontal row of five blue counters. The next row down, left column reads \u201cWe \u2018take away\u2019 3 positives\u201d. Next to this in the right column is a horizontal row of three blue counters, a space, and then two blue counters. The first three blue counters are circled with an arrow. The next line down reads \u201cWe have two positives left.\u201d The line below that reads \u201cThe difference of 5 and 3 is 2.\u201d Next to this in the right column is \u201c2\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td>We start with 5 positives.<\/td>\n<td><span id=\"eip-id1169746620624\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_029a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We \u2018take away\u2019 3 positives.<\/td>\n<td><span id=\"eip-id1169746620641\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_029b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We have 2 positives left.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The difference of 5 and 3 is 2.<\/td>\n<td data-align=\"center\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654932116\">Now we will subtract \\(-5-\\left(-3\\right)\\). Watch for similarities to the last example \\(5-3=2\\).<\/p>\n<p id=\"fs-id1170654936713\">To subtract \\(-5-\\left(-3\\right)\\), we restate this as \\(\\text{\u201c}\u20135\\) take away \\(\u20133\\text{\u201d}\\)<\/p>\n\n<table id=\"eip-id1169750717917\" style=\"width: 100%;\" summary=\"In this image, we have two columns and four rows. The first row, left column reads, \u201cWe start with 5 negatives.\u201d Next to this is a horizontal row of five red counters. The next row down, left column reads \u201cWe \u2018take away\u2019 3 negatives\u201d. Next to this in the right column is a horizontal row of three red counters, a space, and then two red counters. The first three red counters are circled with an arrow. The next line down reads \u201cWe have two negatives left.\u201d The line below that reads \u201cThe difference of negative 5 and negative 3 is negative 2.\u201d Next to this in the right column is \u201cnegative 2\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td>We start with 5 negatives.<\/td>\n<td><span id=\"eip-id1169753098982\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_030a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We \u2018take away\u2019 3 negatives.<\/td>\n<td><span id=\"eip-id1169753098998\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_030b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We have 2 negatives left.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The difference of \u22125 and \u22123 is \u22122.<\/td>\n<td data-align=\"center\">\u22122<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nNotice that these two examples are much alike: The first example, we subtract 3 positives from 5 positives and end up with 2 positives.\n<p id=\"fs-id1170654942784\">In the second example, we subtract 3 negatives from 5 negatives and end up with 2 negatives.<\/p>\n<p id=\"fs-id1170654942787\">Each example used counters of only one color, and the \u201ctake away\u201d model of subtraction was easy to apply.<\/p>\n<span id=\"fs-id1170654942792\" data-type=\"media\" data-alt=\"Two images are shown and labeled. The first image shows five blue counters, three of which are circled with an arrow. Above the counters is the equation \u201c5 minus 3 equals 2.\u201d The second image shows five red counters, three of which are circled with an arrow. Above the counters is the equation \u201cnegative 5, minus, negative 3, equals negative 2.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_031_img_new.jpg\" alt=\"Two images are shown and labeled. The first image shows five blue counters, three of which are circled with an arrow. Above the counters is the equation \u201c5 minus 3 equals 2.\u201d The second image shows five red counters, three of which are circled with an arrow. Above the counters is the equation \u201cnegative 5, minus, negative 3, equals negative 2.\u201d\" data-media-type=\"image\/jpeg\"><\/span>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654941719\" data-type=\"problem\">\n<p id=\"fs-id1170654941105\">Subtract:\u00a0a)\u00a0\\(7-5\\)\u00a0b)\u00a0\\(-7-\\left(-5\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654942825\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-947\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)\nTake 5 positive from 7 positives and get 2 positives.<\/td>\n<td>\\(\\begin{array}{c}7-5\\\\ 2\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)\nTake 5 negatives from 7 negatives and get 2 negatives.<\/td>\n<td>\\(\\begin{array}{c}-7-\\left(-5\\right)\\\\ -2\\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655174379\" data-type=\"problem\">\n<p id=\"fs-id1170655174381\">Subtract:\u00a0a)\u00a0\\(6-4\\)\u00a0b)\u00a0\\(-6-\\left(-4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654942396\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1170654942399\">a)\u00a02\u00a0b)\u00a0\\(-2\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654942577\" data-type=\"problem\">\n<p id=\"fs-id1170654935898\">Subtract:\u00a0a)\u00a0\\(7-4\\)\u00a0b)\u00a0\\(-7-\\left(-4\\right)\\).<\/p>\n\n<\/div>\n&nbsp;\n<div id=\"fs-id1170655208093\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1170655208095\">a)\u00a03\u00a0b)\u00a0\\(-3\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654935830\">What happens when we have to subtract one positive and one negative number? We\u2019ll need to use both white and red counters as well as some <span class=\"no-emphasis\" data-type=\"term\">neutral pairs<\/span>. Adding a neutral pair does not change the value. It is like changing quarters to nickels\u2014the value is the same, but it looks different.<\/p>\n\n<ul id=\"fs-id1166424901740\" data-bullet-style=\"bullet\">\n \t<li>To subtract \\(-5-3\\), we restate it as \\(-5\\) take away 3.<\/li>\n<\/ul>\n<p id=\"fs-id1170654928179\">We start with 5 negatives. We need to take away 3 positives, but we do not have any positives to take away.<\/p>\n<p id=\"fs-id1170654928184\">Remember, a neutral pair has value zero. If we add 0 to 5 its value is still 5. We add neutral pairs to the 5 negatives until we get 3 positives to take away.<\/p>\n\n<table id=\"eip-id1169752192784\" style=\"width: 100%;\" summary=\"In this image, we have two columns and six rows. The first row in the right column reads, \u201cnegative 5 minus 3 means negative 5 take away 3.\u201d The next row down on the left reads, \u201cWe started with five negatives.\u201d Next to this are five red counters in a horizontal row with \u201cnegative\u201d five underneath. The next row reads, \u201cWe now add the neutrals needed to get three positives. Next to this in the right column are five red counters, a space, and three red counters. Under the three red counters are three blue counters. The next row down reads, \u201cWe remove the three positives. Next to this in the right column are the five red counters, a space, and three red counters. Under the three red counters are three blue counters with a circled arrow around them. The next row down reads, \u201cwe are left with eight negatives.\u201d Next to this in the right column in a horizontal row are five red counters, a space, followed by three red counters. Under the counters reads \u201c8 negatives\u201d. The last row in the left column reads, \u201cThe difference of negative 5 and 3 is negative 8.\u201d Next to this in the right column is the equation, \u201cnegative 5 minus 3equals negative eight.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\u22125 \u2212 3 means \u22125 take away 3.<\/td>\n<\/tr>\n<tr>\n<td>We start with 5 negatives.<\/td>\n<td><span id=\"eip-id1169754016089\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_032a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We now add the neutrals needed to get 3 positives.<\/td>\n<td><span id=\"eip-id1169754016106\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_032b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We remove the 3 positives.<\/td>\n<td><span id=\"eip-id1169754016122\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_032c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We are left with 8 negatives.<\/td>\n<td><span id=\"eip-id1169754361424\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_032d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>The difference of \u22125 and 3 is \u22128.<\/td>\n<td>\u22125 \u2212 3 = \u22128<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655261587\">And now, the fourth case, \\(5-\\left(-3\\right)\\). We start with 5 positives. We need to take away 3 negatives, but there are no negatives to take away. So we add neutral pairs until we have 3 negatives to take away.<\/p>\n\n<table id=\"eip-id1169754361484\" style=\"width: 100%;\" summary=\"In this image, we have two columns and six rows. The first row in the right column reads, \u201c5 minus negative 3 means 5 take away negative 3.\u201d The next row down on the left reads, \u201cWe started with five positives.\u201d Next to this are five blue counters in a horizontal row. The next row reads, \u201cWe now add the needed neutral pairs. Next to this in the right column are five blue counters, a space, and three blue counters. Under the three blue counters are three red counters. The next row down reads, \u201cWe remove the 3 negatives. Next to this in the right column are the five blue counters, a space, and three blue counters. Under the three blue counters are three red counters with a circled arrow around them. The next row down reads, \u201cWe are left with eight positives.\u201d Next to this in the right column in a horizontal row are five blue counters, a space, followed by three blue counters. Under the counters reads \u201c8 positives\u201d. The last row in the left column reads, \u201cThe difference of 5 and negative 3 is 8.\u201d Next to this in the right column is the equation, \u201c5 minus negative 3equals eight.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>5 \u2212 (\u22123) means 5 take away \u22123.<\/td>\n<\/tr>\n<tr>\n<td>We start with 5 positives.<\/td>\n<td><span id=\"eip-id1169753968359\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_033a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We now add the needed neutrals pairs.<\/td>\n<td><span id=\"eip-id1169753968375\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_033b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We remove the 3 negatives.<\/td>\n<td><span id=\"eip-id1169753968392\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_033c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>We are left with 8 positives.<\/td>\n<td><span id=\"eip-id1169752181606\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_033d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>The difference of 5 and \u22123 is 8.<\/td>\n<td>5 \u2212 (\u22123) = 8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\"><\/div>\n<div data-type=\"example\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654941998\" data-type=\"problem\">\n<p id=\"fs-id1170654942000\">Subtract:\u00a0a)\u00a0\\(-3-1\\)\u00a0b)\u00a0\\(3-\\left(-1\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654943757\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1167829621734\">a)<\/p>\n\n<table id=\"eip-id1169749482384\" class=\"unnumbered unstyled\" summary=\"Part \u201ca\u201d has three red counters, a space, and one red counter in a horizontal row. Next to this on the right is the equation \u201cnegative 3 minus 1.\u201d The next line down on the left reads,\u201dTake 1 positive from the one added neutral pair\u201d. Next to this on the right is a blue counter circled with an arrow. Next to this reads \u201cnegative 4.\u201d Part \u201cb\u201d has three blue counters, a space, and one blue counter in a horizontal row. Next to this on the right is the equation \u201c3 minus negative 1.\u201d The next line down on the left reads, \u201cTake one negative from the one added neutral pair.\u201d Next to this on the right is a red counter circled with an arrow. Next to this reads \u201c4\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Take 1 positive from the one added neutral pair.<\/td>\n<td><span id=\"eip-id1169749482408\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_034a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span>\n<span id=\"eip-id1169749482428\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_034b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td data-valign=\"top\">\u22123 \u2212 1\n\n\u22124<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167836289563\">b)<\/p>\n\n<table id=\"fs-id1167824767322\" class=\"unnumbered unstyled\" summary=\"Part \u201cb\u201d has three blue counters, a space, and one blue counter in a horizontal row. Next to this on the right is the equation \u201c3 minus negative 1.\u201d The next line down on the left reads, \u201cTake one negative from the one added neutral pair.\u201d Next to this on the right is a red counter circled with an arrow. Next to this reads \u201c4\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Take 1 negative from the one added neutral pair.<\/td>\n<td><span id=\"eip-id1169749482451\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_034c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span>\n<span id=\"eip-id1169749482475\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_034d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td data-align=\"center\" data-valign=\"top\">3 \u2212 (\u22121)\n\n4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654924800\" data-type=\"problem\">\n<p id=\"fs-id1170654941927\">Subtract:\u00a0a)\u00a0\\(-6-4\\)\u00a0b)\u00a0\\(6-\\left(-4\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170654942432\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1170654942434\">a)\\(-10\\) b) 10<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654928213\" data-type=\"problem\">\n<p id=\"fs-id1170654928215\">Subtract:\u00a0a)\u00a0\\(-7-4\\)\u00a0b)\u00a0\\(7-\\left(-4\\right)\\).<\/p>\n\n<\/div>\n<div><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1170655163425\">a)\\(-11\\) b) 11<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nHave you noticed that <em data-effect=\"italics\">subtraction of signed numbers can be done by adding the opposite<\/em>? In <a class=\"autogenerated-content\" href=\"#fs-id1170654941998\">Example 13<\/a>, \\(-3-1\\) is the same as \\(-3+\\left(-1\\right)\\) and \\(3-\\left(-1\\right)\\) is the same as \\(3+1\\). You will often see this idea, the subtraction property, written as follows:\n\n<\/div>\n<div id=\"fs-id1170654903656\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Subtraction Property<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654903661\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(a-b=a+\\left(-b\\right)\\)<\/div>\n<div data-type=\"equation\" data-label=\"\"><\/div>\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\">Subtracting a number is the same as adding its opposite.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654903717\">Look at these two examples.<\/p>\n<span id=\"fs-id1170654962580\" data-type=\"media\" data-alt=\"Two images are shown and labeled. The first image shows four gray spheres drawn next to two gray spheres, where the four are circled in red, with a red arrow leading away to the lower left. This drawing is labeled above as \u201c6 minus 4\u201d and below as \u201c2.\u201d The second image shows four gray spheres and four red spheres, drawn one above the other and circled in red, with a red arrow leading away to the lower left, and two gray spheres drawn to the side of the four gray spheres. This drawing is labeled above as \u201c6 plus, open parenthesis, negative 4, close parenthesis\u201d and below as \u201c2.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_035_img_new.jpg\" alt=\"Two images are shown and labeled. The first image shows four gray spheres drawn next to two gray spheres, where the four are circled in red, with a red arrow leading away to the lower left. This drawing is labeled above as \u201c6 minus 4\u201d and below as \u201c2.\u201d The second image shows four gray spheres and four red spheres, drawn one above the other and circled in red, with a red arrow leading away to the lower left, and two gray spheres drawn to the side of the four gray spheres. This drawing is labeled above as \u201c6 plus, open parenthesis, negative 4, close parenthesis\u201d and below as \u201c2.\u201d\" data-media-type=\"image\/jpeg\"><\/span>\n<div id=\"fs-id1166424959329\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(6-4\\phantom{\\rule{0.2em}{0ex}}\\text{gives the same answer as}\\phantom{\\rule{0.2em}{0ex}}6+\\left(-4\\right)\\).<\/div>\n<p id=\"fs-id1170654962732\">Of course, when you have a subtraction problem that has only positive numbers, like \\(6-4\\), you just do the subtraction. You already knew how to subtract \\(6-4\\) long ago. But <em data-effect=\"italics\">knowing<\/em> that \\(6-4\\) gives the same answer as \\(6+\\left(-4\\right)\\) helps when you are subtracting negative numbers. Make sure that you understand how \\(6-4\\) and \\(6+\\left(-4\\right)\\) give the same results!<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655072283\" data-type=\"problem\">\n<p id=\"fs-id1170655072285\">Simplify:\u00a0a)\u00a0\\(13-8\\) and \\(13+\\left(-8\\right)\\)\u00a0b)\u00a0\\(-17-9\\) and \\(-17+\\left(-9\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655072440\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-475\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)\nSubtract.<\/td>\n<td>\\(\\begin{array}{c}13-8\\\\ 5\\end{array}\\)<\/td>\n<td>\\(\\begin{array}{c}13+\\left(-8\\right)\\\\ 5\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)\nSubtract.<\/td>\n<td>\\(\\begin{array}{c}-17-9\\\\ -29\\end{array}\\)<\/td>\n<td>\\(\\begin{array}{c}-17+\\left(-9\\right)\\\\ -26\\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655073536\" data-type=\"problem\">\n<p id=\"fs-id1170655073538\">Simplify:\u00a0a)\u00a0\\(21-13\\) and \\(21+\\left(-13\\right)\\)\u00a0b)\u00a0\\(-11-7\\) and \\(-11+\\left(-7\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655073718\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1170655073721\">a) \\(8\\) b) \\(-18\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655073755\" data-type=\"problem\">\n<p id=\"fs-id1170655073757\">Simplify:\u00a0a)\u00a0\\(15-7\\) and \\(15+\\left(-7\\right)\\)\u00a0b)\u00a0\\(-14-8\\) and \\(-14+\\left(-8\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655076908\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1170655076910\">a) \\(8\\) b)\\(-22\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655075753\">Look at what happens when we subtract a negative.<\/p>\n<span id=\"fs-id1170655075756\" data-type=\"media\" data-alt=\"This figure is divided vertically into two halves. The left part of the figure contains the expression 8 minus negative 5, where negative 5 is in parentheses. The expression sits above a group of 8 blue counters next to a group of five blue counters in a row, with a space between the two groups. Underneath the group of five blue counters is a group of five red counters, which are circled. The circle has an arrow pointing away toward bottom left of the image, symbolizing subtraction. Below the counters is the number 13. The right part of the figure contains the expression 8 plus 5. The expression sits above a group of 8 blue counters next to a group of five blue counters in a row, with a space between the two groups. Underneath the counters is the number 13.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_036_img_new.jpg\" alt=\"This figure is divided vertically into two halves. The left part of the figure contains the expression 8 minus negative 5, where negative 5 is in parentheses. The expression sits above a group of 8 blue counters next to a group of five blue counters in a row, with a space between the two groups. Underneath the group of five blue counters is a group of five red counters, which are circled. The circle has an arrow pointing away toward bottom left of the image, symbolizing subtraction. Below the counters is the number 13. The right part of the figure contains the expression 8 plus 5. The expression sits above a group of 8 blue counters next to a group of five blue counters in a row, with a space between the two groups. Underneath the counters is the number 13.\" data-media-type=\"image\/jpeg\"><\/span>\n<div id=\"fs-id1166424830896\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(8-\\left(-5\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{gives the same answer as}\\phantom{\\rule{0.2em}{0ex}}8+5\\)<\/div>\n<p id=\"fs-id1170655077076\"><em data-effect=\"italics\">Subtracting a negative number is like adding a positive!<\/em><\/p>\n<p id=\"fs-id1170655076379\">You will often see this written as \\(a-\\left(-b\\right)=a+b\\).<\/p>\n<p id=\"fs-id1170655077196\">Does that work for other numbers, too? Let\u2019s do the following example and see.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655080485\" data-type=\"exercise\">\n<div id=\"fs-id1170655080487\" data-type=\"problem\">\n<p id=\"fs-id1170655080489\">Simplify:\u00a0a)\u00a0\\(9-\\left(-15\\right)\\) and \\(9+15\\)\u00a0b)\u00a0\\(-7-\\left(-4\\right)\\) and \\(-7+4\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655081441\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1166422863906\">a)\n\\(\\begin{array}{ccccccccc}&amp; &amp; &amp; &amp; &amp; \\hfill 9-\\left(-15\\right)\\hfill &amp; &amp; &amp; \\hfill 9+15\\hfill \\\\ \\text{Subtract.}\\hfill &amp; &amp; &amp; &amp; &amp; \\hfill 24\\hfill &amp; &amp; &amp; \\hfill 24\\hfill \\end{array}\\)<\/p>\nb)\n\\(\\begin{array}{ccccccccc}&amp; &amp; &amp; &amp; &amp; \\hfill -7-\\left(-4\\right)\\hfill &amp; &amp; &amp; \\hfill -7+4\\hfill \\\\ \\text{Subtract.}\\hfill &amp; &amp; &amp; &amp; &amp; \\hfill -3\\hfill &amp; &amp; &amp; \\hfill -3\\hfill \\end{array}\\)\n\n<\/div>\n<\/div>\n<table id=\"eip-660\" summary=\".\">\n<tbody>\n<tr>\n<td>a)\nSubtract.<\/td>\n<td>\\(\\begin{array}{c}9-\\left(-15\\right)\\\\ 24\\end{array}\\)<\/td>\n<td>\\(\\begin{array}{c}9+15\\\\ 24\\end{array}\\)<\/td>\n<\/tr>\n<tr>\n<td>b)\nSubtract.<\/td>\n<td>\\(\\begin{array}{c}-7-\\left(-4\\right)\\\\ -3\\end{array}\\)<\/td>\n<td>\\(\\begin{array}{c}-7+4\\\\ -3\\end{array}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655084099\" data-type=\"problem\">\n<p id=\"fs-id1170655084101\">Simplify:\u00a0a)\u00a0\\(6-\\left(-13\\right)\\) and \\(6+13\\)\u00a0b)\u00a0\\(-5-\\left(-1\\right)\\) and \\(-5+1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655059484\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1170655061855\">a)\\(19\\) b)\\(-4\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655061672\" data-type=\"problem\">\n<p id=\"fs-id1170655061674\">Simplify:\u00a0a)\u00a0\\(4-\\left(-19\\right)\\) and \\(4+19\\)\u00a0b)\u00a0\\(-4-\\left(-7\\right)\\) and \\(-4+7\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655084120\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1170655089691\">a)\u00a023\u00a0b) 3<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655089698\">Let\u2019s look again at the results of subtracting the different combinations of \\(5,-5\\) and \\(3,-3\\).<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Subtraction of Integers<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\n\\(\\begin{array}{cccc}\\hfill 5-3\\hfill &amp; &amp; &amp; \\hfill -5-\\left(-3\\right)\\hfill \\\\ \\hfill 2\\hfill &amp; &amp; &amp; \\hfill -2\\hfill \\\\ \\hfill 5\\phantom{\\rule{0.2em}{0ex}}\\text{positives take away}\\phantom{\\rule{0.2em}{0ex}}3\\phantom{\\rule{0.2em}{0ex}}\\text{positives}\\hfill &amp; &amp; &amp; \\hfill 5\\phantom{\\rule{0.2em}{0ex}}\\text{negatives take away}\\phantom{\\rule{0.2em}{0ex}}3\\phantom{\\rule{0.2em}{0ex}}\\text{negatives}\\hfill \\\\ \\hfill 2\\phantom{\\rule{0.2em}{0ex}}\\text{positives}\\hfill &amp; &amp; &amp; \\hfill 2\\phantom{\\rule{0.2em}{0ex}}\\text{negatives}\\hfill \\end{array}\\)\n\nWhen there would be enough counters of the colour to take away, subtract.\\(\\begin{array}{cccc}\\hfill -5-3\\hfill &amp; &amp; &amp; \\hfill 5-\\left(-3\\right)\\hfill \\\\ \\hfill -8\\hfill &amp; &amp; &amp; \\hfill 8\\hfill \\\\ \\hfill 5\\phantom{\\rule{0.2em}{0ex}}\\text{negatives, want to take away}\\phantom{\\rule{0.2em}{0ex}}3\\phantom{\\rule{0.2em}{0ex}}\\text{positives}\\hfill &amp; &amp; &amp; \\hfill 5\\phantom{\\rule{0.2em}{0ex}}\\text{positives, want to take away}\\phantom{\\rule{0.2em}{0ex}}3\\phantom{\\rule{0.2em}{0ex}}\\text{negatives}\\hfill \\\\ \\hfill \\text{need neutral pairs}\\hfill &amp; &amp; &amp; \\hfill \\text{need neutral pairs}\\hfill \\end{array}\\)\n\nWhen there would be not enough counters of the colour to take away, add.\n\n<\/div>\n<\/div>\n<p id=\"fs-id1170654962473\">What happens when there are more than three integers? We just use the order of operations as usual.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655084026\" data-type=\"problem\">\n<p id=\"fs-id1170655084028\">Simplify: \\(7-\\left(-4-3\\right)-9\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655083647\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-942\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(7-\\left(-4-3\\right)-9\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify inside the parentheses first.<\/td>\n<td>\\(7-\\left(-7\\right)-9\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract left to right.<\/td>\n<td>\\(14-9\\)<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>\\(5\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655091566\" data-type=\"problem\">\n<p id=\"fs-id1170655091568\">Simplify: \\(8-\\left(-3-1\\right)-9\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655090951\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1170655090953\">3<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655092082\" data-type=\"problem\">\n<p id=\"fs-id1170655092190\">Simplify: \\(12-\\left(-9-6\\right)-14\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1170655095593\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1170655095595\">13<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655091187\" class=\"media-2\" data-type=\"note\">\n<p id=\"fs-id1170655091191\">Access these online resources for additional instruction and practice with adding and subtracting integers. You will need to enable Java in your web browser to use the applications.<\/p>\n\n<ul id=\"fs-id1170655096461\" data-display=\"block\">\n \t<li><a href=\"https:\/\/openstax.org\/l\/11AddColorChip\">Add Colored Chip<\/a><\/li>\n \t<li><a href=\"https:\/\/openstax.org\/l\/11SubtrColorChp\">Subtract Colored Chip<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1170655097500\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">Addition of Positive and Negative Integers<\/strong>\n\\(\\begin{array}{cccc}5+3\\hfill &amp; &amp; &amp; \\phantom{\\rule{2.5em}{0ex}}-5+\\left(-3\\right)\\hfill \\\\ \\phantom{\\rule{0.95em}{0ex}}8\\hfill &amp; &amp; &amp; \\phantom{\\rule{3.45em}{0ex}}-8\\hfill \\\\ \\text{both positive,}\\hfill &amp; &amp; &amp; \\phantom{\\rule{2.5em}{0ex}}\\text{both negative,}\\hfill \\\\ \\text{sum positive}\\hfill &amp; &amp; &amp; \\phantom{\\rule{2.5em}{0ex}}\\text{sum negative}\\hfill \\\\ \\\\ \\\\ -5+3\\hfill &amp; &amp; &amp; \\phantom{\\rule{2.5em}{0ex}}5+\\left(-3\\right)\\hfill \\\\ \\phantom{\\rule{0.95em}{0ex}}-2\\hfill &amp; &amp; &amp; \\phantom{\\rule{3.45em}{0ex}}2\\hfill \\\\ \\text{different signs,}\\hfill &amp; &amp; &amp; \\phantom{\\rule{2.5em}{0ex}}\\text{different signs,}\\hfill \\\\ \\text{more negatives}\\hfill &amp; &amp; &amp; \\phantom{\\rule{2.5em}{0ex}}\\text{more positives}\\hfill \\\\ \\text{sum negative}\\hfill &amp; &amp; &amp; \\phantom{\\rule{2.5em}{0ex}}\\text{sum positive}\\hfill \\end{array}\\)<\/li>\n \t<li><strong data-effect=\"bold\">Property of Absolute Value<\/strong>: \\(|n|\\ge 0\\) for all numbers. Absolute values are always greater than or equal to zero!<\/li>\n \t<li><strong data-effect=\"bold\">Subtraction of Integers<\/strong>\n\\(\\begin{array}{cccc}5-3\\hfill &amp; &amp; &amp; -5-\\left(-3\\right)\\hfill \\\\ \\phantom{\\rule{0.95em}{0ex}}2\\hfill &amp; &amp; &amp; \\phantom{\\rule{0.95em}{0ex}}-2\\hfill \\\\ 5\\phantom{\\rule{0.2em}{0ex}}\\text{positives}\\hfill &amp; &amp; &amp; 5\\phantom{\\rule{0.2em}{0ex}}\\text{negatives}\\hfill \\\\ \\text{take away}\\phantom{\\rule{0.2em}{0ex}}3\\phantom{\\rule{0.2em}{0ex}}\\text{positives}\\hfill &amp; &amp; &amp; \\text{take away}\\phantom{\\rule{0.2em}{0ex}}3\\phantom{\\rule{0.2em}{0ex}}\\text{negatives}\\hfill \\\\ \\text{2 positives}\\hfill &amp; &amp; &amp; \\text{2 negatives}\\hfill \\\\ \\\\ \\\\ -5-3\\hfill &amp; &amp; &amp; 5-\\left(-3\\right)\\hfill \\\\ \\phantom{\\rule{0.95em}{0ex}}-8\\hfill &amp; &amp; &amp; \\phantom{\\rule{0.95em}{0ex}}8\\hfill \\\\ 5\\phantom{\\rule{0.2em}{0ex}}\\text{negatives, want to}\\hfill &amp; &amp; &amp; 5\\phantom{\\rule{0.2em}{0ex}}\\text{positives, want to}\\hfill \\\\ \\text{subtract}\\phantom{\\rule{0.2em}{0ex}}3\\phantom{\\rule{0.2em}{0ex}}\\text{positives}\\hfill &amp; &amp; &amp; \\text{subtract}\\phantom{\\rule{0.2em}{0ex}}3\\phantom{\\rule{0.2em}{0ex}}\\text{negatives}\\hfill \\\\ \\text{need neutral pairs}\\hfill &amp; &amp; &amp; \\text{need neutral pairs}\\hfill \\end{array}\\)<\/li>\n \t<li><strong data-effect=\"bold\">Subtraction Property:<\/strong> Subtracting a number is the same as adding its opposite.<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1166424847478\">\n \t<dt>absolute value<\/dt>\n \t<dd id=\"fs-id1166424809754\">The absolute value of a number is its distance from 0 on the number line. The absolute value of a number \\(n\\) is written as \\(|n|\\).<\/dd>\n<\/dl>\n<dl id=\"fs-id1166424772590\">\n \t<dt>integers<\/dt>\n \t<dd id=\"fs-id1166424772595\">The whole numbers and their opposites are called the integers: ...\u22123, \u22122, \u22121, 0, 1, 2, 3...<\/dd>\n<\/dl>\n<dl id=\"fs-id1166422694257\">\n \t<dt>opposite<\/dt>\n \t<dd id=\"fs-id1166422694262\">The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero: \\(-a\\) means the opposite of the number. The notation \\(-a\\) is read \u201cthe opposite of \\(a\\).\u201d<\/dd>\n<\/dl>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Use Negatives and Opposites of Integers<\/h2>\n<p id=\"fs-id1166422643633\">In the following exercises, order each of the following pairs of numbers, using &lt; or &gt;.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1.\na) \\(9\\)___\\(4\\)\nb) \\(-3\\)___\\(6\\)\nc) \\(-8\\)___\\(-2\\)\nd) \\(1\\)___\\(-10\\)<\/td>\n<td style=\"width: 50%;\">2.\na) \\(-7\\)___\\(3\\)\nb) \\(-10\\)___\\(-5\\)\nc) \\(2\\)___\\(-6\\)\nd) \\(8\\)___\\(9\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655068522\">In the following exercises, find the opposite of each number.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">3.\na) 2\nb) \\(-6\\)<\/td>\n<td style=\"width: 50%;\">4.\na) 9\nb) \\(-4\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655098081\">In the following exercises, simplify.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">5. \\(-\\left(-4\\right)\\)<\/td>\n<td style=\"width: 50%;\">6. \\(-\\left(-8\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. \\(-\\left(-15\\right)\\)<\/td>\n<td style=\"width: 50%;\">8. \\(-\\left(-11\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655058115\">In the following exercises, evaluate.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">9. \\(- c\\) when\na) \\(c=12\\)\nb) \\(c=-12\\)<\/td>\n<td style=\"width: 50%;\">10. \\(- d\\) when\na) \\(d=21\\)\nb) \\(d=-21\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions with Absolute Value<\/h2>\n<p id=\"fs-id1171791388513\">In the following exercises, simplify.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">11.\na) \\(|-32|\\)\nb) \\(|0|\\)\nc) \\(|16|\\)<\/td>\n<td style=\"width: 50%;\">12.\na) \\(|0|\\)\nb) \\(|-40|\\)\nc) \\(|22|\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655355498\">In the following exercises, fill in &lt;, &gt;, or \\(=\\) for each of the following pairs of numbers.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">13.\na) \\(-6\\)___\\(|-6|\\)\nb) \\(-|-3|\\)___\\(-3\\)<\/td>\n<td style=\"width: 50%;\">14.\na) \\(|-5|\\)___\\(-|-5|\\)\nb) \\(9\\)___\\(-|-9|\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655215530\">In the following exercises, simplify.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">15. \\(-\\left(-5\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}-|-5|\\)<\/td>\n<td style=\"width: 50%;\">16. \\(-|-9|\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}-\\left(-9\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. \\(8|-7|\\)<\/td>\n<td style=\"width: 50%;\">18. \\(5|-5|\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. \\(|15-7|-|14-6|\\)<\/td>\n<td style=\"width: 50%;\">20. \\(|17-8|-|13-4|\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21. \\(18-|2\\left(8-3\\right)|\\)<\/td>\n<td style=\"width: 50%;\">22. \\(18-|3\\left(8-5\\right)|\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655213986\">In the following exercises, evaluate.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">23.\na) \\(-|p|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}p=19\\)\nb) \\(-|q|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}q=-33\\)<\/td>\n<td style=\"width: 50%;\">24.\na) \\(-|a|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}a=60\\)\nb) \\(-|b|\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}b=-12\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Add Integers<\/h2>\n<p id=\"fs-id1166424899765\">In the following exercises, simplify each expression.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">25. \\(-21+\\left(-59\\right)\\)<\/td>\n<td style=\"width: 50%;\">26. \\(-35+\\left(-47\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">27. \\(48+\\left(-16\\right)\\)<\/td>\n<td style=\"width: 50%;\">28. \\(34+\\left(-19\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">29. \\(-14+\\left(-12\\right)+4\\)<\/td>\n<td style=\"width: 50%;\">30. \\(-17+\\left(-18\\right)+6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31. \\(135+\\left(-110\\right)+83\\)<\/td>\n<td style=\"width: 50%;\">32. 6 \\(-38+27+\\left(-8\\right)+126\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">33. \\(19+2\\left(-3+8\\right)\\)<\/td>\n<td style=\"width: 50%;\">34. \\(24+3\\left(-5+9\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Subtract Integers<\/h2>\n<p id=\"fs-id1166422656200\">In the following exercises, simplify.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">35. \\(8-2\\)<\/td>\n<td style=\"width: 50%;\">36. \\(-6-\\left(-4\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">37. \\(-5-4\\)<\/td>\n<td style=\"width: 50%;\">38. \\(-7-2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">39. \\(8-\\left(-4\\right)\\)<\/td>\n<td style=\"width: 50%;\">40. \\(7-\\left(-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">41.\na) \\(44-28\\)\nb) \\(44+\\left(-28\\right)\\)<\/td>\n<td style=\"width: 50%;\">42.\na) \\(35-16\\)\nb) \\(35+\\left(-16\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">43.\na) \\(27-\\left(-18\\right)\\)\nb) \\(27+18\\)<\/td>\n<td style=\"width: 50%;\">44.\na) \\(46-\\left(-37\\right)\\)\nb) \\(46+37\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655166333\">In the following exercises, simplify each expression.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 135px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">45. \\(15-\\left(-12\\right)\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">46. \\(14-\\left(-11\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">47. \\(48-87\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">48. \\(45-69\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">49. \\(-17-42\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">50. \\(-19-46\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">51. \\(-103-\\left(-52\\right)\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">52. \\(-105-\\left(-68\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">53. \\(-45-\\left(54\\right)\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">54. \\(-58-\\left(-67\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">55. \\(8-3-7\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">56. \\(9-6-5\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">57. \\(-5-4+7\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">58. \\(-3-8+4\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">59. \\(-14-\\left(-27\\right)+9\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">60. \\(64+\\left(-17\\right)-9\\)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">61. \\(\\left(2-7\\right)-\\left(3-8\\right)\\left(2\\right)\\)<\/td>\n<td style=\"width: 50%; height: 15px;\">62. \\(\\left(1-8\\right)-\\left(2-9\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">63. \\(-\\left(6-8\\right)-\\left(2-4\\right)\\)<\/td>\n<td style=\"width: 50%;\">64. \\(-\\left(4-5\\right)-\\left(7-8\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">65. \\(25-\\left[10-\\left(3-12\\right)\\right]\\)<\/td>\n<td style=\"width: 50%;\">66. \\(32-\\left[5-\\left(15-20\\right)\\right]\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">67. \\(6.3-4.3-7.2\\)<\/td>\n<td style=\"width: 50%;\">68. \\(5.7-8.2-4.9\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">69. \\({5}^{2}-{6}^{2}\\)<\/td>\n<td style=\"width: 50%;\">70. \\({6}^{2}-{7}^{2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%; height: 204px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 174px;\">\n<td style=\"width: 50%; height: 174px;\">\n<p id=\"fs-id1170655189386\">71. <strong data-effect=\"bold\">Elevation<\/strong> The highest elevation in North America is Mount McKinley, Alaska, at 20,320 feet above sea level. The lowest elevation is Death Valley, California, at 282 feet below sea level.<\/p>\n<p id=\"fs-id1170655190223\">Use integers to write the elevation of:<\/p>\n<p id=\"fs-id1167270974732\">a) Mount McKinley.\nb) Death Valley.<\/p>\n<\/td>\n<td style=\"width: 50%; height: 174px;\">\n<p id=\"fs-id1170655224555\">72.<strong data-effect=\"bold\"> Extreme temperatures<\/strong> The highest recorded temperature on Earth was \\(58\\)\u00b0 Celsius, recorded in the Sahara Desert in 1922. The lowest recorded temperature was \\(90\\)\u00b0 below \\(0\\)\u00b0 Celsius, recorded in Antarctica in 1983<\/p>\n<p id=\"fs-id1170655222289\">Use integers to write the:<\/p>\na) highest recorded temperature.\n\nb) lowest recorded temperature.<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">\n<p id=\"fs-id1170654920103\">73. <strong>Provincial budgets<\/strong> For 2019 the province of Quebec estimated it would have a budget surplus of \\$5.6 million. That same year, Alberta estimated it would have a budget deficit of \\$7.5 million.<\/p>\n<p id=\"fs-id1170655202258\">Use integers to write the budget of:<\/p>\n<p id=\"fs-id1167267728858\">a) Quebec.\nb) Alberta.<\/p>\n<\/td>\n<td style=\"width: 50%; height: 15px;\">74. <strong>University enrolments<\/strong>The number of international students enrolled in Canadian postsecondary institutions has been on the rise for two decades, with their numbers increasing at a higher rate than that of Canadian students. Enrolments of international students rose by 24,315 from 2015 to 2017. Meanwhile, there was a slight decline in the number of Canadian students, by 912 for the same fiscal years.\n\nUse integers to write the change:\n\na)\u00a0in International Student enrolment from Fall 2015 to Fall 2017.\n\nb)\u00a0in Canadian student enrolment from Fall 2015 to Fall 2017.<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">\n<div id=\"fs-id1170655195270\" data-type=\"exercise\">\n<div data-type=\"problem\">\n\n75. <strong style=\"text-align: initial;\" data-effect=\"bold\">Stock Market<\/strong> The week of September 15, 2008 was one of the most volatile weeks ever for the US stock market. The closing numbers of the Dow Jones Industrial Average each day were:\n\n<\/div>\n<\/div>\n<div id=\"fs-id1170655219716\" data-type=\"exercise\">\n<div id=\"fs-id1170655219718\" data-type=\"problem\">\n<table id=\"fs-id1170655204215\" class=\"unnumbered\" summary=\"This table has two rows and five columns. In the first row, the cells read left to right: \u201cMonday\u201d and \u201cnegative 504\u201d. In the second row, the cells read left to right: \u201cTuesday\u201d and \u201cpositive 142\u201d. In the third row, the cells read left to right \u201cWednesday\u201d and negative 449. In the fourth row, the cells read left to right: \u201cThursday\u201d and \u201cpositive 410\u201d. In the fifth and final row, the cells read left to right: \u201cFriday\u201d and \u201cpositive 369\u201d.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Monday<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(-504\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Tuesday<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(+142\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Wednesday<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(-449\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Thursday<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(+410\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Friday<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(+369\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654965472\">What was the overall change for the week? Was it positive or negative?<\/p>\n\n<\/div>\n<\/div><\/td>\n<td style=\"width: 50%; height: 15px;\">\n<p id=\"fs-id1170655232454\">76. <strong data-effect=\"bold\">Stock Market<\/strong> During the week of June 22, 2009, the closing numbers of the Dow Jones Industrial Average each day were:<\/p>\n\n<table id=\"fs-id1170655226595\" class=\"unnumbered\" summary=\"This table has two rows and five columns. In the first row, the cells read left to right: \u201cMonday\u201d and \u201cnegative 201\u201d. In the second row, the cells read left to right: \u201cTuesday\u201d and \u201cnegative 16\u201d. In the third row, the cells read left to right \u201cWednesday\u201d and \u201cnegative 23\u201d. In the fourth row, the cells read left to right: \u201cThursday\u201d and \u201cpositive 172\u201d. In the fifth and final row, the cells read left to right: \u201cFriday\u201d and \u201cnegative 34\u201d.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Monday<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(-201\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Tuesday<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(-16\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Wednesday<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(-23\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Thursday<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(+172\\)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Friday<\/td>\n<td data-valign=\"top\" data-align=\"left\">\\(-34\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655348632\">What was the overall change for the week? Was it positive or negative?<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">77. Give an example of a negative number from your life experience.<\/td>\n<td style=\"width: 50%;\">78. What are the three uses of the \\(\\text{\u201c}-\\text{\u201d}\\) sign in algebra? Explain how they differ.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">79. Explain why the sum of \\(-8\\) and 2 is negative, but the sum of 8 and \\(-2\\) is positive.<\/td>\n<td style=\"width: 50%;\">80. Give an example from your life experience of adding two negative numbers.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<div data-type=\"glossary\">\n<table style=\"border-collapse: collapse; width: 100%; height: 237px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">1. a) &gt; b) &lt; c) &lt; d) &gt;<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">3. a)\\(-2\\)b) 6<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">5. 4<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">7. 15<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">9. a)\\(-12\\)b) 12<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">11. a) 32 b) 0 c) 16<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">13. a) &lt; b) \\(=\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">15. \\(5,-5\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">17. 56<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">19. 0<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">21. 8<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">23. a) \\(-19\\) b) \\(-33\\)<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">25. \\(-80\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">27. 32<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">29. \\(-22\\)<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">31. 108<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">33. 29<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">35. 6<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">37. \\(-9\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">39. 12<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">41. a) 16 b) 16<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">43. a) 45 b) 45<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">45. 27<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">47. \\(-39\\)<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">49. \\(-59\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">51. \\(-51\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">53. -99<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">55. \\(-2\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">57. \\(-2\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">59. 22<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">61. \\(-15\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">63. 0<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">65. 6<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">67. \\(-5.2\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">69. \\(-11\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">71. a) 20,320\u00a0b) \\(-282\\)<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">73. a) \\$5.6 million b) \\(-\\$7.5\\) million<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">75. \\(-32\\)<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">77. Answers may vary<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">79.\u00a0Answers may vary<\/td>\n<td style=\"width: 33.3333%; height: 16px;\"><\/td>\n<td style=\"width: 33.3333%; height: 16px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cAdd and Subtract Integers\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em><\/a> (OpenStax) by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.\n\n<\/div>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Use negatives and opposites<\/li>\n<li>Simplify: expressions with absolute value<\/li>\n<li>Add integers<\/li>\n<li>Subtract integers<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Use Negatives and Opposites<\/h1>\n<p id=\"fs-id1170655222181\">Our work so far has only included the counting numbers and the whole numbers. But if you have ever experienced a temperature below zero or accidentally overdrawn your checking account, you are already familiar with negative numbers. <strong data-effect=\"bold\">Negative numbers<\/strong> are numbers less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>. The <span class=\"no-emphasis\" data-type=\"term\">negative numbers<\/span> are to the left of zero on the number line. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_03_001_new\">Figure 1<\/a>.<\/p>\n<figure style=\"width: 389px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_01_03_001_new.jpg\" alt=\"A number line extends from negative 4 to 4. A bracket is under the values \u201cnegative 4\u201d to \u201c0\u201d and is labeled \u201cNegative numbers\u201d. Another bracket is under the values 0 to 4 and labeled \u201cpositive numbers\u201d. There is an arrow in between both brackets pointing upward to zero.\" width=\"389\" height=\"113\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 1 The number line shows the location of positive and negative numbers.<\/figcaption><\/figure>\n<p>The arrows on the ends of the number line indicate that the numbers keep going forever. There is no biggest positive number, and there is no smallest negative number.<\/p>\n<p id=\"fs-id1170655007025\">Is zero a positive or a negative number? Numbers larger than zero are positive, and numbers smaller than zero are negative. Zero is neither positive nor negative.<\/p>\n<p>Consider how numbers are ordered on the number line. Going from left to right, the numbers increase in value. Going from right to left, the numbers decrease in value. See <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_03_002_new\">Figure 2<\/a>.<\/p>\n<div id=\"CNX_ElemAlg_Figure_01_03_002_new\" class=\"bc-figure figure\">\n<figure style=\"width: 440px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_002_new.jpg\" alt=\"A number line ranges from negative 4 to 4. An arrow above the number line extends from negative 1 towards 4 and is labeled \u201clarger\u201d. An arrow below the number line extends from 1 towards negative 4 and is labeled \u201csmaller\u201d.\" width=\"440\" height=\"102\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 2 The numbers on a number line increase in value going from left to right and decrease in value going from right to left.<\/figcaption><\/figure>\n<\/div>\n<div class=\"textbox shaded\">\n<p>Remember that we use the notation:<\/p>\n<p id=\"fs-id1170654965355\"><em data-effect=\"italics\">a<\/em> &lt; <em data-effect=\"italics\">b<\/em> (read \u201ca is less than b\u201d) when a is to the left of b on the number line.<\/p>\n<p id=\"fs-id1170654901053\"><em data-effect=\"italics\">a<\/em> &gt; <em data-effect=\"italics\">b<\/em> (read \u201c<em data-effect=\"italics\">a<\/em> is greater than <em data-effect=\"italics\">b<\/em>\u201d) when <em data-effect=\"italics\">a<\/em> is to the right of <em data-effect=\"italics\">b<\/em> on the number line.<\/p>\n<\/div>\n<p id=\"fs-id1170654965087\">Now we need to extend the number line which showed the whole numbers to include negative numbers, too. The numbers marked by points in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_03_003_new\">Figure 3<\/a> are called the integers. The integers are the numbers <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-759e65d987e3039dac89a95f0411c0c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#8230;&#125;&#45;&#51;&#44;&#45;&#50;&#44;&#45;&#49;&#44;&#48;&#44;&#49;&#44;&#50;&#44;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#8230;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"154\" style=\"vertical-align: -4px;\" \/><\/p>\n<div id=\"CNX_ElemAlg_Figure_01_03_003_new\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\"><\/div>\n<figure style=\"width: 401px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_003_new.jpg\" alt=\"A number line extends from negative four to four. Points are plotted at negative four, negative three, negative two, negative one, zero, one, two, 3, and four.\" width=\"401\" height=\"44\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 3 All the marked numbers are called integers.<\/figcaption><\/figure>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655160945\" data-type=\"problem\">\n<p id=\"fs-id1170654952892\">Order each of the following pairs of numbers, using &lt; or &gt;: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b93660fe4bfeaf9a69e38dd0cba4d18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655177826\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170655192048\">It may be helpful to refer to the number line shown.<\/p>\n<p><span id=\"fs-id1170655201463\" data-type=\"media\" data-alt=\"A number line ranges from negative twenty to fifteen with ticks marks between numbers. Every fifth tick mark is labeled a number. Points are plotted at points negative twenty, negative 4, negative 1, 2, 6, 9 and 14.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_004_img_new.jpg\" alt=\"A number line ranges from negative twenty to fifteen with ticks marks between numbers. Every fifth tick mark is labeled a number. Points are plotted at points negative twenty, negative 4, negative 1, 2, 6, 9 and 14.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<table id=\"eip-672\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a) 14 is to the right of 6 on the number line.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b) \u22121 is to the left of 9 on the number line.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d6df449ad747b18616e15bc67d0f6820_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#60;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"54\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>c) \u22121 is to the right of \u22124 on the number line.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>d) 2 is to the right of \u221220 on the number line.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b93660fe4bfeaf9a69e38dd0cba4d18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b93660fe4bfeaf9a69e38dd0cba4d18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655162060\" data-type=\"problem\">\n<p id=\"fs-id1170654967573\">Order each of the following pairs of numbers, using &lt; or &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da2df9cb14c5b957b4e7f8568a97d9e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"3\" style=\"vertical-align: 0px;\" \/> a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00c6d30c5f7439a21caf981437f64be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a516826583d9ebf41e251f45bc98b74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"31\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654978104\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654967500\">a) &gt; b) &lt; c) &gt; d) &gt;<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655162421\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170655203196\" data-type=\"exercise\">\n<div id=\"fs-id1170655162060\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654880201\" data-type=\"problem\">\n<p id=\"fs-id1170654981845\">Order each of the following pairs of numbers, using &lt; or &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da2df9cb14c5b957b4e7f8568a97d9e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"3\" style=\"vertical-align: 0px;\" \/> a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-837d0d6b05c238eddf106b68ec9dcfd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2cae475c6cc4ade824f228f09d1e1ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654902746\">a) &lt; b) &gt; c) &lt; d) &gt;<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655114791\">You may have noticed that, on the <span class=\"no-emphasis\" data-type=\"term\">number line<\/span>, the negative numbers are a mirror image of the positive numbers, with zero in the middle. Because the numbers 2 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> are the same distance from zero, they are called opposite<strong data-effect=\"bold\">s<\/strong>. The opposite of 2 is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/>, and the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> is 2<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Opposite<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>The <strong data-effect=\"bold\">opposite<\/strong> of a number is the number that is the same distance from zero on the number line but on the opposite side of zero.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654959734\"><a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_03_005_new\">(Figure 4)<\/a> illustrates the definition.<\/p>\n<p>The opposite of 3 is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div id=\"CNX_ElemAlg_Figure_01_03_005_new\" class=\"bc-figure figure\">\n<figure style=\"width: 440px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_005_new.jpg\" alt=\"A number line ranges from negative 4 to 4. There are two brackets above the number line. The bracket on the left spans from negative three to 0. The bracket on the right spans from zero to three. Points are plotted on both negative three and three.\" width=\"440\" height=\"81\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 4<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1170655163898\">Sometimes in algebra the same symbol has different meanings. Just like some words in English, the specific meaning becomes clear by looking at how it is used. You have seen the symbol \u201c\u2212\u201d used in three different ways.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b95c3b7c44302979303edb49958fdb40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#49;&#48;&#45;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#101;&#116;&#119;&#101;&#101;&#110;&#32;&#116;&#119;&#111;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#44;&#32;&#105;&#116;&#32;&#105;&#110;&#100;&#105;&#99;&#97;&#116;&#101;&#115;&#32;&#116;&#104;&#101;&#32;&#111;&#112;&#101;&#114;&#97;&#116;&#105;&#111;&#110;&#32;&#111;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#116;&#114;&#97;&#99;&#116;&#105;&#111;&#110;&#125;&#125;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#101;&#32;&#114;&#101;&#97;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#48;&#45;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#96;&#96;&#125;&#49;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#105;&#110;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#46;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#39;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#45;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#110;&#32;&#102;&#114;&#111;&#110;&#116;&#32;&#111;&#102;&#32;&#97;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#44;&#32;&#105;&#116;&#32;&#105;&#110;&#100;&#105;&#99;&#97;&#116;&#101;&#115;&#32;&#97;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#117;&#109;&#98;&#101;&#114;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#101;&#32;&#114;&#101;&#97;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#115;&#32;&#96;&#96;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#32;&#101;&#105;&#103;&#104;&#116;&#46;&#39;&#39;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#45;&#120;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#110;&#32;&#102;&#114;&#111;&#110;&#116;&#32;&#111;&#102;&#32;&#97;&#32;&#118;&#97;&#114;&#105;&#97;&#98;&#108;&#101;&#44;&#32;&#105;&#116;&#32;&#105;&#110;&#100;&#105;&#99;&#97;&#116;&#101;&#115;&#32;&#116;&#104;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#112;&#112;&#111;&#115;&#105;&#116;&#101;&#125;&#125;&#46;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#101;&#32;&#114;&#101;&#97;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#120;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#115;&#32;&#96;&#96;&#116;&#104;&#101;&#32;&#111;&#112;&#112;&#111;&#115;&#105;&#116;&#101;&#32;&#111;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#46;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#39;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#114;&#101;&#32;&#116;&#104;&#101;&#114;&#101;&#32;&#97;&#114;&#101;&#32;&#116;&#119;&#111;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#96;&#96;&#125;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#39;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#105;&#103;&#110;&#115;&#46;&#32;&#84;&#104;&#101;&#32;&#111;&#110;&#101;&#32;&#105;&#110;&#32;&#116;&#104;&#101;&#32;&#112;&#97;&#114;&#101;&#110;&#116;&#104;&#101;&#115;&#101;&#115;&#32;&#116;&#101;&#108;&#108;&#115;&#32;&#117;&#115;&#32;&#116;&#104;&#101;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#32;&#105;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#46;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#111;&#110;&#101;&#32;&#111;&#117;&#116;&#115;&#105;&#100;&#101;&#32;&#116;&#104;&#101;&#32;&#112;&#97;&#114;&#101;&#110;&#116;&#104;&#101;&#115;&#101;&#115;&#32;&#116;&#101;&#108;&#108;&#115;&#32;&#117;&#115;&#32;&#116;&#111;&#32;&#116;&#97;&#107;&#101;&#32;&#116;&#104;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#109;&#97;&#116;&#104;&#105;&#116;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#112;&#112;&#111;&#115;&#105;&#116;&#101;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#50;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#101;&#32;&#114;&#101;&#97;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#115;&#32;&#96;&#96;&#116;&#104;&#101;&#32;&#111;&#112;&#112;&#111;&#115;&#105;&#116;&#101;&#32;&#111;&#102;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#32;&#116;&#119;&#111;&#46;&#39;&#39;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"172\" width=\"740\" style=\"vertical-align: -82px;\" \/><\/p>\n<table id=\"eip-36\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 316.705px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0eb549abad7904fc328c94df193ff83b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 857.614px;\">Between two numbers, it indicates the operation of <em data-effect=\"italics\">subtraction<\/em>.<br \/>\nWe read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0eb549abad7904fc328c94df193ff83b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: -1px;\" \/> as &#8220;10 minus 4.&#8221;<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 316.705px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca32393b1b5af7c55a95d89cf9d610f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 857.614px;\">In front of a number, it indicates a <em data-effect=\"italics\">negative<\/em> number.<br \/>\nWe read \u22128 as &#8220;negative eight.&#8221;<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 316.705px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6cacb15a7aa187378723791e7a017ae0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"23\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 857.614px;\">In front of a variable, it indicates the <em data-effect=\"italics\">opposite<\/em>. We read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6cacb15a7aa187378723791e7a017ae0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"23\" style=\"vertical-align: 0px;\" \/> as &#8220;the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>.&#8221;<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 316.705px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f96c38defe3363a99afc062429029a3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 857.614px;\">Here there are two &#8220;\u2212&#8221; signs. The one in the parentheses tells us the number is negative 2. The one outside the parentheses tells us to take the <em data-effect=\"italics\">opposite<\/em> of \u22122.<br \/>\nWe read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f96c38defe3363a99afc062429029a3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/> as &#8220;the opposite of negative two.&#8221;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1170655189167\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Opposite Notation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170655174724\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-236972f3904fc6d64d7fafb16c1fe32d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"22\" style=\"vertical-align: 0px;\" \/> means the opposite of the number <em data-effect=\"italics\">a<\/em>.<\/p>\n<p id=\"fs-id1170655160739\">The notation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-236972f3904fc6d64d7fafb16c1fe32d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"22\" style=\"vertical-align: 0px;\" \/> is read as \u201cthe opposite of <em data-effect=\"italics\">a<\/em>.\u201d<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654943981\" data-type=\"problem\">\n<p id=\"fs-id1170655120989\">Find: a) the opposite of 7 b) the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24329a36a4e10288288979f77a565ca2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-25fae79ddde29b842687e8838ec6e729_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654978387\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169750893702\" style=\"width: 100%;\" summary=\"This figure has three parts: a , b, and c. Each part has text on the left and a corresponding number line on the right. The text for part \u201ca\u201d reads \u201cnegative seven is the same distance from zero as seven, but on the opposite side of zero.\u201d To the right is a number line ranging from negative seven to seven. There are two brackets above the number line. The first bracket is from negative 7 to zero. Above this bracket reads \u201c10\u201d. The second bracket is from 0 to seven. Above this bracket reads \u201c10\u201d. Under the number line it reads \u201cThe opposite of seven is negative seven\u201d. Points are plotted on negative seven and seven. The text for part \u201cb\u201d reads \u201cten is the same distance from zero as negative 10, but on the opposite side of zero.\u201d To the right is is a number line ranging from negative ten to ten. There are two brackets above the number line. The first bracket is from negative 10 to zero. Above this bracket reads \u201c10\u201d. The second bracket is from 0 to ten. Above this bracket reads \u201c10\u201d. Under the number line it reads \u201cThe opposite of negative ten is ten\u201d. Points are plotted on negative 10 and 10. The text for part \u201cc\u201d is an algebraic term: negative sign, open parenthesis, negative 6, close parenthesis. To the right is a number line ranging from negative six to six. There are two brackets above the number line. The first bracket is from negative 6 to zero. Above this bracket reads \u201c6\u201d. The second bracket is from 0 to 6. Above this bracket reads \u201csix\u201d. Under the number line it reads \u201cThe opposite of negative 6 is six\u201d. Points are plotted on negative 6 and 6.\" data-label=\"\">\n<tbody>\n<tr>\n<td>a) \u22127 is the same distance from 0 as 7, but on the opposite side of 0.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169750893747\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><br \/>\nThe opposite of 7 is \u22127.<\/td>\n<\/tr>\n<tr>\n<td>b) 10 is the same distance from 0 as \u221210, but on the opposite side of 0.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169750893770\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><br \/>\nThe opposite of \u221210 is 10.<\/td>\n<\/tr>\n<tr>\n<td>c) \u2212(\u22126)<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169746122554\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><br \/>\nThe opposite of \u2212(\u22126) is \u22126.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655219776\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170655004578\" data-type=\"exercise\">\n<div id=\"fs-id1170654916783\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655020985\" data-type=\"problem\">\n<p id=\"fs-id1170655026818\">Find: a) the opposite of 4 b) the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-540af695d1625b991454f0ae27e2b163_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654916783\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654952585\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> b) 3 c) 1<\/p>\n<\/details>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655105370\" data-type=\"problem\">\n<p id=\"fs-id1170655229618\">Find: a) the opposite of 8 b) the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c08d50dd0fdd7a6e29864d545f623cf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655113221\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655155259\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca32393b1b5af7c55a95d89cf9d610f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> b) 5 c) 5<\/p>\n<\/details>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654920902\">Our work with opposites gives us a way to define the integers.The whole numbers and their opposites are called the integers. The integers are the numbers <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-759e65d987e3039dac89a95f0411c0c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#8230;&#125;&#45;&#51;&#44;&#45;&#50;&#44;&#45;&#49;&#44;&#48;&#44;&#49;&#44;&#50;&#44;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#8230;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"154\" style=\"vertical-align: -4px;\" \/><\/p>\n<div id=\"fs-id1170655134778\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Integers<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170654954489\">The whole numbers and their opposites are called the <strong data-effect=\"bold\">integers<\/strong>.<\/p>\n<p id=\"fs-id1170654878555\">The integers are the numbers<\/p>\n<div id=\"fs-id1170655114692\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-759e65d987e3039dac89a95f0411c0c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#8230;&#125;&#45;&#51;&#44;&#45;&#50;&#44;&#45;&#49;&#44;&#48;&#44;&#49;&#44;&#50;&#44;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#8230;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"154\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654999979\">When evaluating the opposite of a <span class=\"no-emphasis\" data-type=\"term\">variable<\/span>, we must be very careful. Without knowing whether the variable represents a positive or negative number, we don\u2019t know whether <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6cacb15a7aa187378723791e7a017ae0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"23\" style=\"vertical-align: 0px;\" \/> is positive or negative. We can see this in <a class=\"autogenerated-content\" href=\"#fs-id1170655134821\">Example 3<\/a>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655134821\" data-type=\"problem\">\n<p id=\"fs-id1170655353645\">Evaluate a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6cacb15a7aa187378723791e7a017ae0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"23\" style=\"vertical-align: 0px;\" \/>, when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1dc438da70f358c2eb1bf64a8b7ea4b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6cacb15a7aa187378723791e7a017ae0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"23\" style=\"vertical-align: 0px;\" \/>, when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7852d0704798164bd2ce5b572ac50cd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654982628\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<ol id=\"fs-id1166422695391\" class=\"circled\" type=\"a\">\n<li>\n<table id=\"eip-id1169754061868\" class=\"unnumbered unstyled\" summary=\"This is an image of a solution in two columns, with text in the left column and math in the right column. In the first row of the first column, the text reads, \u201cTo evaluate when x equals 8 means to substitute 8 for x,\u201d where the number 8 is written in red. The next line down in the right column is negative x. The second line down in the left column, the text reads, \u201cSubstitute 8 for x.\u201d Next to this in the right column is the term negative sign, open parenthesis, 8, close parenthesis, where the number 8 is written in red. The next line down in the left column, the text reads \u201cWrite the opposite of 8.\u201d Next to this in the right column is negative 8.\" data-label=\"\">\n<tbody>\n<tr>\n<td><span id=\"eip-id1169754061885\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">\u2212<em data-effect=\"italics\">x<\/em><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169752188793\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752188805\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the opposite of 8.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169752188824\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_007d_img.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/li>\n<li>\n<table id=\"eip-id1169754029691\" class=\"unnumbered unstyled\" summary=\"This is an image of a solution in two columns, with text in the left column and math in the right column. In the first row of the first column, the text reads, \u201cTo evaluate when x equals negative 8 means to substitute negative 8 for x,\u201d where the number negative 8 is written in red. The next line down in the right column is negative x. The second line down in the left column, the text reads, \u201cSubstitute negative 8 for x.\u201d Next to this in the right column is the term negative sign, open parenthesis, negative 8, close parenthesis, where the number negative 8 is written in red. The next line down in the left column, the text reads \u201cWrite the opposite of negative 8.\u201d Next to this in the right column is the number 8.\" data-label=\"\">\n<tbody>\n<tr>\n<td><span id=\"fs-id1169754375291\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">\u2212<em data-effect=\"italics\">x<\/em><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169754029738\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169751926699\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Write the opposite of \u22128.<\/td>\n<td data-align=\"center\">8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654985194\" data-type=\"problem\">\n<p id=\"fs-id1170654964972\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-54b60de5f209e337503a581593773b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"24\" style=\"vertical-align: 0px;\" \/>, when a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3d48be04aadb63e5661f86d0948d7553_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f987ffcdf7980187121e48d72e16e121_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655022421\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655022423\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> b) 4<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654984479\" data-type=\"problem\">\n<p id=\"fs-id1170654984481\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-661b902eb4b921bb4f69fd1c2513be80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"28\" style=\"vertical-align: 0px;\" \/>, when a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e0bd29c065ea1ce55ed48d1c73859cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-82def9fcaea736bec5b29e90f15647cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"70\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654966628\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654943547\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2981688f5b26fd15fa08c897afa741ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/> b) 11<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify: Expressions with Absolute Value<\/h1>\n<p>We saw that numbers such as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aee857b753e29d0e6e2ae6913ee8a710_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"74\" style=\"vertical-align: 0px;\" \/> are opposites because they are the same distance from 0 on the number line. They are both two units from 0. The distance between 0 and any number on the number line is called the <strong data-effect=\"bold\">absolute value<\/strong> of that number.<\/p>\n<div id=\"fs-id1170655195725\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Absolute Value<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170655354299\">The absolute value of a number is its distance from 0 on the number line.<\/p>\n<p id=\"fs-id1170654982157\">The absolute value of a number <em data-effect=\"italics\">n<\/em> is written as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b38a586dc76a31dfa818cbaca2da26f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#110;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"17\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655160915\">For example,<\/p>\n<ul id=\"fs-id1166424918316\" data-bullet-style=\"bullet\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c33bb96d6d1c81da55e768cda4296ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/> units away from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, so <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-43406138e38267e27d0754c1694527ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#53;&#124;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\" \/>.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2e1b7d211219fce780f09660c400f8b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#54;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: 0px;\" \/> units away from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, so <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6f2f975fcc9d23abe8391088e7b567a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#53;&#124;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"48\" style=\"vertical-align: -5px;\" \/>.<\/li>\n<\/ul>\n<p id=\"fs-id1170655134144\"><a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_01_03_009_new\">Figure 5<\/a> illustrates this idea.<\/p>\n<p>The integers <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb86c74560a3d761e1fa66a8f0a38756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#32;&#97;&#114;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"82\" style=\"vertical-align: -1px;\" \/> units away from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div id=\"CNX_ElemAlg_Figure_01_03_009_new\" class=\"bc-figure figure\">\n<figure style=\"width: 385px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_009_new.jpg\" alt=\"A number line is shown ranging from negative 5 to 5. A bracket labeled \u201c5 units\u201d lies above the points negative 5 to 0. An arrow labeled \u201cnegative 5 is 5 units from 0, so absolute value of negative 5 equals 5.\u201d is written above the labeled bracket. A bracket labeled \u201c5 units\u201d lies above the points \u201c0\u201d to \u201c5\u201d. An arrow labeled \u201c5 is 5 units from 0, so absolute value of 5 equals 5.\u201d and is written above the labeled bracket.\" width=\"385\" height=\"130\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 5<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1170654957170\">The absolute value of a number is never negative (because distance cannot be negative). The only number with absolute value equal to zero is the number zero itself, because the distance from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-95801e7762090eef6337adf96db73f82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#111;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\" \/> on the number line is zero units.<\/p>\n<div id=\"fs-id1170654997376\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Property of Absolute Value<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170654916082\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b6cd98f4266f7f491a976c3270ec303d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#110;&#124;&#92;&#103;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> for all numbers<\/p>\n<p id=\"fs-id1170655074945\">Absolute values are always greater than or equal to zero!<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655150245\">Mathematicians say it more precisely, \u201cabsolute values are always non-negative.\u201d Non-negative means greater than or equal to zero.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655164890\" data-type=\"problem\">\n<p id=\"fs-id1170655164892\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87f810b4b629fae318134b52c7adc57f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#51;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d392a34a8207aa1aa4ac2a97dddabf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#52;&#52;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"46\" style=\"vertical-align: -4px;\" \/>\u00a0c)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3a2c72b2b6c1d226f102034f66b93ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#48;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655213327\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170654944089\">The absolute value of a number is the distance between the number and zero. Distance is never negative, so the absolute value is never negative.<\/p>\n<p id=\"fs-id1166424887501\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87f810b4b629fae318134b52c7adc57f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#51;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b32a7d27ae3987e04d57cc347c4f32cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/p>\n<p>b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d392a34a8207aa1aa4ac2a97dddabf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#52;&#52;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"46\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-208b78e6414745ae3bc25f5465c1df5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/><\/p>\n<p>c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3a2c72b2b6c1d226f102034f66b93ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#48;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fb9a9e4954a2381b702ec733a76df155_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655074703\" data-type=\"problem\">\n<p id=\"fs-id1170655178086\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a97639a72b2f49a10646865ea7d7e6b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#52;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c057723d9ce4e2bcbed4fdd3cb7254a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#50;&#56;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"46\" style=\"vertical-align: -4px;\" \/>\u00a0c)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3a2c72b2b6c1d226f102034f66b93ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#48;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655161378\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655161380\">a)\u00a04\u00a0b)\u00a028\u00a0c)\u00a00<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655160962\" data-type=\"problem\">\n<p id=\"fs-id1170655000504\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-491ee238f24d36c3b7d1198ec4b325c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#49;&#51;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"46\" style=\"vertical-align: -4px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ecba465829d2eae71c523dae3c937e50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#52;&#55;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"24\" style=\"vertical-align: -4px;\" \/>\u00a0c)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3a2c72b2b6c1d226f102034f66b93ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#48;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655026795\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655026797\">a)\u00a013\u00a0b)\u00a047\u00a0c) 0<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654887750\">In the next example, we\u2019ll order expressions with absolute values. Remember, positive numbers are always greater than negative numbers!<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1170654953584\">Fill in &lt;, &gt;, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e675109dbfb543da39879cbe413a3064_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"37\" style=\"vertical-align: 0px;\" \/> for each of the following pairs of numbers:<\/p>\n<p id=\"fs-id1170654916476\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29f80c98885a0c2b74a1fc1f5e6d86b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#53;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-545b962a2ddeb7bc62f8baebcaa3d5b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#45;&#53;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c22585d424149a2f06385206336c56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#45;&#56;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\" \/>c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7db1529cce29849fd2d8a54b0fa1440_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#45;&#57;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\" \/> d) &#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60f20f07f8f7c62331f2d8fe388a61b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97965dd09e44097632b9a81977b96c4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#45;&#49;&#54;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1170655106909\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%; height: 184px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29f80c98885a0c2b74a1fc1f5e6d86b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#53;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/>___ &#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29f80c98885a0c2b74a1fc1f5e6d86b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#53;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td>a) Simplify.<br \/>\nOrder.<\/td>\n<td>5 ___ -5<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td>5\u00a0 &gt; -5<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29f80c98885a0c2b74a1fc1f5e6d86b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#53;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/>\u00a0 &gt; &#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29f80c98885a0c2b74a1fc1f5e6d86b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#53;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td>b) Simplify.<br \/>\nOrder.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> ___ &#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4edbd13afbf91b71c1d89205f3d7869d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#56;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td>8 ___ -8<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td>8 &gt; -8<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td><\/td>\n<td>8 &gt; &#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4edbd13afbf91b71c1d89205f3d7869d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#56;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td>c) Simplify.<br \/>\nOrder.<\/td>\n<td>9 ___ &#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4d077845d89c58590a6bd9ef094faa4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#57;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/><\/p>\n<p>-9 ___ -9<\/p>\n<p>-9 = -9<\/p>\n<p>-9 = &#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4d077845d89c58590a6bd9ef094faa4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#57;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td>d) Simplify.<br \/>\nOrder.<\/td>\n<td>&#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-890d448b349cb30ba797bda0ae641dbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#45;&#49;&#54;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/> ___ &#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40fd066ba59d22d02733456214eb81cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#49;&#54;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -5px;\" \/><\/p>\n<p>16 ____ -16<\/p>\n<p>16 &gt; -16<\/p>\n<p>&#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-890d448b349cb30ba797bda0ae641dbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#45;&#49;&#54;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/> &gt; &#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40fd066ba59d22d02733456214eb81cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#49;&#54;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655121090\" data-type=\"problem\">\n<p id=\"fs-id1170655099637\">Fill in &lt;, &gt;, or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8690b7efd237bfe32a6e92e3b699b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"4\" width=\"13\" style=\"vertical-align: 2px;\" \/> for each of the following pairs of numbers:\u00a0a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4d077845d89c58590a6bd9ef094faa4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#57;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/>___-<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4d077845d89c58590a6bd9ef094faa4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#57;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/>___-<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f109d5404c977d1a4cd37023190a812_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#50;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca32393b1b5af7c55a95d89cf9d610f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4edbd13afbf91b71c1d89205f3d7869d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#56;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cb4cc8cbcb582b264a149b5a50dd8df6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#45;&#40;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"29\" style=\"vertical-align: -5px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7db1529cce29849fd2d8a54b0fa1440_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#45;&#57;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655228722\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655352028\">a)\u00a0&gt;\u00a0b)\u00a0&gt;\u00a0c)\u00a0&lt;\u00a0d)\u00a0&gt;<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655083336\" data-type=\"problem\">\n<p id=\"fs-id1170655065401\">Fill in &lt;, &gt;, or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8690b7efd237bfe32a6e92e3b699b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"4\" width=\"13\" style=\"vertical-align: 2px;\" \/> for each of the following pairs of numbers:\u00a0a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/>___-<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-592bb1091b7b31ea7257153a9cd47e8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#55;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e03ffec41d1d742df04a39acfd178c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#45;&#40;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\" \/>___-<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-376845b9a193feeada254438aa9864d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#49;&#48;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -5px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8d40ba9179c144491b0c8df571d46672_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#52;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-910b68b1c62dc05d2f22e902f823c777_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#45;&#52;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7a88add9e6af2c18b8db7cb1f051868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#49;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655003444\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655157651\">a)\u00a0&gt;\u00a0b)\u00a0&gt;\u00a0c)\u00a0&gt;\u00a0d) &lt;<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655060167\">We now add absolute value bars to our list of grouping symbols. When we use the order of operations, first we simplify inside the absolute value bars as much as possible, then we take the <span class=\"no-emphasis\" data-type=\"term\">absolute value<\/span> of the resulting number.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<caption>Grouping Symbols<\/caption>\n<tbody>\n<tr>\n<td style=\"width: 50%;\">Parentheses<\/td>\n<td style=\"width: 50%;\">( )<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Brackets<\/td>\n<td style=\"width: 50%;\">[ ]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Braces<\/td>\n<td style=\"width: 50%;\">{ }<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Absolute value<\/td>\n<td style=\"width: 50%;\">| |<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655103794\">In the next example, we simplify the expressions inside absolute value bars first, just like we do with parentheses.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655218379\" data-type=\"problem\">\n<p id=\"fs-id1170655000668\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d8edc5774e4274d735ff981d931a1f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#45;&#124;&#49;&#57;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"155\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654968392\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-46\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d8edc5774e4274d735ff981d931a1f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#45;&#124;&#49;&#57;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"155\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Work inside parentheses first: subtract 2 from 6.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5b2eba697acad7bccc802b9eb876a5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#45;&#124;&#49;&#57;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply 3(4).<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6009efcc047f5b92d5a99dc4f37f5346_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#45;&#124;&#49;&#57;&#45;&#49;&#50;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract inside the absolute value bars.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-43d89b4f0f228bd9a08f73f516854081_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#45;&#124;&#55;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5eaef3ba285fc7d0ae3dfdd9efe6149_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b976c8c10558ac50c42d953f3ee38707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655222089\" data-type=\"problem\">\n<p id=\"fs-id1170655222091\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-092df2527fd0d339aadc373741e4f2dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;&#45;&#124;&#49;&#49;&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"154\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654963377\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654963379\">16<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654931969\" data-type=\"problem\">\n<p id=\"fs-id1170654931971\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4f24d6d68a38ea651287768a6240e243_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#45;&#124;&#56;&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"137\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655150934\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655269907\">9<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655194444\" data-type=\"problem\">\n<p id=\"fs-id1170655218370\">Evaluate: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e47998044ecaee793c58133cbbee363_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#120;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#45;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1726e1061201ed96e88acd1fc8da2bff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#121;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -5px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2c61e6f15b2524c55a91e8ba3cc75f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#117;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#117;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"131\" style=\"vertical-align: -5px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68f23e8babe36ec516673a21c3112e01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#112;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#112;&#61;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655030077\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1166425224104\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e47998044ecaee793c58133cbbee363_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#120;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#45;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/p>\n<table id=\"eip-id1169747671487\" class=\"unnumbered unstyled\" summary=\"This image shows a solution in two columns. In the right column is the term \u201cabsolute value of x.\u201d One row down, the text in the left column reads \u201cSubstitute negative 35 for x.\u201d Next to this in the right column is the term \u201cabsolute value of negative 35\u201d, where negative 35 is written in red. One row down, the text in the left column reads \u201cTake the absolute value.\u201d Next to this in the right column is 35.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-10645fbf1606a0f1e256929461fbc6e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#120;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"16\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169747671518\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-align=\"right\"><span id=\"eip-id1169747671530\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td data-align=\"right\">35<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1726e1061201ed96e88acd1fc8da2bff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#121;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -5px;\" \/><\/p>\n<table id=\"eip-id1169752110168\" class=\"unnumbered unstyled\" summary=\"This image shows a solution in two columns. In the right column is the term \u201cabsolute value of negative y\u201d . One row down, the text in the left column reads \u201cSubstitute negative 20 for y.\u201d Next to this in the right column is the term \u201cabsolute value of negative sign, partenthesis, negative 20, close parenthesis.\u201d Negative 20 is written in red. One row down, the text in the left column row reads \u201cSimplify.\u201dNext to this in the right column is the term \u201cabsolute value of 20\u201d. One row down, the text in the left column reads \u201cTake the absolute value.\u201d Next to this in the right column is 20.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-892fb3241a8118c5028e7f705acfd2be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#121;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169749467086\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_011a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-align=\"right\"><span id=\"eip-id1169749467098\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_011b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc5398b36051b1f3c17d641bcbb88c54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#50;&#48;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"24\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td data-align=\"right\">20<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>c)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2c61e6f15b2524c55a91e8ba3cc75f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#117;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#117;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"131\" style=\"vertical-align: -5px;\" \/><\/p>\n<table id=\"eip-id1169750879718\" class=\"unnumbered unstyled\" summary=\"This image shows a solution in two columns. In the right column is the term \u201cnegative sign, absolute value of u\u201d. One row down, the text in the left column reads \u201cSubstitute 12 for u.\u201d Next to this in the right column is the term \u201cnegative sign, absolute value of 12\u201d, where 12 is written in red. One row down, the text in the left column reads \u201cTake the absolute value.\u201d Next to this in the right column is negative 12.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d1c6dbbb8e8683dac6f9b033e945268f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#117;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"31\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169753237141\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_012a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-align=\"right\"><span id=\"eip-id1169753237153\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_012b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9eae543c53f9301fa411ef541a1f4433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>d)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68f23e8babe36ec516673a21c3112e01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#112;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#112;&#61;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -5px;\" \/><\/p>\n<table id=\"eip-id1169754142438\" class=\"unnumbered unstyled\" summary=\"This image shows a solution in two columns. In the right column is the term \u201cnegative sign, absolute value of p\u201d. One row down, the text in the left column reads \u201cSubstitute negative 14 for p.\u201d Next to this in the right column is the term \u201cnegative sign, absolute value of negative 14\u201d, where negative 14 is written in red. One row down, the text in the left column reads \u201cTake the absolute value.\u201d Next to this in the right column is negative 14.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-84ee71dbdd1630ee4e272b6512e8e944_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#112;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"30\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169754142474\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-align=\"right\"><span id=\"eip-id1169754130713\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Take the absolute value.<\/td>\n<td data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4066673cb5834f8ce47cc6896c29963a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655193881\" data-type=\"problem\">\n<p id=\"fs-id1170655193884\">Evaluate: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f6500c3fecf4d75779a724c5b17272c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#120;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#45;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"131\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec1b540dd99e68a3991e909f07a57f2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#121;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#45;&#51;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -5px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bd33db68e4d49dd8f21f34696160089d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#109;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#109;&#61;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-776999507ec0a86b5dca8502dd7ab330_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#112;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#112;&#61;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655129135\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655129137\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b976c8c10558ac50c42d953f3ee38707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a3db773b3fb1c245f782b7a601d70917_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-851674cf8d214f2dc493930ee7e6ee73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2981688f5b26fd15fa08c897afa741ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655355508\" data-type=\"problem\">\n<p>Evaluate: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-807bcb784a0b7246f7a1929382c5083e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#121;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#45;&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b99eb738959d81ec61b0d7452c9cd034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#121;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#45;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"150\" style=\"vertical-align: -5px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c961b2f13802a644d160b0fe8cea1174_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#110;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#61;&#51;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2eb6aec0c657d315a91d2d37e31471d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#113;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#113;&#61;&#45;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654902359\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655098975\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e554ca92166de4bd98acfbef8f678cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b44aa122f73c22d86f2d764af01f919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a59867b5a3525d9c7f91084fbd12ef9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87b45b657a37f37cb779527d2a666770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Add Integers<\/h1>\n<p id=\"fs-id1170654942147\">Most students are comfortable with the addition and subtraction facts for positive numbers. But doing addition or subtraction with both positive and negative numbers may be more challenging.<\/p>\n<p id=\"fs-id1170654982815\">We will use two colour counters to model addition and subtraction of negatives so that you can visualize the procedures instead of memorizing the rules.<\/p>\n<p id=\"fs-id1170654940836\">We let one colour (blue) represent positive. The other colour (red) will represent the negatives. If we have one positive counter and one negative counter, the value of the pair is zero. They form a neutral pair. The value of this neutral pair is zero.<\/p>\n<p><span id=\"fs-id1170654940841\" data-type=\"media\" data-alt=\"In this image we have a blue counter above a red counter with a circle around both. The equation to the right is 1 plus negative 1 equals 0.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_014_img_new.jpg\" alt=\"In this image we have a blue counter above a red counter with a circle around both. The equation to the right is 1 plus negative 1 equals 0.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170654925278\">We will use the counters to show how to add the four addition facts using the numbers <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a46791a391dd60ec10b6fdd529ca8ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#44;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"39\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c8f99a729c7a37f3083f2bbfa4f2a1af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#44;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a5cb80ca32bb44bfa32aca2af8b6463_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#43;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#43;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"386\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1170654942111\">To add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-801284eae9d4b66b01d49ee1b141eddc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: -2px;\" \/>, we realize that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-801284eae9d4b66b01d49ee1b141eddc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: -2px;\" \/> means the sum of 5 and 3<\/p>\n<table id=\"eip-id1169751875448\" style=\"width: 100%;\" summary=\"In this figure, there are two columns and three rows. The left column, first row reads \u201cwe start with 5 positives.\u201d Next to this in the right column are 5 positive counters with the number 5 underneath. In the next row, it reads, \u201cAnd then we add 3 positives. Next to this is a group of 5 positive counters, separated by a space and then 3 positive counters. The next row down reads, \u201cWe now have eight positives. The sum of 5 and 3 is 8.\u201d Next to this are eight positive counters. with the label \u201c8 positives\u201d written underneath.\" data-label=\"\">\n<tbody>\n<tr>\n<td>We start with 5 positives.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169754176959\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_015a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>And then we add 3 positives.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169754176978\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_015b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We now have 8 positives. The sum of 5 and 3 is 8.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169753253870\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_015c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654940990\">Now we will add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f038be4d73190fbbca15c96b19f33edd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/>. Watch for similarities to the last example <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5dce190f8255da0639b153cba584d9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#51;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"72\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p id=\"fs-id1170655170230\">To add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f038be4d73190fbbca15c96b19f33edd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/>, we realize this means the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c7f25b3fa804af465d8a457b48be9da1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"88\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<table id=\"eip-id1169751926722\" style=\"width: 100%;\" summary=\"In this figure, there are two columns and three rows. The left column, first row reads \u201cwe start with 5 negatives.\u201d Next to this in the right column are 5 negative counters with the numeral negative 5 underneath. In the next row, it reads, \u201cAnd then we add 3 negatives. Next to this is a group of 5 negative counters, separated by a space and then 3 negative counters. The next row down reads, \u201cWe now have eight negatives. The sum of negative 5 and negative 3 is negative 8.\u201d Next to this are eight negative counters. with the label \u201c8 negatives\u201d written underneath.\" data-label=\"\">\n<tbody>\n<tr>\n<td>We start with 5 negatives.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169751926744\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_018a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>And then we add 3 negatives.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169754029689\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_018b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We now have 8 negatives. The sum of \u22125 and \u22123 is \u22128.<\/td>\n<td data-align=\"center\"><span id=\"eip-id1169754029708\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_018c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654905072\">In what ways were these first two examples similar?<\/p>\n<ul id=\"fs-id1166424896444\" data-bullet-style=\"bullet\">\n<li>The first example adds 5 positives and 3 positives\u2014both positives.<\/li>\n<li>The second example adds 5 negatives and 3 negatives\u2014both negatives.<\/li>\n<\/ul>\n<p id=\"fs-id1170654905046\">In each case we got 8\u2014either 8 positives or 8 negatives.<\/p>\n<p id=\"fs-id1170654905109\">When the signs were the same, the counters were all the same color, and so we added them.<\/p>\n<p><span id=\"fs-id1170655040356\" data-type=\"media\" data-alt=\"This figure is divided into two columns. In the left column there are eight blue counters in a horizontal row. Under them is the text \u201c8 positives.\u201d Centred under this is the equation 5 plus 3 equals 8. In the right column are eight red counters in a horizontal row which are labled below with the phrase \u201c8 negatives\u201d. Centred under this is the equation negative 5 plus negative 3 equals negative 8, where negative 3 is in parentheses.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_021_img_new.jpg\" alt=\"This figure is divided into two columns. In the left column there are eight blue counters in a horizontal row. Under them is the text \u201c8 positives.\u201d Centred under this is the equation 5 plus 3 equals 8. In the right column are eight red counters in a horizontal row which are labled below with the phrase \u201c8 negatives\u201d. Centred under this is the equation negative 5 plus negative 3 equals negative 8, where negative 3 is in parentheses.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655040352\" data-type=\"problem\">\n<p id=\"fs-id1170655030146\">Add:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3660200ebc9a68a2aedc08f1a9096b0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"39\" style=\"vertical-align: -2px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-929de2c2af9a64f22297516f77f37aa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655030382\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p>a)<\/p>\n<figure style=\"width: 270px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_022_img_new.jpg\" alt=\".\" width=\"270\" height=\"75\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">1 positive plus 4 positives is 5 positives.<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p id=\"fs-id1169145731676\">b)<\/p>\n<figure style=\"width: 285px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_023_img_new.jpg\" alt=\".\" width=\"285\" height=\"72\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">1 negative plus 4 negatives is 5 negatives.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655040471\" data-type=\"problem\">\n<p id=\"fs-id1170655040473\">Add:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-478e6fd121a53f274a0ec8a5d4f032a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0210f277e32ab025744cce7d267b17c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655040605\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655040607\">a)\u00a06\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655040652\" data-type=\"problem\">\n<p id=\"fs-id1170655040655\">Add:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-52df114854223c7d3f012e204cccbbdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: -2px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f0c2d36ef70e9e10fd645e5b1e254fa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655040708\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655040710\">a)\u00a07\u00a0b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00c6d30c5f7439a21caf981437f64be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655030242\">So what happens when the signs are different? Let\u2019s add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9db94c4517228eb349cd4426ad66e71b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"52\" style=\"vertical-align: -2px;\" \/>. We realize this means the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/> and 3. When the counters were the same color, we put them in a row. When the counters are a different color, we line them up under each other.<\/p>\n<table id=\"eip-id1169750997833\" style=\"width: 100%;\" summary=\"This figure is divided into two columns. Text at the top of the image in the right column reads \u201cnegative 5 plus 3 means the sum of negative 5 and 3.\u201d One line down in the left column, the text reads \u201cWe start with 5 negatives.\u201d In the right column are five red counters. One line down in the left column, the text reads \u201cAnd then we add 3 positives\u201d. Next to this in the right column is a horizontal row of five red counters drawn above three blue counters. One line down, the text in the left column reads \u201cWe remove any neutral pairs.\u201d Next to this in the right column are three pairs of one red counter and one blue counter, each pair circled. There are two remaining red counters to the right of the paired counters. One line down, the text in the left column reads \u201cWe have 2 negatives left.\u201d Next to this in the right column are two red counters labeled \u201c2 negatives\u201d. In the last row, the text in the left column reads \u201cThe sum of negative 5 and 3 is negative 2.\u201d Next to this in the right column is the equation negative 5 plus 3 equals negative 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\u22125 + 3 means the sum of \u22125 and 3.<\/td>\n<\/tr>\n<tr>\n<td>We start with 5 negatives.<\/td>\n<td><span id=\"eip-id1169750997858\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_024a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>And then we add 3 positives.<\/td>\n<td><span id=\"eip-id1169750997874\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_024b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We remove any neutral pairs.<\/td>\n<td><span id=\"eip-id1169747671495\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_024c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We have 2 negatives left.<\/td>\n<td><span id=\"eip-id1169747671512\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_024d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The sum of \u22125 and 3 is \u22122.<\/td>\n<td>\u22125 + 3 = \u22122<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654936878\">Notice that there were more negatives than positives, so the result was negative.<\/p>\n<p>Let\u2019s now add the last combination, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cd386991eb516c110c242436558446ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table id=\"eip-id1169754030168\" style=\"width: 100%;\" summary=\"This figure is divided into two columns. Text at the top of the image in the right column reads \u201c5 plus negative 3 means the sum of negative 5 and 3.\u201d One line down in the left column, the text reads \u201cWe start with 5 positives.\u201d In the right column are five blue counters. One line down in the left column, the text reads \u201cAnd then we add 3 negatives\u201d. Next to this in the right column is a horizontal row of five blue counters drawn above three red counters. One line down, the text in the left column reads \u201cWe remove any neutral pairs.\u201d Next to this in the right column are three pairs of one blue counter and one red counter, each pair circled. There are two remaining blue counters to the right of the paired counters. One line down, the text in the left column reads \u201cWe have 2 positives left.\u201d Next to this in the right column are two blue counters labeled \u201c2 positives\u201d. In the last row, the text in the left column reads \u201cThe sum of 5 and negative 3 is 2.\u201d Next to this in the right column is the equation 5 plus negative 3 equals 2, where negative 3 is in parentheses.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>5 + (\u22123) means the sum of 5 and \u22123.<\/td>\n<\/tr>\n<tr>\n<td>We start with 5 positives.<\/td>\n<td><span id=\"eip-id1169754030192\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_025a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>And then we add 3 negatives.<\/td>\n<td><span id=\"eip-id1169754030208\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_025b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We remove any neutral pairs.<\/td>\n<td><span id=\"eip-id1169754030225\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_025c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We have 2 positives left.<\/td>\n<td><span id=\"eip-id1169748875617\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_025d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The sum of 5 and \u22123 is 2.<\/td>\n<td>5 + (\u22123) = 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655057773\">When we use counters to model addition of positive and negative integers, it is easy to see whether there are more positive or more negative counters. So we know whether the sum will be positive or negative.<\/p>\n<p><span id=\"fs-id1170655058518\" data-type=\"media\" data-alt=\"Two images are shown and labeled. The left image shows five red counters in a horizontal row drawn above three blue counters in a horizontal row, where the first three pairs of red and blue counters are circled. Above this diagram is written \u201cnegative 5 plus 3\u201d and below is written \u201cMore negatives \u2013 the sum is negative.\u201d The right image shows five blue counters in a horizontal row drawn above three red counters in a horizontal row, where the first three pairs of red and blue counters are circled. Above this diagram is written \u201c5 plus negative 3\u201d and below is written \u201cMore positives \u2013 the sum is positive.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_026_img_new.jpg\" alt=\"Two images are shown and labeled. The left image shows five red counters in a horizontal row drawn above three blue counters in a horizontal row, where the first three pairs of red and blue counters are circled. Above this diagram is written \u201cnegative 5 plus 3\u201d and below is written \u201cMore negatives \u2013 the sum is negative.\u201d The right image shows five blue counters in a horizontal row drawn above three red counters in a horizontal row, where the first three pairs of red and blue counters are circled. Above this diagram is written \u201c5 plus negative 3\u201d and below is written \u201cMore positives \u2013 the sum is positive.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655058550\" data-type=\"problem\">\n<p id=\"fs-id1170655058552\">Add: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1211b5f02078795082d5e423b624cad8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"51\" style=\"vertical-align: -2px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b070b9d885ab879390b3c67d95240032_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655029787\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1166422829183\">a)<\/p>\n<table id=\"eip-id1169754360753\" class=\"unnumbered unstyled\" summary=\"In this image we have two columns. The top of the right column has the equation \u201cnegative 1 plus 5.\u201d The next line down in the left column reads, \u201cThere are more positives, so the sum is positive.\u201d Next to this in the right column are five blue counters. Under this, one red counter. The first blue counter and the single red counter are circled. Under this in the same column it says \u201c4.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\">\u22121 + 5<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169749528166\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_027_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>There are more positives, so the sum is positive.<\/td>\n<td data-align=\"center\">4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>b)<\/p>\n<table id=\"eip-id1169750608265\" class=\"unnumbered unstyled can-break\" summary=\"In this image we have two columns. The top of the right column has the equation \u201c1 plus negative 5.\u201d The next line down in the left column reads, \u201cThere are more negatives, so the sum is negative.\u201d Next to this in the right column is one blue counter. Under this, five red counters. The single blue counter and the first of the five red counters is circled. Under this in the same column it says \u201cnegative 4.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\">1 + (\u22125)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169750608293\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_028_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>There are more negatives, so the sum is negative.<\/td>\n<td data-align=\"center\">\u22124<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654904893\" data-type=\"problem\">\n<p id=\"fs-id1170654904895\">Add:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6a4dcc55080d931ad32225aa3a323aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"52\" style=\"vertical-align: -2px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2251ca4270ec721714b863c4dbed86f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655066666\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655066668\">a)\u00a02\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655066631\" data-type=\"problem\">\n<p id=\"fs-id1170655066633\">Add:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d37ddf9df3c0b876ebeed0ce08e85bca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"51\" style=\"vertical-align: -2px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c76ff948804380f0df9b1e4bdecfd7bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655066149\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655066151\">a)\u00a03\u00a0b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655066171\">Now that we have added small positive and negative integers with a model, we can visualize the model in our minds to simplify problems with any numbers.<\/p>\n<p id=\"fs-id1170655067182\">When you need to add numbers such as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfa527ceb2ba44255562b4665edb273b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#55;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\" \/>, you really don\u2019t want to have to count out 37 blue counters and 53 red counters. With the model in your mind, can you visualize what you would do to solve the problem?<\/p>\n<p id=\"fs-id1170655067203\">Picture 37 blue counters with 53 red counters lined up underneath. Since there would be more red (negative) counters than blue (positive) counters, the sum would be <em data-effect=\"italics\">negative<\/em>. How many more red counters would there be? Because <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b09d319d46b6d8d70bfc4295bb36ed39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#51;&#45;&#51;&#55;&#61;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"99\" style=\"vertical-align: 0px;\" \/>, there are 16 more red counters.<\/p>\n<p id=\"fs-id1170655067279\">Therefore, the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bfa527ceb2ba44255562b4665edb273b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#55;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60f20f07f8f7c62331f2d8fe388a61b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<div id=\"fs-id1170655067436\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b09dba2d0eb6159497a0515ef08f5bfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#55;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"140\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"fs-id1170655069654\">Let\u2019s try another one. We\u2019ll add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-98f58f6d65f00c5cded6b2d78160a1ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\" \/>. Again, imagine 74 red counters and 27 more red counters, so we\u2019d have 101 red counters. This means the sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bef0630181569824ae99bb7fcbc6cc43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32463a2e4155942839d70fc5b66fd3b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#48;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"161\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1170655069404\">Let\u2019s look again at the results of adding the different combinations of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a46791a391dd60ec10b6fdd529ca8ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#44;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"39\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c8f99a729c7a37f3083f2bbfa4f2a1af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#44;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Addition of Positive and Negative Integers<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655069465\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bef4f6998ff330d86687184477372218_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#43;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#111;&#116;&#104;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#44;&#32;&#115;&#117;&#109;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#111;&#116;&#104;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#44;&#32;&#115;&#117;&#109;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"477\" style=\"vertical-align: -25px;\" \/><\/div>\n<p id=\"fs-id1170655072721\">When the signs are the same, the counters would be all the same color, so add them.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0ad585088aeed787d8a28255a8db63cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#43;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#102;&#102;&#101;&#114;&#101;&#110;&#116;&#32;&#115;&#105;&#103;&#110;&#115;&#44;&#32;&#109;&#111;&#114;&#101;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#44;&#32;&#115;&#117;&#109;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#102;&#102;&#101;&#114;&#101;&#110;&#116;&#32;&#115;&#105;&#103;&#110;&#115;&#44;&#32;&#109;&#111;&#114;&#101;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#44;&#32;&#115;&#117;&#109;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"732\" style=\"vertical-align: -25px;\" \/><\/p>\n<p id=\"fs-id1170655163407\">When the signs are different, some of the counters would make neutral pairs, so subtract to see how many are left.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654942464\">Visualize the model as you simplify the expressions in the following examples.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654932186\" data-type=\"problem\">\n<p id=\"fs-id1170654932188\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-214c9b1a981dd7bff53ffa89ff9c703c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -4px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-95d33e01b1413af803051b0d9cc018be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654942539\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<ol id=\"fs-id1166422639606\" class=\"circled\" type=\"a\">\n<li>\u00a0Since the signs are different, we subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ed34c712e502aaff1fa3497a37fcfb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#57;&#32;&#102;&#114;&#111;&#109;&#32;&#52;&#55;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"86\" style=\"vertical-align: -1px;\" \/> The answer will be negative because there are more negatives than positives.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7800ea26f03c2ce5a096bbfa4c067c98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#57;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#100;&#100;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#50;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"176\" style=\"vertical-align: -12px;\" \/><\/li>\n<li>\u00a0Since the signs are the same, we add. The answer will be negative because there are only negatives.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d19bd2ae53ecc454ac47c49561c5f9a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#100;&#100;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"185\" style=\"vertical-align: -12px;\" \/><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654941250\" data-type=\"problem\">\n<p id=\"fs-id1170654941252\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1fe9638fae9c4a1075a1341898477240_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"97\" style=\"vertical-align: -4px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3bcd2a87adedafbd2452193e94c40563_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654941827\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655215496\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-862746467ef7a474e7ee68e5f343ac7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a516826583d9ebf41e251f45bc98b74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655226063\" data-type=\"problem\">\n<p id=\"fs-id1170655226065\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-995073bb3ad53aa2d03f7ef99ecd638b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#50;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"97\" style=\"vertical-align: -4px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b512ac355a93153e7ddc60b58d50d65f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655165460\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655165462\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf41452ef9253aeacf471ced6e53e4d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3d317efb244f5cda02f971b5e4865cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654944039\">The techniques used up to now extend to more complicated problems, like the ones we\u2019ve seen before. Remember to follow the order of operations!<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654929156\" data-type=\"problem\">\n<p id=\"fs-id1170654929159\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-448672ff0a1ac55cbe96ad8d96b0b670_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"121\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654934976\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-256\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-448672ff0a1ac55cbe96ad8d96b0b670_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify inside the parentheses.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8be44f2d6976b8defb59f8d2a28324be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"77\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-59c7a6beeb76118dfdb9dcdde558098a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add left to right.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654936188\" data-type=\"problem\">\n<p id=\"fs-id1170654936190\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a13f9dcea68de157b63e9ecf5b06c754_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#43;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"121\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654944107\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654944110\">13<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div>\n<p id=\"fs-id1170655111076\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-21a74a52544c94aba6590a7de850f868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"121\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654944573\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654944575\">0<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Subtract Integers<\/h1>\n<p id=\"fs-id1170654921208\">We will continue to use counters to model the subtraction. Remember, the blue counters represent positive numbers and the red counters represent negative numbers.<\/p>\n<p id=\"fs-id1170654921213\">Perhaps when you were younger, you read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1c2458401e1ba61cb79b5e0d0af7783f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#96;&#96;&#125;&#53;&#45;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#39;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-562942cc14b3e1da3b517d2a107b8a5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#96;&#96;&#125;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"15\" style=\"vertical-align: 0px;\" \/> take away <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1a0d80aaea08b754c67895d1d8974745_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#39;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> When you use counters, you can think of subtraction the same way!<\/p>\n<p id=\"fs-id1170654932154\">We will model the four subtraction facts using the numbers <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div id=\"fs-id1170654936672\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-931460af5fd03a39bd83c51d7b4bb9df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"386\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"fs-id1170654939339\">To subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18bf6d724d73aae9898903e03b095aa6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: 0px;\" \/>, we restate the problem as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-562942cc14b3e1da3b517d2a107b8a5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#96;&#96;&#125;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"15\" style=\"vertical-align: 0px;\" \/> take away <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1a0d80aaea08b754c67895d1d8974745_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#39;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/p>\n<table id=\"eip-id1169750607921\" style=\"width: 100%;\" summary=\"In this image, we have two columns and four rows. The first row, left column reads, \u201cWe start with 5 positives.\u201d Next to this is a horizontal row of five blue counters. The next row down, left column reads \u201cWe \u2018take away\u2019 3 positives\u201d. Next to this in the right column is a horizontal row of three blue counters, a space, and then two blue counters. The first three blue counters are circled with an arrow. The next line down reads \u201cWe have two positives left.\u201d The line below that reads \u201cThe difference of 5 and 3 is 2.\u201d Next to this in the right column is \u201c2\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td>We start with 5 positives.<\/td>\n<td><span id=\"eip-id1169746620624\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_029a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We \u2018take away\u2019 3 positives.<\/td>\n<td><span id=\"eip-id1169746620641\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_029b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We have 2 positives left.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The difference of 5 and 3 is 2.<\/td>\n<td data-align=\"center\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654932116\">Now we will subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a6f34cb022a06be1d1b66093dbee0c0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/>. Watch for similarities to the last example <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e70987854823bc2eb243f70dbdb4de55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#45;&#51;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"71\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id1170654936713\">To subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a6f34cb022a06be1d1b66093dbee0c0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/>, we restate this as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4b5f14e7661367138eeafd18db5105f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#96;&#96;&#125;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"37\" style=\"vertical-align: 0px;\" \/> take away <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e2e5633e9ba16b7b2164fdd7ec80834d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#39;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"29\" style=\"vertical-align: 0px;\" \/><\/p>\n<table id=\"eip-id1169750717917\" style=\"width: 100%;\" summary=\"In this image, we have two columns and four rows. The first row, left column reads, \u201cWe start with 5 negatives.\u201d Next to this is a horizontal row of five red counters. The next row down, left column reads \u201cWe \u2018take away\u2019 3 negatives\u201d. Next to this in the right column is a horizontal row of three red counters, a space, and then two red counters. The first three red counters are circled with an arrow. The next line down reads \u201cWe have two negatives left.\u201d The line below that reads \u201cThe difference of negative 5 and negative 3 is negative 2.\u201d Next to this in the right column is \u201cnegative 2\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td>We start with 5 negatives.<\/td>\n<td><span id=\"eip-id1169753098982\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_030a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We \u2018take away\u2019 3 negatives.<\/td>\n<td><span id=\"eip-id1169753098998\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_030b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We have 2 negatives left.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The difference of \u22125 and \u22123 is \u22122.<\/td>\n<td data-align=\"center\">\u22122<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that these two examples are much alike: The first example, we subtract 3 positives from 5 positives and end up with 2 positives.<\/p>\n<p id=\"fs-id1170654942784\">In the second example, we subtract 3 negatives from 5 negatives and end up with 2 negatives.<\/p>\n<p id=\"fs-id1170654942787\">Each example used counters of only one color, and the \u201ctake away\u201d model of subtraction was easy to apply.<\/p>\n<p><span id=\"fs-id1170654942792\" data-type=\"media\" data-alt=\"Two images are shown and labeled. The first image shows five blue counters, three of which are circled with an arrow. Above the counters is the equation \u201c5 minus 3 equals 2.\u201d The second image shows five red counters, three of which are circled with an arrow. Above the counters is the equation \u201cnegative 5, minus, negative 3, equals negative 2.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_031_img_new.jpg\" alt=\"Two images are shown and labeled. The first image shows five blue counters, three of which are circled with an arrow. Above the counters is the equation \u201c5 minus 3 equals 2.\u201d The second image shows five red counters, three of which are circled with an arrow. Above the counters is the equation \u201cnegative 5, minus, negative 3, equals negative 2.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654941719\" data-type=\"problem\">\n<p id=\"fs-id1170654941105\">Subtract:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-78e552704b5580cc0fe0662d3471c164_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d30d63edafff07cad2ccb2b0b647e14d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654942825\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-947\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nTake 5 positive from 7 positives and get 2 positives.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-69f9fcbe81f7038865d7b1c4da46787a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#55;&#45;&#53;&#92;&#92;&#32;&#50;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"39\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nTake 5 negatives from 7 negatives and get 2 negatives.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5967184936a7160e4b7fe4a63c0bdd5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#45;&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#45;&#50;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"79\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655174379\" data-type=\"problem\">\n<p id=\"fs-id1170655174381\">Subtract:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5998bc2d047a935f18b7f8b1bead811_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-717239a47bf9731de552df2098d9058f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654942396\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654942399\">a)\u00a02\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654942577\" data-type=\"problem\">\n<p id=\"fs-id1170654935898\">Subtract:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ad08e565aed640d068767233478786cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d54412b4ab04674969c56370bac23fe3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div id=\"fs-id1170655208093\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655208095\">a)\u00a03\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654935830\">What happens when we have to subtract one positive and one negative number? We\u2019ll need to use both white and red counters as well as some <span class=\"no-emphasis\" data-type=\"term\">neutral pairs<\/span>. Adding a neutral pair does not change the value. It is like changing quarters to nickels\u2014the value is the same, but it looks different.<\/p>\n<ul id=\"fs-id1166424901740\" data-bullet-style=\"bullet\">\n<li>To subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a029da03c39ec48a0d5bebd17696a97b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: 0px;\" \/>, we restate it as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/> take away 3.<\/li>\n<\/ul>\n<p id=\"fs-id1170654928179\">We start with 5 negatives. We need to take away 3 positives, but we do not have any positives to take away.<\/p>\n<p id=\"fs-id1170654928184\">Remember, a neutral pair has value zero. If we add 0 to 5 its value is still 5. We add neutral pairs to the 5 negatives until we get 3 positives to take away.<\/p>\n<table id=\"eip-id1169752192784\" style=\"width: 100%;\" summary=\"In this image, we have two columns and six rows. The first row in the right column reads, \u201cnegative 5 minus 3 means negative 5 take away 3.\u201d The next row down on the left reads, \u201cWe started with five negatives.\u201d Next to this are five red counters in a horizontal row with \u201cnegative\u201d five underneath. The next row reads, \u201cWe now add the neutrals needed to get three positives. Next to this in the right column are five red counters, a space, and three red counters. Under the three red counters are three blue counters. The next row down reads, \u201cWe remove the three positives. Next to this in the right column are the five red counters, a space, and three red counters. Under the three red counters are three blue counters with a circled arrow around them. The next row down reads, \u201cwe are left with eight negatives.\u201d Next to this in the right column in a horizontal row are five red counters, a space, followed by three red counters. Under the counters reads \u201c8 negatives\u201d. The last row in the left column reads, \u201cThe difference of negative 5 and 3 is negative 8.\u201d Next to this in the right column is the equation, \u201cnegative 5 minus 3equals negative eight.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\u22125 \u2212 3 means \u22125 take away 3.<\/td>\n<\/tr>\n<tr>\n<td>We start with 5 negatives.<\/td>\n<td><span id=\"eip-id1169754016089\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_032a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We now add the neutrals needed to get 3 positives.<\/td>\n<td><span id=\"eip-id1169754016106\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_032b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We remove the 3 positives.<\/td>\n<td><span id=\"eip-id1169754016122\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_032c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We are left with 8 negatives.<\/td>\n<td><span id=\"eip-id1169754361424\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_032d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The difference of \u22125 and 3 is \u22128.<\/td>\n<td>\u22125 \u2212 3 = \u22128<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655261587\">And now, the fourth case, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f95d94f6a2040d6be872ba37f3614152_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/>. We start with 5 positives. We need to take away 3 negatives, but there are no negatives to take away. So we add neutral pairs until we have 3 negatives to take away.<\/p>\n<table id=\"eip-id1169754361484\" style=\"width: 100%;\" summary=\"In this image, we have two columns and six rows. The first row in the right column reads, \u201c5 minus negative 3 means 5 take away negative 3.\u201d The next row down on the left reads, \u201cWe started with five positives.\u201d Next to this are five blue counters in a horizontal row. The next row reads, \u201cWe now add the needed neutral pairs. Next to this in the right column are five blue counters, a space, and three blue counters. Under the three blue counters are three red counters. The next row down reads, \u201cWe remove the 3 negatives. Next to this in the right column are the five blue counters, a space, and three blue counters. Under the three blue counters are three red counters with a circled arrow around them. The next row down reads, \u201cWe are left with eight positives.\u201d Next to this in the right column in a horizontal row are five blue counters, a space, followed by three blue counters. Under the counters reads \u201c8 positives\u201d. The last row in the left column reads, \u201cThe difference of 5 and negative 3 is 8.\u201d Next to this in the right column is the equation, \u201c5 minus negative 3equals eight.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>5 \u2212 (\u22123) means 5 take away \u22123.<\/td>\n<\/tr>\n<tr>\n<td>We start with 5 positives.<\/td>\n<td><span id=\"eip-id1169753968359\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_033a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We now add the needed neutrals pairs.<\/td>\n<td><span id=\"eip-id1169753968375\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_033b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We remove the 3 negatives.<\/td>\n<td><span id=\"eip-id1169753968392\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_033c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>We are left with 8 positives.<\/td>\n<td><span id=\"eip-id1169752181606\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_033d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The difference of 5 and \u22123 is 8.<\/td>\n<td>5 \u2212 (\u22123) = 8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\"><\/div>\n<div data-type=\"example\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654941998\" data-type=\"problem\">\n<p id=\"fs-id1170654942000\">Subtract:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b1d1c3eed482bbd31339b691e61cf6ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"51\" style=\"vertical-align: -1px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5b23456808ccbcc7fc4f81a2a5bac91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654943757\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1167829621734\">a)<\/p>\n<table id=\"eip-id1169749482384\" class=\"unnumbered unstyled\" summary=\"Part \u201ca\u201d has three red counters, a space, and one red counter in a horizontal row. Next to this on the right is the equation \u201cnegative 3 minus 1.\u201d The next line down on the left reads,\u201dTake 1 positive from the one added neutral pair\u201d. Next to this on the right is a blue counter circled with an arrow. Next to this reads \u201cnegative 4.\u201d Part \u201cb\u201d has three blue counters, a space, and one blue counter in a horizontal row. Next to this on the right is the equation \u201c3 minus negative 1.\u201d The next line down on the left reads, \u201cTake one negative from the one added neutral pair.\u201d Next to this on the right is a red counter circled with an arrow. Next to this reads \u201c4\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Take 1 positive from the one added neutral pair.<\/td>\n<td><span id=\"eip-id1169749482408\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_034a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><br \/>\n<span id=\"eip-id1169749482428\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_034b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-valign=\"top\">\u22123 \u2212 1<\/p>\n<p>\u22124<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167836289563\">b)<\/p>\n<table id=\"fs-id1167824767322\" class=\"unnumbered unstyled\" summary=\"Part \u201cb\u201d has three blue counters, a space, and one blue counter in a horizontal row. Next to this on the right is the equation \u201c3 minus negative 1.\u201d The next line down on the left reads, \u201cTake one negative from the one added neutral pair.\u201d Next to this on the right is a red counter circled with an arrow. Next to this reads \u201c4\u201d.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Take 1 negative from the one added neutral pair.<\/td>\n<td><span id=\"eip-id1169749482451\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_034c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><br \/>\n<span id=\"eip-id1169749482475\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_034d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-align=\"center\" data-valign=\"top\">3 \u2212 (\u22121)<\/p>\n<p>4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654924800\" data-type=\"problem\">\n<p id=\"fs-id1170654941927\">Subtract:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b6302a9df0c3462c19601388a3e35158_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-50136d0783a08d899f96aa2473b2eb31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654942432\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654942434\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24329a36a4e10288288979f77a565ca2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> b) 10<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654928213\" data-type=\"problem\">\n<p id=\"fs-id1170654928215\">Subtract:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c4fefb3a4e0684f1bdfa5cf519f4e71f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"52\" style=\"vertical-align: -1px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6cee7a76361bdd47d987d55f5c44a907_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655163425\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2981688f5b26fd15fa08c897afa741ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/> b) 11<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>Have you noticed that <em data-effect=\"italics\">subtraction of signed numbers can be done by adding the opposite<\/em>? In <a class=\"autogenerated-content\" href=\"#fs-id1170654941998\">Example 13<\/a>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b1d1c3eed482bbd31339b691e61cf6ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"51\" style=\"vertical-align: -1px;\" \/> is the same as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-75db80a14417df8d60e8ec6d03bb6f06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5b23456808ccbcc7fc4f81a2a5bac91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/> is the same as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0086024923882694cf8386d01386dde5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"39\" style=\"vertical-align: -2px;\" \/>. You will often see this idea, the subtraction property, written as follows:<\/p>\n<\/div>\n<div id=\"fs-id1170654903656\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Subtraction Property<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654903661\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2500da82de4ecc9460ada1e9df0cd6dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#98;&#61;&#97;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"equation\" data-label=\"\"><\/div>\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\">Subtracting a number is the same as adding its opposite.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654903717\">Look at these two examples.<\/p>\n<p><span id=\"fs-id1170654962580\" data-type=\"media\" data-alt=\"Two images are shown and labeled. The first image shows four gray spheres drawn next to two gray spheres, where the four are circled in red, with a red arrow leading away to the lower left. This drawing is labeled above as \u201c6 minus 4\u201d and below as \u201c2.\u201d The second image shows four gray spheres and four red spheres, drawn one above the other and circled in red, with a red arrow leading away to the lower left, and two gray spheres drawn to the side of the four gray spheres. This drawing is labeled above as \u201c6 plus, open parenthesis, negative 4, close parenthesis\u201d and below as \u201c2.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_035_img_new.jpg\" alt=\"Two images are shown and labeled. The first image shows four gray spheres drawn next to two gray spheres, where the four are circled in red, with a red arrow leading away to the lower left. This drawing is labeled above as \u201c6 minus 4\u201d and below as \u201c2.\u201d The second image shows four gray spheres and four red spheres, drawn one above the other and circled in red, with a red arrow leading away to the lower left, and two gray spheres drawn to the side of the four gray spheres. This drawing is labeled above as \u201c6 plus, open parenthesis, negative 4, close parenthesis\u201d and below as \u201c2.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-id1166424959329\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-912270a66466a24c6ced13bfec698783_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#45;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#105;&#118;&#101;&#115;&#32;&#116;&#104;&#101;&#32;&#115;&#97;&#109;&#101;&#32;&#97;&#110;&#115;&#119;&#101;&#114;&#32;&#97;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#54;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"306\" style=\"vertical-align: -5px;\" \/>.<\/div>\n<p id=\"fs-id1170654962732\">Of course, when you have a subtraction problem that has only positive numbers, like <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5998bc2d047a935f18b7f8b1bead811_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/>, you just do the subtraction. You already knew how to subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5998bc2d047a935f18b7f8b1bead811_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/> long ago. But <em data-effect=\"italics\">knowing<\/em> that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5998bc2d047a935f18b7f8b1bead811_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/> gives the same answer as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-599bd531dc22ff1a8c27da9267a11c3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/> helps when you are subtracting negative numbers. Make sure that you understand how <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5998bc2d047a935f18b7f8b1bead811_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-599bd531dc22ff1a8c27da9267a11c3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/> give the same results!<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655072283\" data-type=\"problem\">\n<p id=\"fs-id1170655072285\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-943e7adbeeef4dc05755b90ce9c5b2b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d2d8f34ecb522efb4afe43fc9df2a9b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f472d3b8c713d824953c1df6887c61f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#55;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6f5defab49e5e2d67bc530493611b02d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#55;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"88\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655072440\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-475\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nSubtract.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e7a1e0a41147f1e463d7ce1eb011a80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#49;&#51;&#45;&#56;&#92;&#92;&#32;&#53;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"47\" style=\"vertical-align: -11px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3da9730e179799cb0beaa5a0d53ebc02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#49;&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#53;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"74\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nSubtract.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fae5867191fe0ee96baab35b8c3e6269_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#45;&#49;&#55;&#45;&#57;&#92;&#92;&#32;&#45;&#50;&#57;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"61\" style=\"vertical-align: -11px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c93e71dd32c7f6d4a5c0eb6b9d6f4564_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#45;&#49;&#55;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#45;&#50;&#54;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"88\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655073536\" data-type=\"problem\">\n<p id=\"fs-id1170655073538\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a8d1db3b80dc35b7b60d36b8b0f75e81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40d01dceba05f67e282cc39583a98104_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"84\" style=\"vertical-align: -4px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1bfa277e8ad3a65864851171edca3c6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f575a5be244e8ae7126a8516466fdfe8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655073718\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655073721\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb9e52ddecc045b16dbf509b1c89f11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655073755\" data-type=\"problem\">\n<p id=\"fs-id1170655073757\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-44a108bd66b3875a41f393bf24c495f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"47\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b0576267e3a19ae5f4481d2457da7cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6798c1ffabed81d68e9b74dda10cf202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#52;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-90212d6f23a201afff9d58ad62bc3458_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655076908\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655076910\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-851674cf8d214f2dc493930ee7e6ee73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655075753\">Look at what happens when we subtract a negative.<\/p>\n<p><span id=\"fs-id1170655075756\" data-type=\"media\" data-alt=\"This figure is divided vertically into two halves. The left part of the figure contains the expression 8 minus negative 5, where negative 5 is in parentheses. The expression sits above a group of 8 blue counters next to a group of five blue counters in a row, with a space between the two groups. Underneath the group of five blue counters is a group of five red counters, which are circled. The circle has an arrow pointing away toward bottom left of the image, symbolizing subtraction. Below the counters is the number 13. The right part of the figure contains the expression 8 plus 5. The expression sits above a group of 8 blue counters next to a group of five blue counters in a row, with a space between the two groups. Underneath the counters is the number 13.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_01_03_036_img_new.jpg\" alt=\"This figure is divided vertically into two halves. The left part of the figure contains the expression 8 minus negative 5, where negative 5 is in parentheses. The expression sits above a group of 8 blue counters next to a group of five blue counters in a row, with a space between the two groups. Underneath the group of five blue counters is a group of five red counters, which are circled. The circle has an arrow pointing away toward bottom left of the image, symbolizing subtraction. Below the counters is the number 13. The right part of the figure contains the expression 8 plus 5. The expression sits above a group of 8 blue counters next to a group of five blue counters in a row, with a space between the two groups. Underneath the counters is the number 13.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-id1166424830896\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-df6027bd25c49d4e73342911fadc3a23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#105;&#118;&#101;&#115;&#32;&#116;&#104;&#101;&#32;&#115;&#97;&#109;&#101;&#32;&#97;&#110;&#115;&#119;&#101;&#114;&#32;&#97;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"309\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"fs-id1170655077076\"><em data-effect=\"italics\">Subtracting a negative number is like adding a positive!<\/em><\/p>\n<p id=\"fs-id1170655076379\">You will often see this written as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc2443b6ace73e73410ffb046fb33f86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#97;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p id=\"fs-id1170655077196\">Does that work for other numbers, too? Let\u2019s do the following example and see.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655080485\" data-type=\"exercise\">\n<div id=\"fs-id1170655080487\" data-type=\"problem\">\n<p id=\"fs-id1170655080489\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cd833b6f4419d5b777515813efd64512_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"75\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e7c6f979c580aadf3daff79575ff86d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: -2px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d54412b4ab04674969c56370bac23fe3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cc1c6c1bd765502fa4c0854c57316b51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"52\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655081441\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1166422863906\">a)<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b7da85f6efb2330b156368d40c7ddff9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#43;&#49;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#117;&#98;&#116;&#114;&#97;&#99;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"325\" style=\"vertical-align: -12px;\" \/><\/p>\n<p>b)<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f0c646bbf9f8515d8f62d447409817eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#55;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#117;&#98;&#116;&#114;&#97;&#99;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"336\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/div>\n<\/div>\n<table id=\"eip-660\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nSubtract.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-56c15ae1c1be12fc7d4900bdef03639e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#57;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#50;&#52;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"76\" style=\"vertical-align: -12px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-146c16e6e7c368c2e9778ec55d57ad6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#57;&#43;&#49;&#53;&#92;&#92;&#32;&#50;&#52;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"48\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nSubtract.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c0015ff3fd5ae7b90e0ae8144b5ea6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#45;&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#45;&#51;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"79\" style=\"vertical-align: -11px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cdd536e5f1a33721552b4fcfa51f9f6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#45;&#55;&#43;&#52;&#92;&#92;&#32;&#45;&#51;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"52\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655084099\" data-type=\"problem\">\n<p id=\"fs-id1170655084101\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b41f96b708c4cfc76755ff21ecdf264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"75\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9ba9ad1085e91165970318aae353eb86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#43;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -2px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-697ebdd76454722d1ddf2380fd4f5084_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-83130c7409bff8acd6967133d0dbc99e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"51\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655059484\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655061855\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23ae1c0b89342725f5c66b11294f8bcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655061672\" data-type=\"problem\">\n<p id=\"fs-id1170655061674\">Simplify:\u00a0a)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-922ae15bd0c3c3939f7ee8be178a9342_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"75\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cafcd1114e77b18b2c610269afde9c86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#43;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -2px;\" \/>\u00a0b)\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a36cddef0e4e628976a53a80f1a1ed36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d479c324aed4e88dab137c8dbb33eb80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"52\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655084120\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655089691\">a)\u00a023\u00a0b) 3<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655089698\">Let\u2019s look again at the results of subtracting the different combinations of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a46791a391dd60ec10b6fdd529ca8ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#44;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"39\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c8f99a729c7a37f3083f2bbfa4f2a1af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#44;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Subtraction of Integers<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1a75cd89bd8806c8ca97cfb75313482c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#32;&#116;&#97;&#107;&#101;&#32;&#97;&#119;&#97;&#121;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#32;&#116;&#97;&#107;&#101;&#32;&#97;&#119;&#97;&#121;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"83\" width=\"546\" style=\"vertical-align: -36px;\" \/><\/p>\n<p>When there would be enough counters of the colour to take away, subtract.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7335e3afa8b758bae7136b6a25e888d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#44;&#32;&#119;&#97;&#110;&#116;&#32;&#116;&#111;&#32;&#116;&#97;&#107;&#101;&#32;&#97;&#119;&#97;&#121;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#44;&#32;&#119;&#97;&#110;&#116;&#32;&#116;&#111;&#32;&#116;&#97;&#107;&#101;&#32;&#97;&#119;&#97;&#121;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#101;&#100;&#32;&#110;&#101;&#117;&#116;&#114;&#97;&#108;&#32;&#112;&#97;&#105;&#114;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#101;&#100;&#32;&#110;&#101;&#117;&#116;&#114;&#97;&#108;&#32;&#112;&#97;&#105;&#114;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"83\" width=\"686\" style=\"vertical-align: -36px;\" \/><\/p>\n<p>When there would be not enough counters of the colour to take away, add.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654962473\">What happens when there are more than three integers? We just use the order of operations as usual.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655084026\" data-type=\"problem\">\n<p id=\"fs-id1170655084028\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5bfb5f0bf8c4079f491cc6417a833b49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655083647\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-942\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5bfb5f0bf8c4079f491cc6417a833b49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify inside the parentheses first.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf972ec3e8e35cb44cc7225bbc3e7154_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"98\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract left to right.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6404bcd9f623bc44bff5de5a6d38ff60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655091566\" data-type=\"problem\">\n<p id=\"fs-id1170655091568\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-72b526e3b44869aac5ad9869f11658bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655090951\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655090953\">3<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655092082\" data-type=\"problem\">\n<p id=\"fs-id1170655092190\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8de914babf9524771eb499847a91ae1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"145\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655095593\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655095595\">13<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655091187\" class=\"media-2\" data-type=\"note\">\n<p id=\"fs-id1170655091191\">Access these online resources for additional instruction and practice with adding and subtracting integers. You will need to enable Java in your web browser to use the applications.<\/p>\n<ul id=\"fs-id1170655096461\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/11AddColorChip\">Add Colored Chip<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/11SubtrColorChp\">Subtract Colored Chip<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1170655097500\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Addition of Positive and Negative Integers<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49e6bf8e8d878820068288f8323fc0bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#53;&#43;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#57;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#52;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#111;&#116;&#104;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#44;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#111;&#116;&#104;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#44;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#109;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#109;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#45;&#53;&#43;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#57;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#52;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#102;&#102;&#101;&#114;&#101;&#110;&#116;&#32;&#115;&#105;&#103;&#110;&#115;&#44;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#102;&#102;&#101;&#114;&#101;&#110;&#116;&#32;&#115;&#105;&#103;&#110;&#115;&#44;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#111;&#114;&#101;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#111;&#114;&#101;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#109;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#109;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"237\" width=\"320\" style=\"vertical-align: -113px;\" \/><\/li>\n<li><strong data-effect=\"bold\">Property of Absolute Value<\/strong>: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b6cd98f4266f7f491a976c3270ec303d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#110;&#124;&#92;&#103;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> for all numbers. Absolute values are always greater than or equal to zero!<\/li>\n<li><strong data-effect=\"bold\">Subtraction of Integers<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc255b92a82dd3fd642e90f94d38cd9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#53;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#45;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#57;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#57;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#97;&#107;&#101;&#32;&#97;&#119;&#97;&#121;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#97;&#107;&#101;&#32;&#97;&#119;&#97;&#121;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#32;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#32;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#45;&#53;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#57;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#57;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#44;&#32;&#119;&#97;&#110;&#116;&#32;&#116;&#111;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#44;&#32;&#119;&#97;&#110;&#116;&#32;&#116;&#111;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#116;&#114;&#97;&#99;&#116;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#111;&#115;&#105;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#116;&#114;&#97;&#99;&#116;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#103;&#97;&#116;&#105;&#118;&#101;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#101;&#100;&#32;&#110;&#101;&#117;&#116;&#114;&#97;&#108;&#32;&#112;&#97;&#105;&#114;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#101;&#100;&#32;&#110;&#101;&#117;&#116;&#114;&#97;&#108;&#32;&#112;&#97;&#105;&#114;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"259\" width=\"372\" style=\"vertical-align: -124px;\" \/><\/li>\n<li><strong data-effect=\"bold\">Subtraction Property:<\/strong> Subtracting a number is the same as adding its opposite.<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1166424847478\">\n<dt>absolute value<\/dt>\n<dd id=\"fs-id1166424809754\">The absolute value of a number is its distance from 0 on the number line. The absolute value of a number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> is written as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b38a586dc76a31dfa818cbaca2da26f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#110;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"17\" style=\"vertical-align: -4px;\" \/>.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166424772590\">\n<dt>integers<\/dt>\n<dd id=\"fs-id1166424772595\">The whole numbers and their opposites are called the integers: &#8230;\u22123, \u22122, \u22121, 0, 1, 2, 3&#8230;<\/dd>\n<\/dl>\n<dl id=\"fs-id1166422694257\">\n<dt>opposite<\/dt>\n<dd id=\"fs-id1166422694262\">The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-236972f3904fc6d64d7fafb16c1fe32d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"22\" style=\"vertical-align: 0px;\" \/> means the opposite of the number. The notation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-236972f3904fc6d64d7fafb16c1fe32d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"22\" style=\"vertical-align: 0px;\" \/> is read \u201cthe opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.\u201d<\/dd>\n<\/dl>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Use Negatives and Opposites of Integers<\/h2>\n<p id=\"fs-id1166422643633\">In the following exercises, order each of the following pairs of numbers, using &lt; or &gt;.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca32393b1b5af7c55a95d89cf9d610f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24329a36a4e10288288979f77a565ca2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">2.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00c6d30c5f7439a21caf981437f64be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24329a36a4e10288288979f77a565ca2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655068522\">In the following exercises, find the opposite of each number.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">3.<br \/>\na) 2<br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">4.<br \/>\na) 9<br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655098081\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-285025f2d56e3a92c33647cc6b63ed5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-81ba43480a1f627fa2ce80f5f3febac4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-050892e2f608a145f4727a57803412bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f41c64ab84504e8c0180719d43c1b0ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655058115\">In the following exercises, evaluate.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-438fc4166d7b6c641b588cd014f176f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#32;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"21\" style=\"vertical-align: 0px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-854d67085d86215e6bf5bb19cab7cdef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: -1px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e0ab392273fb389c5b0a2dc7c16b750_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#61;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bba3d2a4d50f8da63250745b3ca7a29d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#32;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c2d8c1b14f80da9d4ec0547486e73764_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"50\" style=\"vertical-align: -1px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-04a4384db3f499b6da4ca848a5f1cd25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#45;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"64\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions with Absolute Value<\/h2>\n<p id=\"fs-id1171791388513\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">11.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf59ae45f118aabfd9dbcd53d172d47d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#51;&#50;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"46\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3a2c72b2b6c1d226f102034f66b93ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#48;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-58539f6df9ac445c3f81bf3233b2dfe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#49;&#54;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"24\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">12.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3a2c72b2b6c1d226f102034f66b93ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#48;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-471a5f02482d345154ecf450675c7575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#52;&#48;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"46\" style=\"vertical-align: -4px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5674cd93cb3661713dd0f000833e3896_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#50;&#50;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"24\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655355498\">In the following exercises, fill in &lt;, &gt;, or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8690b7efd237bfe32a6e92e3b699b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"4\" width=\"13\" style=\"vertical-align: 2px;\" \/> for each of the following pairs of numbers.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">13.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6a85299f81969ab364296f0c764c3640_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#54;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3f8a38c993190bb32bb9fed507e2a202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#45;&#51;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">14.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-29f80c98885a0c2b74a1fc1f5e6d86b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#53;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-545b962a2ddeb7bc62f8baebcaa3d5b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#45;&#53;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>___<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7db1529cce29849fd2d8a54b0fa1440_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#45;&#57;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655215530\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60683e15f2e6872938e897e32db83a14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#124;&#45;&#53;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c9ba6b48f3df41aa88eed72e7ca42952_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#45;&#57;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a0698468bdb5d50245a3670bd550c597_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#124;&#45;&#55;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8f56d528d31f38aceed08354e04c6f1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#124;&#45;&#53;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c025cb6f15bed386886aa63a6e7ab57a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#49;&#53;&#45;&#55;&#124;&#45;&#124;&#49;&#52;&#45;&#54;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"134\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b1375f94792dd48ba0f73c476b92186_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#49;&#55;&#45;&#56;&#124;&#45;&#124;&#49;&#51;&#45;&#52;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"134\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7817b31b5d79341c225c1a320bddd44a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#45;&#124;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6eacd919fb2a55f3816baaa47166208f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#45;&#124;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655213986\">In the following exercises, evaluate.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">23.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb4b22edd1e6e092da0c426a42a30e87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#112;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#112;&#61;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -5px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-982f5e1037038c9efce873e95250de53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#113;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#113;&#61;&#45;&#51;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;\">24.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-848f6caa1e573f2abd6fe43d766e262f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#97;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#61;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -5px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-279c803f160c9a81d94212b5d4fa4a58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#124;&#98;&#124;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;&#61;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Add Integers<\/h2>\n<p id=\"fs-id1166424899765\">In the following exercises, simplify each expression.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be75ab12ebe65505f17f14e762893b68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#49;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-16d39262279b35b20dcf99b7fbd2bba6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5347e78e1388867c78f84257e82214bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"84\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-288c931cb2f8a6e3d2228e3c03dc1af8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"84\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-070ef83fdc77ea566edbd4518f4c8c3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07755c6ff6fa8706c39591961a371300_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#55;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a41443d259e033deeaf23df0ae06bb8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#56;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"141\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">32. 6 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-77fba0b5692e50dbd90d83c9bcee73ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#56;&#43;&#50;&#55;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#49;&#50;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"177\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-918e4de58e3bd439d356305182c48d8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ba44c0b49b4c239fdec18f97acb9339_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Subtract Integers<\/h2>\n<p id=\"fs-id1166422656200\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0ce3eef413b98f0c4e456f424b41fff5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-717239a47bf9731de552df2098d9058f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02fcf1c91b817070cf9422bae84727ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"52\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fe94650169db3e7da0c964c14d664030_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"51\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c72327a70078ba8cd7a16901f1e23351_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97d39d65d187e21610bd1967de4cacf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">41.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f6e73a75721e926ae49e3abb7b13a4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#52;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2c343faa3d44761a7060b26e307afcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"84\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">42.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e3081f7139091f0f4177c8720d811cca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"57\" style=\"vertical-align: -1px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-acf31906464b025c7c1e4c67b8ed6766_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"84\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">43.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c731405c20b6850ef82dba43e0fc598b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"84\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c25edd25eccda1d968816153366e08f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#43;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;\">44.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ba3739ae38961e4faadab8a591ad110_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#54;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"84\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3309d8c2eff4737b32b60b60659ccdb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#54;&#43;&#51;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"57\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655166333\">In the following exercises, simplify each expression.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 135px;\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c927e3aec0bb8d8fbb7123a337953c86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9cb6ea6d34767c52b01f2e28474c035c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cff4290119b5d26303e75458d7fa0f10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;&#45;&#56;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"57\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2332dd811c053d486f32ace92af31450_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;&#45;&#54;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"57\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-edd48401ecbeced99097cef4de7a30e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#55;&#45;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"69\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68693f5d64bb166df3034487799f0eec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#57;&#45;&#52;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"70\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-33bba2ed0a23d94f22907adacee12146_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#51;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"106\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c297025c8959fdf9c69602141e7998b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"106\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4ff85d3fb26c79ccc9a42174b998e58a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49a167f3520739b34343d60162587522_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#56;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7998a7664747147b3bf95fc27b9d3ff9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#51;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-69ca09bc50962357748238310961ed6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#45;&#54;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"69\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c9845a10ae5cfef299283be86446d6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#45;&#52;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"83\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d81932804eec78eaf67276adde025b61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#45;&#56;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"83\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18410c1f656e226b5e7a70abf2d5196c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#52;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9c9f40df2aca63b40512242cccfc97b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e1d3f441ec8cd0340f54042a985dd6c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7693ebcc77a2316b7f5b785bd496073e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"126\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-99fbba525ec68f743df0b10075df01b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"143\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-94ed012da035759c28890103b5828fae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"143\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-93bff9c2baf995720da4030aee245f22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#091;&#49;&#48;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cb825f53789b236f424ae01b5da9a187_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;&#45;&#92;&#108;&#101;&#102;&#116;&#091;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#45;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c0c067cb4ca65625221f9489630fb8c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#51;&#45;&#52;&#46;&#51;&#45;&#55;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"111\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%;\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-02261c03380dc12d96a4a6a007723a1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#55;&#45;&#56;&#46;&#50;&#45;&#52;&#46;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"112\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fe86fd15a2527313d188aeee5053560b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#53;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#54;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\">70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-31fc1b427deb4de7912ecbe662bafd6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#54;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#55;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%; height: 204px;\">\n<tbody>\n<tr style=\"height: 174px;\">\n<td style=\"width: 50%; height: 174px;\">\n<p id=\"fs-id1170655189386\">71. <strong data-effect=\"bold\">Elevation<\/strong> The highest elevation in North America is Mount McKinley, Alaska, at 20,320 feet above sea level. The lowest elevation is Death Valley, California, at 282 feet below sea level.<\/p>\n<p id=\"fs-id1170655190223\">Use integers to write the elevation of:<\/p>\n<p id=\"fs-id1167270974732\">a) Mount McKinley.<br \/>\nb) Death Valley.<\/p>\n<\/td>\n<td style=\"width: 50%; height: 174px;\">\n<p id=\"fs-id1170655224555\">72.<strong data-effect=\"bold\"> Extreme temperatures<\/strong> The highest recorded temperature on Earth was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c04d88fcf64566a852d0a051ac00e70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/>\u00b0 Celsius, recorded in the Sahara Desert in 1922. The lowest recorded temperature was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b5f1c3a0e1ca514e4e63519e4d0c016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>\u00b0 below <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a5e437be25f29374d30f66cd46adf81c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>\u00b0 Celsius, recorded in Antarctica in 1983<\/p>\n<p id=\"fs-id1170655222289\">Use integers to write the:<\/p>\n<p>a) highest recorded temperature.<\/p>\n<p>b) lowest recorded temperature.<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">\n<p id=\"fs-id1170654920103\">73. <strong>Provincial budgets<\/strong> For 2019 the province of Quebec estimated it would have a budget surplus of &#36;5.6 million. That same year, Alberta estimated it would have a budget deficit of &#36;7.5 million.<\/p>\n<p id=\"fs-id1170655202258\">Use integers to write the budget of:<\/p>\n<p id=\"fs-id1167267728858\">a) Quebec.<br \/>\nb) Alberta.<\/p>\n<\/td>\n<td style=\"width: 50%; height: 15px;\">74. <strong>University enrolments<\/strong>The number of international students enrolled in Canadian postsecondary institutions has been on the rise for two decades, with their numbers increasing at a higher rate than that of Canadian students. Enrolments of international students rose by 24,315 from 2015 to 2017. Meanwhile, there was a slight decline in the number of Canadian students, by 912 for the same fiscal years.<\/p>\n<p>Use integers to write the change:<\/p>\n<p>a)\u00a0in International Student enrolment from Fall 2015 to Fall 2017.<\/p>\n<p>b)\u00a0in Canadian student enrolment from Fall 2015 to Fall 2017.<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">\n<div id=\"fs-id1170655195270\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<p>75. <strong style=\"text-align: initial;\" data-effect=\"bold\">Stock Market<\/strong> The week of September 15, 2008 was one of the most volatile weeks ever for the US stock market. The closing numbers of the Dow Jones Industrial Average each day were:<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655219716\" data-type=\"exercise\">\n<div id=\"fs-id1170655219718\" data-type=\"problem\">\n<table id=\"fs-id1170655204215\" class=\"unnumbered\" summary=\"This table has two rows and five columns. In the first row, the cells read left to right: \u201cMonday\u201d and \u201cnegative 504\u201d. In the second row, the cells read left to right: \u201cTuesday\u201d and \u201cpositive 142\u201d. In the third row, the cells read left to right \u201cWednesday\u201d and negative 449. In the fourth row, the cells read left to right: \u201cThursday\u201d and \u201cpositive 410\u201d. In the fifth and final row, the cells read left to right: \u201cFriday\u201d and \u201cpositive 369\u201d.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Monday<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3255fd0ee2b76a67eb41a876d2525128_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#48;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Tuesday<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e6a0d0d755c61a6fac9f059779568cf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#43;&#49;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Wednesday<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e726ac97cec34d36ec3e0662d5bccb9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Thursday<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c467679f8d92979af58b4aae3d13b5ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#43;&#52;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Friday<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f370b909766b13e71f2e93ffa2cb527b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#43;&#51;&#54;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654965472\">What was the overall change for the week? Was it positive or negative?<\/p>\n<\/div>\n<\/div>\n<\/td>\n<td style=\"width: 50%; height: 15px;\">\n<p id=\"fs-id1170655232454\">76. <strong data-effect=\"bold\">Stock Market<\/strong> During the week of June 22, 2009, the closing numbers of the Dow Jones Industrial Average each day were:<\/p>\n<table id=\"fs-id1170655226595\" class=\"unnumbered\" summary=\"This table has two rows and five columns. In the first row, the cells read left to right: \u201cMonday\u201d and \u201cnegative 201\u201d. In the second row, the cells read left to right: \u201cTuesday\u201d and \u201cnegative 16\u201d. In the third row, the cells read left to right \u201cWednesday\u201d and \u201cnegative 23\u201d. In the fourth row, the cells read left to right: \u201cThursday\u201d and \u201cpositive 172\u201d. In the fifth and final row, the cells read left to right: \u201cFriday\u201d and \u201cnegative 34\u201d.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Monday<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-46fb4a9da1c3ff2eaaa2237bd26445e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#48;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Tuesday<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-60f20f07f8f7c62331f2d8fe388a61b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Wednesday<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd97a36455222fbbcd36f22967b75707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Thursday<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2ab05f9f5253d3ec39bf521f8ae17647_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#43;&#49;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Friday<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2ba600f80daa65c3d14ce4938e8b8e29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170655348632\">What was the overall change for the week? Was it positive or negative?<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">77. Give an example of a negative number from your life experience.<\/td>\n<td style=\"width: 50%;\">78. What are the three uses of the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4413f371de6dab6d421b15637b968021_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#96;&#96;&#125;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#39;&#39;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"36\" style=\"vertical-align: 4px;\" \/> sign in algebra? Explain how they differ.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">79. Explain why the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca32393b1b5af7c55a95d89cf9d610f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> and 2 is negative, but the sum of 8 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> is positive.<\/td>\n<td style=\"width: 50%;\">80. Give an example from your life experience of adding two negative numbers.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<div data-type=\"glossary\">\n<table style=\"border-collapse: collapse; width: 100%; height: 237px;\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">1. a) &gt; b) &lt; c) &lt; d) &gt;<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">3. a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/>b) 6<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">5. 4<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">7. 15<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">9. a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9eae543c53f9301fa411ef541a1f4433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>b) 12<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">11. a) 32 b) 0 c) 16<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">13. a) &lt; b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8690b7efd237bfe32a6e92e3b699b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"4\" width=\"13\" style=\"vertical-align: 2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a46791a391dd60ec10b6fdd529ca8ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#44;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">17. 56<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">19. 0<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">21. 8<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">23. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e22bf27371ae8e82f2cf9857cc59c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-339284e2c7623b6c8fcd81c06e00da3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3f7920c1ff891a318599e38fe5bcd7ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">27. 32<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-851674cf8d214f2dc493930ee7e6ee73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">31. 108<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">33. 29<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">35. 6<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9672181aec15f8334b80ada7de4e4fc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">39. 12<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">41. a) 16 b) 16<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">43. a) 45 b) 45<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">45. 27<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf64b03624682b0a337c10836b136ca1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c8592fdae394223d029fcc21317133ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20a7f6e08b5f463553128808e5b96339_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">53. -99<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">59. 22<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0329d19b932005c996d83dbb9e09ffed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">63. 0<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">65. 6<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-65f7efd0fbf95ed3f6862d4633b9b62b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2981688f5b26fd15fa08c897afa741ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">71. a) 20,320\u00a0b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e062ba5bc70ca2bfa246981984d55d18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#56;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">73. a) &#36;5.6 million b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b639daa2e3da1c3138a62bb15a983679_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#36;&#55;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"44\" style=\"vertical-align: -1px;\" \/> million<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fce2979511e6a27a1bd61ca970c655b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">77. Answers may vary<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">79.\u00a0Answers may vary<\/td>\n<td style=\"width: 33.3333%; height: 16px;\"><\/td>\n<td style=\"width: 33.3333%; height: 16px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cAdd and Subtract Integers\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em><\/a> (OpenStax) by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n<\/div>\n","protected":false},"author":90,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-217","chapter","type-chapter","status-publish","hentry"],"part":20,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/217","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/217\/revisions"}],"predecessor-version":[{"id":218,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/217\/revisions\/218"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/20"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/217\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=217"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=217"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=217"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}