{"id":902,"date":"2020-08-12T14:17:59","date_gmt":"2020-08-12T18:17:59","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-equations-using-the-division-and-multiplication-properties-of-equality-2\/"},"modified":"2021-03-24T10:55:02","modified_gmt":"2021-03-24T14:55:02","slug":"solve-equations-using-the-division-and-multiplication-properties-of-equality-2","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-equations-using-the-division-and-multiplication-properties-of-equality-2\/","title":{"raw":"5.2 Solve Equations Using the Division and Multiplication Properties of Equality","rendered":"5.2 Solve Equations Using the Division and Multiplication Properties of Equality"},"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>Solve equations using the Division and Multiplication Properties of Equality<\/li>\n \t<li>Solve equations that need to be simplified<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div id=\"fs-id1699358\" class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Solve Equations Using the Division and Multiplication Properties of Equality<\/h1>\n<p id=\"fs-id1168344118142\">You may have noticed that all of the equations we have solved so far have been of the form \\(x+a=b\\) or \\(x-a=b\\). We were able to isolate the variable by adding or subtracting the constant term on the side of the equation with the variable. Now we will see how to solve equations that have a variable multiplied by a constant and so will require division to isolate the variable.<\/p>\n<p id=\"fs-id1168344149320\">Let\u2019s look at our puzzle again with the envelopes and counters in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_02_02_001\">(Figure 1)<\/a>.<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_02_02_001\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"215\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_02_02_001_img_new.jpg\" alt=\"Figure 1. Described in the previous paragraph.\" width=\"215\" height=\"163\" data-media-type=\"image\/jpeg\"> Figure .1[\/caption]\n\n<\/div>\n<p id=\"fs-id1168343008949\">In the illustration there are two identical envelopes that contain the same number of counters. Remember, the left side of the workspace must equal the right side, but the counters on the left side are \u201chidden\u201d in the envelopes. So how many counters are in each envelope?<\/p>\n<p id=\"fs-id1168344520671\">How do we determine the number? We have to separate the counters on the right side into two groups of the same size to correspond with the two envelopes on the left side. The 6 counters divided into 2 equal groups gives 3 counters in each group (since \\(6 \\div 2=3\\)).<\/p>\n<p id=\"fs-id1168344620823\">What equation models the situation shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_02_02_002\">(Figure 2)<\/a>? There are two envelopes, and each contains \\(x\\) counters. Together, the two envelopes must contain a total of 6 counters.<\/p>\n\n<div id=\"CNX_ElemAlg_Figure_02_02_002\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"211\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_02_002_img_new.jpg\" alt=\"Figure 2. Described in the previous paragraph.\" width=\"211\" height=\"193\" data-media-type=\"image\/jpeg\"> Figure .2[\/caption]\n\n<\/div>\n<table id=\"eip-id1169754148524\" class=\"unnumbered unstyled\" summary=\"This figure shows the steps for solving the equation 2x equals 6. The figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the equation 2 x equals 6. One line down on the left, the instructions say: \u201cIf we divide both sides of the equation by 2, as we did with the envelopes and counters, we get\u201d. To the right of this phrase is the same equation divided by 2 on both sides: 2 x over 2 equals 6 over 2, with divided by 2 written in red on both sides. Another line down to the right is the answer to the equation: x equals 3.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169751932125\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_02_003a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">If we divide both sides of the equation by 2, as we did with the envelopes and counters,<\/td>\n<td data-valign=\"top\"><span id=\"eip-id1169751896413\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_02_003b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">we get:<\/td>\n<td data-valign=\"top\"><span id=\"eip-id1169752207643\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_02_003c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344314572\">We found that each envelope contains 3 counters. Does this check? We know \\(2\\times3=6\\), so it works! Three counters in each of two envelopes does equal six!<\/p>\n<p id=\"fs-id1168342996883\">This example leads to the Division Property of Equality.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Division and Multiplication Properties of Equality<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166482132232\" data-type=\"note\">\n<p id=\"fs-id1470202\"><span class=\"no-emphasis\" data-type=\"term\">Division Property of Equality<\/span>: For all real numbers \\(a,b,c\\), and \\(c\\ne 0\\), if \\(a=b\\), then \\(\\frac{a}{c}=\\frac{b}{c}\\).<\/p>\n<p id=\"fs-id1166491226917\"><span class=\"no-emphasis\" data-type=\"term\">Multiplication Property of Equality<\/span>: For all real numbers \\(a,b,c\\), if \\(a=b\\), then \\(ac=bc\\).<\/p>\n\n<\/div>\n<p id=\"fs-id1166497355943\"><\/p>\n\n<\/div>\n<\/div>\nWhen you divide or multiply both sides of an equation by the same quantity, you still have equality.\n<p id=\"eip-742\">Let\u2019s review how these properties of equality can be applied in order to solve equations. Remember, the goal is to \u2018undo\u2019 the operation on the variable. In the example below the variable is multiplied by \\(4\\), so we will divide both sides by \\(4\\) to \u2018undo\u2019 the multiplication.<\/p>\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-id1166490872658\" data-type=\"problem\">\n<p id=\"fs-id2048614\">Solve: \\(4x=-28\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166491249070\" data-type=\"solution\">\n<p id=\"fs-id1166497438504\">We use the Division Property of Equality to divide both sides by \\(4\\).<\/p>\n\n<table id=\"eip-id1168469858566\" style=\"width: 100%;\" summary=\"The top line shows 4x equals negative 28. The next line says \u201cDivide both sides by 4 to undo the multiplication\u201d and shows 4x over a red 4 equals negative 28 over a red 4. The next step says \u201cSimplify\u201d and shows x equal negative seven. The next line says \u201cCheck your answer. Let x equal negative seven.\u201d and shows 4x equals negative 28. The next line shows four times negative seven may be equal to negative twenty-eight. The last line shows that negative twenty-eight equals negative twenty-eight with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468329066\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 4 to undo the multiplication.<\/td>\n<td><span id=\"eip-id1168469640578\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468462500\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let \\(x=-7\\).<\/td>\n<td><span id=\"eip-id1168468413048\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168468512983\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168467108975\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166482394409\">Since this is a true statement, \\(x=-7\\) is a solution to \\(4x=-28\\).<\/p>\n\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-id1166497294315\" data-type=\"problem\">\n<p id=\"fs-id1166491296845\">Solve: \\(3y=-48\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1856865\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1477744\"><em data-effect=\"italics\">y<\/em> = \u221216<\/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 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166494737904\" data-type=\"problem\">\n<p id=\"fs-id1166489098464\">Solve: \\(4z=-52\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1215549\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166491297204\"><em data-effect=\"italics\">z<\/em> = \u221213<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166484167968\">In the previous example, to \u2018undo\u2019 multiplication, we divided. How do you think we \u2018undo\u2019 division?<\/p>\n\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-id1270894\" data-type=\"problem\">\n\nSolve: \\(\\frac{\\phantom{\\rule{0.4em}{0ex}}a}{-7}=-42\\).\n\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166484059715\" data-type=\"solution\">\n<p id=\"fs-id1166484082960\">Here \\(a\\) is divided by \\(-7\\). We can multiply both sides by \\(-7\\) to isolate \\(a\\).<\/p>\n\n<table id=\"eip-id1168468288515\" class=\"unnumbered unstyled\" summary=\"The top shows a over negative 7 equals negative 42. The next line says \u201cMultiply both sides by negative 7\u201d and shows a red negative 7 times a over negative 7 equals a red negative 7 times negative 42. The next step shows negative 7a over negative 7 equals 294. The next line says \u201cSimplify\u201d and shows a equals 294. The next line says \u201cCheck your answer. Let a equal 294.\u201d and shows a over negative 7 equals negative 42. The next line shows 294 over negative seven may be equal to negative 42. The last line shows that negative 42 equals negative 42 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469493043\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by \\(-7\\).<\/td>\n<td><span id=\"eip-id1168469494749\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n<span id=\"eip-id1168469803678\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469473089\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let \\(a=294\\).<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469837940\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469546102\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168466076220\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/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 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1548304\" data-type=\"problem\">\n<p id=\"fs-id1166497442521\">Solve: \\(\\frac{\\phantom{\\rule{0.4em}{0ex}}b}{-6}=-24\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1788930\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1337807\"><em data-effect=\"italics\">b<\/em> = 144<\/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 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1944777\" data-type=\"problem\">\n<p id=\"fs-id1166497327451\">Solve: \\(\\frac{\\phantom{\\rule{0.4em}{0ex}}c}{-8}=-16\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1388172\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1166482443506\"><em data-effect=\"italics\">c<\/em> = 128<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1484125\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1481497\" data-type=\"exercise\">\n<div id=\"fs-id1548304\" data-type=\"problem\">\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-id829704\" data-type=\"problem\">\n\nSolve: \\(-r=2\\).\n\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1430634\" data-type=\"solution\">\n<p id=\"fs-id1166484083423\">Remember \\(-r\\) is equivalent to \\(-1r\\).<\/p>\n\n<table id=\"eip-id1168469604717\" class=\"unnumbered unstyled\" summary=\"The first line says negative r equals 2. The next line says \u201cRewrite negative r as negative 1 times r\u201d and shows negative 1r equals 2. The next line says \u201cDivide both sides by negative 1\u201d and shows negative 1r over red negative 1 equals 2 over red negative 1. The next line says to divide and shows r equals negative 2. The next line says to check and shows negative r equals 2. It then says to substitute r equals negative 2 and shows negative red negative 2 followed by an equal sign with a question mark and then a 2. The last line says to simplify and shows that 2 equals 2, followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168468268336\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Rewrite \\(-r\\) as \\(-1r\\).<\/td>\n<td><span id=\"eip-id1168468466657\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Divide both sides by \\(-1\\).<\/td>\n<td><span id=\"eip-id1168467108096\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168468270294\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<\/td>\n<td><span id=\"eip-id1168467243838\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute \\(r=-2\\)<\/td>\n<td><span id=\"eip-id1168468391711\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468572983\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166486741570\">We see that there are two other ways to solve \\(-r=2\\).<\/p>\n<p id=\"fs-id1499512\">We could multiply both sides by \\(-1\\).<\/p>\n<p id=\"fs-id1525632\">We could take the opposite of both sides.<\/p>\n\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-id1446828\" data-type=\"problem\">\n<p id=\"fs-id1555639\">Solve: \\(-k=8\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166497278036\" data-type=\"solution\"><details><summary>Show answer<\/summary><em data-effect=\"italics\">k<\/em> = \u22128\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-id1581535\" data-type=\"problem\">\n<p id=\"fs-id1525856\">Solve: \\(-g=3\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1537458\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1479537\"><em data-effect=\"italics\">g<\/em> = \u22123<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1439000\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1870080\" data-type=\"exercise\">\n<div id=\"fs-id1446828\" data-type=\"problem\">\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-id1166492357106\" data-type=\"problem\">\n\nSolve: \\(\\frac{2}{3}\\phantom{\\rule{0.1em}{0ex}}x=18\\).\n\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1481662\" data-type=\"solution\">\n<p id=\"fs-id1358253\">Since the product of a number and its reciprocal is \\(1\\), our strategy will be to isolate \\(x\\) by multiplying by the reciprocal of \\(\\frac{2}{3}\\).<\/p>\n\n<table id=\"eip-id1168468646645\" style=\"width: 100%;\" summary=\"The first line shows two-thirds x equals 18. The next line says \u201cMultiply by the reciprocal of two-thirds\u201d and shows a red 3 over 2 times two-thirds x equals a red 3 over 2 times 18. The next line says \u201cReciprocals multiply to 1\u201d and shows 1x equals 3 over 2 times 18 over 1. The next line says \u201cMultiply\u201d and shows x equals 27. The next line says \u201cCheck your answer. Let x equal 27 and shows two-thirds x equals 18. The next line shows two-thirds times 27 may equal 18. The last line shows that 18 equals 18 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467105901\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply by the reciprocal of \\(\\frac{2}{3}\\).<\/td>\n<td><span id=\"eip-id1168468293976\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Reciprocals multiply to one.<\/td>\n<td><span id=\"eip-id1168468384024\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168467173189\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let \\(x=27\\)<\/td>\n<td><span id=\"eip-id1168468609890\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168468389040\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467391760\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166492770982\">Notice that we could have divided both sides of the equation \\(\\frac{2}{3}\\phantom{\\rule{0.1em}{0ex}}x=18\\) by \\(\\frac{2}{3}\\) to isolate \\(x\\). While this would work, multiplying by the reciprocal requires fewer steps.<\/p>\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-id1517745\" data-type=\"problem\">\n<p id=\"fs-id1486445\">Solve: \\(\\frac{2}{5}\\phantom{\\rule{0.1em}{0ex}}n=14\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1297414\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1331214\"><em data-effect=\"italics\">n<\/em> = 35<\/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-id1448929\" data-type=\"problem\">\n<p id=\"fs-id1701200\">Solve: \\(\\frac{5}{6}\\phantom{\\rule{0.1em}{0ex}}y=15\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166492694533\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1360078\"><em data-effect=\"italics\">y<\/em> = 18<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Solve Equations That Need to be Simplified<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166490756880\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1166491281668\">Many equations start out more complicated than the ones we\u2019ve just solved. First, we need to simplify both sides of the equation as much as possible<\/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 id=\"fs-id1166497362242\" data-type=\"problem\">\n<p id=\"fs-id1438546\">Solve: \\(8x+9x-5x=-3+15\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166497454283\" data-type=\"solution\">\n<p id=\"fs-id1166488297763\">Start by combining like terms to simplify each side.<\/p>\n\n<table id=\"eip-id1168466098204\" class=\"unnumbered unstyled\" style=\"height: 220px;\" summary=\"The first line says \u201cGiven\u201d and shows 8x plus 9x minus 5x equals negative 3 plus 15. The next line says \u201cCombine like terms\u201d and shows 12x equals 12. The next line says \u201cDivide both sides by 12 to isolate x\u201d and shows 12x over a red 12 equals 12 over a red 12. The next line says \u201cSimplify\u201d and shows x equals 1. The next line says \u201cCheck your answer. Let x equal 1.\u201d and shows 8x plus 9x minus 5x equals negative 3 plus 15. The next line shows 8 times 1 plus 9 times 1 minus 5 times 1 may equal negative 3 plus 15. The next line shows 8 plus 9 minus 5 may equal negative 3 plus 15. The last line shows 12 equals 12 with a check mark.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 21px;\">\n<td style=\"height: 21px; width: 304.85px;\"><\/td>\n<td style=\"height: 21px; width: 305.15px;\"><span id=\"eip-id1168469437898\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 304.85px;\">Combine like terms.<\/td>\n<td style=\"height: 20px; width: 305.15px;\"><span id=\"eip-id1168469741226\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 42px;\">\n<td style=\"height: 42px; width: 304.85px;\">Divide both sides by 12 to isolate x.<\/td>\n<td style=\"height: 42px; width: 305.15px;\"><span id=\"eip-id1168466783373\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 304.85px;\">Simplify.<\/td>\n<td style=\"height: 19px; width: 305.15px;\"><span id=\"eip-id1168466094134\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 304.85px;\">Check your answer. Let \\(x=1\\)<\/td>\n<td style=\"height: 16px; width: 305.15px;\"><span id=\"eip-id1168469420018\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168469804185\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168469873842\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168469846182\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/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 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166497359409\">Solve: \\(7x+6x-4x=-8+26\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166491249036\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166488294380\"><em data-effect=\"italics\">x<\/em> = 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 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1194556\" data-type=\"problem\">\n\nSolve: \\(11n-3n-6n=7-17\\).\n\n<\/div>\n<div id=\"fs-id1287170\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id882539\"><em data-effect=\"italics\">n<\/em> = \u22125<\/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 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166494771813\" data-type=\"problem\">\n<p id=\"fs-id1482144\">Solve: \\(11-20=17y-8y-6y\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1166498049545\" data-type=\"solution\">\n<p id=\"fs-id1166491231401\">Simplify each side by combining like terms.<\/p>\n\n<table id=\"eip-id1168466111452\" class=\"unnumbered unstyled\" summary=\"The first line shows 11 minus 20 equals 17y minus 8y minus 6y. The next line says \u201cSimplify each side\u201d and shows negative 9 equals 3y. The next line says \u201cDivide both sides by 3 to isolate y\u201d and shows negative 9 over a red 3 equals 3y over a red 3. The next line shows negative 3 equals y. The next line says \u201cCheck your answer. Let y equal negative 3.\u201d and shows 11 minus 20 equals 17y minus 8y minus 6y. The next line shows that 11 minus 20 may equal 17 times negative 3 minus 8 times negative 3 minus six times negative 3. The next line shows that 11 minus 20 may equal negative 51 plus 24 plus 18. The last line shows negative 9 equals negative 9 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466275525\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify each side.<\/td>\n<td><span id=\"eip-id1168469468521\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 3 to isolate y.<\/td>\n<td><span id=\"eip-id1168469486411\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466644732\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let \\(y=-3\\)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469490886\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469876517\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168466014831\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168466804792\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166497359226\">Notice that the variable ended up on the right side of the equal sign when we solved the equation. You may prefer to take one more step to write the solution with the variable on the left side of the equal sign.<\/p>\n\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 data-type=\"problem\">\n<p id=\"fs-id1483059\">Solve: \\(18-27=15c-9c-3c\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166490789685\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166483071329\"><em data-effect=\"italics\">c<\/em> = \u22123<\/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-id1504324\" data-type=\"problem\">\n\nSolve: \\(18-22=12x-x-4x\\).\n\n<\/div>\n<div id=\"fs-id1166494585908\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1487028\">\\(x=-\\frac{4}{7}\\)<\/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-id1166490920541\" data-type=\"problem\">\n<p id=\"fs-id1337655\">Solve: \\(-3\\left(n-2\\right)-6=21\\).<\/p>\n<strong>Solution<\/strong>\n\n<\/div>\n<div id=\"fs-id1797147\" data-type=\"solution\">\n<p id=\"fs-id1166497370385\">Remember\u2014always simplify each side first.<\/p>\n\n<table id=\"eip-id1168468278405\" style=\"width: 100%;\" summary=\"The first line shows negative 3 times parentheses n minus 2 minus 6 equals 21. The next line says \u201cDistribute\u201d and shows negative 3n plus 6 minus 6 equals 21. The next line says \u201cSimplify\u201d and shows negative 3n equals 21. The next line says \u201cDivide both sides by negative 3 to isolate n\u201d and shows negative 3n over a red negative 3 equals 21 over a red negative 3. The next line says \u201cDivide\u201d and shows n equals negative 7. The next line says \u201cCheck your answer. Let n equal negative 7.\u201d and shows negative 3 times parentheses n minus 2 minus 6 equals 21. The next line shows negative 3 times parentheses negative 7 minus 2 minus 6 may equal 21. The next line shows negative 3 times negative 9 minus 6 may equal 21. The next line shows 27 minus 6 may equal 21. The last line shows 21 equals 21 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466025611\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168466335764\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466131101\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by -3 to isolate n.<\/td>\n<td><span id=\"eip-id1168469668348\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n<span id=\"eip-id1168469628218\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let \\(n=-7\\).<\/td>\n<td><span id=\"eip-id1168465999518\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168469429073\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168469838157\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168469767068\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span id=\"eip-id1168466203164\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1314922\" data-type=\"exercise\">\n<div id=\"fs-id1166494585908\" data-type=\"solution\">\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-id1534798\" data-type=\"problem\">\n<p id=\"fs-id1166483061910\">Solve: \\(-4\\left(n-2\\right)-8=24\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1789275\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1536515\"><em data-effect=\"italics\">n<\/em> = \u22126<\/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-id1454602\" data-type=\"problem\">\n<p id=\"fs-id1430740\">Solve: \\(-6\\left(n-2\\right)-12=30\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1407319\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1166490739724\"><em data-effect=\"italics\">n<\/em> = \u22125<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166483693638\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1534798\" data-type=\"problem\">\n<ul>\n \t<li><strong>Division and Multiplication Properties of Equality<\/strong>\n<ul id=\"eip-id1170323851320\">\n \t<li><strong>Division Property of Equality:<\/strong> For all real numbers <em data-effect=\"italics\">a, b, c,<\/em> and \\(c\\ne 0\\), if \\(a=b\\), then \\(ac=bc\\).<\/li>\n \t<li><strong>Multiplication Property of Equality:<\/strong> For all real numbers <em data-effect=\"italics\">a, b, c,<\/em> if \\(a=b\\), then \\(ac=bc\\).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166479094172\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1407319\" data-type=\"solution\">\n<h1 id=\"fs-id1166490739724\">Practice Makes Perfect<\/h1>\n<div id=\"fs-id1230757\" class=\"practice-perfect\" data-depth=\"2\">\n<h2 id=\"fs-id1166492789212\">Solve Equations Using the Division and Multiplication Properties of Equality<\/h2>\n<p id=\"eip-743\">In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.<\/p>\n\n<table style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td>1. \\(7p=63\\)<\/td>\n<td>2. \\(8x=32\\)<\/td>\n<\/tr>\n<tr>\n<td>3. \\(-9x=-27\\)<\/td>\n<td>4. \\(-5c=55\\)<\/td>\n<\/tr>\n<tr>\n<td>5. \\(-72=12y\\)<\/td>\n<td>6. \\(-90=6y\\)<\/td>\n<\/tr>\n<tr>\n<td>7. \\(-8m=-56\\)<\/td>\n<td>8. \\(-16p=-64\\)<\/td>\n<\/tr>\n<tr>\n<td>9. \\(0.75a=11.25\\)<\/td>\n<td>10. \\(0.25z=3.25\\)<\/td>\n<\/tr>\n<tr>\n<td>11. \\(4x=0\\)<\/td>\n<td>12. \\(-3x=0\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166478989761\">In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.<\/p>\n\n<table style=\"height: 126px; width: 100%;\" border=\"0\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">13. \\(\\frac{z}{2}=14\\)<\/td>\n<td style=\"height: 18px; width: 444.717px;\">14. \\(\\frac{x}{4}=15\\)<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">15. \\(\\frac{\\phantom{\\rule{0.4em}{0ex}}c}{-3}=-12\\)<\/td>\n<td style=\"height: 18px; width: 444.717px;\">16. \\(-20=\\frac{\\phantom{\\rule{0.4em}{0ex}}q}{-5}\\)<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">17. \\(\\frac{q}{6}=-8\\)<\/td>\n<td style=\"height: 18px; width: 444.717px;\">18. \\(\\frac{y}{9}=-6\\)<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">19. \\(-4=\\frac{p}{-20}\\)<\/td>\n<td style=\"height: 18px; width: 444.717px;\">20. \\(\\frac{m}{-12}=5\\)<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">21. \\(\\frac{3}{5}\\phantom{\\rule{0.1em}{0ex}}r=15\\)<\/td>\n<td style=\"height: 18px; width: 444.717px;\">22. \\(\\frac{2}{3}\\phantom{\\rule{0.1em}{0ex}}y=18\\)<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">23. \\(24=-\\frac{3}{4}\\phantom{\\rule{0.1em}{0ex}}x\\)<\/td>\n<td style=\"height: 18px; width: 444.717px;\">24. \\(-\\frac{5}{8}\\phantom{\\rule{0.1em}{0ex}}w=40\\)<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">25. \\(-\\frac{1}{3}\\phantom{\\rule{0.1em}{0ex}}q=-\\frac{5}{6}\\)<\/td>\n<td style=\"height: 18px; width: 444.717px;\">26. \\(-\\frac{2}{5}=\\frac{1}{10}\\phantom{\\rule{0.1em}{0ex}}a\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Solve Equations That Need to be Simplified<\/h2>\n<p id=\"eip-78\">In the following exercises, solve the equation.<\/p>\n\n<table border=\"0\">\n<tbody>\n<tr>\n<td>27. \\(6y-3y+12y=-43+28\\)<\/td>\n<td>28. \\(8a+3a-6a=-17+27\\)<\/td>\n<\/tr>\n<tr>\n<td>29. \\(-5m+7m-8m=-6+36\\)<\/td>\n<td>30. \\(-9x-9x+2x=50-2\\)<\/td>\n<\/tr>\n<tr>\n<td>31. \\(-18-7=5t-9t-6t\\)<\/td>\n<td>32. \\(100-16=4p-10p-p\\)<\/td>\n<\/tr>\n<tr>\n<td>33. \\(\\frac{5}{12}\\phantom{\\rule{0.1em}{0ex}}q+\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}q=25-3\\)<\/td>\n<td>34. \\(\\frac{7}{8}\\phantom{\\rule{0.1em}{0ex}}n-\\frac{3}{4}\\phantom{\\rule{0.1em}{0ex}}n=9+2\\)<\/td>\n<\/tr>\n<tr>\n<td>35. \\(0.05p-0.01p=2+0.24\\)<\/td>\n<td>36. \\(0.25d+0.10d=6-0.75\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1166475101787\" class=\"writing\" data-depth=\"2\">\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table border=\"0\">\n<tbody>\n<tr>\n<td><strong data-effect=\"bold\">37. Teaching<\/strong> Connie\u2019s kindergarten class has \\(24\\) children. She wants them to get into \\(4\\) equal groups. Find the number of children in each group, \\(g\\), by solving the equation \\(4g=24\\).<\/td>\n<td><strong data-effect=\"bold\">38. Balloons<\/strong> Ramona bought \\(18\\) balloons for a party. She wants to make \\(3\\) equal bunches. Find the number of balloons in each bunch, \\(b\\), by solving the equation \\(3b=18\\).<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">39. Unit price<\/strong> Nishant paid \\(\\text{\\$12.96}\\) for a pack of \\(12\\) juice bottles. Find the price of each bottle, \\(b\\), by solving the equation \\(12b=12.96\\).<\/td>\n<td><strong data-effect=\"bold\">40. Ticket price<\/strong> Daria paid \\(\\text{\\$36.25}\\) for \\(5\\) children\u2019s tickets at the ice skating rink. Find the price of each ticket, \\(p\\), by solving the equation \\(5p=36.25\\).<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">41. Fabric<\/strong> The drill team used \\(14\\) yards of fabric to make flags for one-third of the members. Find how much fabric, \\(f\\), they would need to make flags for the whole team by solving the equation \\(\\frac{1}{3}\\phantom{\\rule{0.1em}{0ex}}f=14\\).<\/td>\n<td><strong data-effect=\"bold\">42. Fuel economy<\/strong> Tania\u2019s SUV gets half as many miles per gallon (mpg) as her husband\u2019s hybrid car. The SUV gets \\(\\text{18 mpg}\\). Find the miles per gallons, \\(m\\), of the hybrid car, by solving the equation \\(\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}m=18\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1166475099267\" class=\"writing\" data-depth=\"2\">\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table border=\"0\">\n<tbody>\n<tr>\n<td>43. Emiliano thinks \\(x=40\\) is the solution to the equation \\(\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}x=80\\). Explain why he is wrong.<\/td>\n<td>44. Frida started to solve the equation \\(-3x=36\\) by adding \\(3\\) to both sides. Explain why Frida\u2019s method will result in the correct solution.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 33%;\">1. 9<\/td>\n<td style=\"width: 33%;\">3. 3<\/td>\n<td style=\"width: 33%;\">5. \u22126<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">7. 7<\/td>\n<td style=\"width: 33%;\">9. 15<\/td>\n<td style=\"width: 33%;\">11. 0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">13. 28<\/td>\n<td style=\"width: 33%;\">15. 36<\/td>\n<td style=\"width: 33%;\">17. \u221248<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">19. 80<\/td>\n<td style=\"width: 33%;\">21. 25<\/td>\n<td style=\"width: 33%;\">23. \u221232<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">25. 5\/2<\/td>\n<td style=\"width: 33%;\">27. y = \u22121<\/td>\n<td style=\"width: 33%;\">29. m = \u22125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">31. \\(t=\\frac{5}{2}\\)<\/td>\n<td style=\"width: 33%;\">33. q = 24<\/td>\n<td style=\"width: 33%;\">35. p = 56<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">37. 6 children<\/td>\n<td style=\"width: 33%;\">39. \\$1.08<\/td>\n<td style=\"width: 33%;\">41. 42 yards<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">43. Answer will vary.<\/td>\n<td style=\"width: 33%;\"><\/td>\n<td style=\"width: 33%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cSolve Equations Using the Division and Multiplication Properties of Equality\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, 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.","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>Solve equations using the Division and Multiplication Properties of Equality<\/li>\n<li>Solve equations that need to be simplified<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div id=\"fs-id1699358\" class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Solve Equations Using the Division and Multiplication Properties of Equality<\/h1>\n<p id=\"fs-id1168344118142\">You may have noticed that all of the equations we have solved so far have been of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9502a527c5531ce10fb0c7ccc3be8f5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -2px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2623e885804358807eb0a4192f3b80c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"73\" style=\"vertical-align: 0px;\" \/>. We were able to isolate the variable by adding or subtracting the constant term on the side of the equation with the variable. Now we will see how to solve equations that have a variable multiplied by a constant and so will require division to isolate the variable.<\/p>\n<p id=\"fs-id1168344149320\">Let\u2019s look at our puzzle again with the envelopes and counters in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_02_02_001\">(Figure 1)<\/a>.<\/p>\n<div id=\"CNX_ElemAlg_Figure_02_02_001\" class=\"bc-figure figure\">\n<figure style=\"width: 215px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_02_02_001_img_new.jpg\" alt=\"Figure 1. Described in the previous paragraph.\" width=\"215\" height=\"163\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .1<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1168343008949\">In the illustration there are two identical envelopes that contain the same number of counters. Remember, the left side of the workspace must equal the right side, but the counters on the left side are \u201chidden\u201d in the envelopes. So how many counters are in each envelope?<\/p>\n<p id=\"fs-id1168344520671\">How do we determine the number? We have to separate the counters on the right side into two groups of the same size to correspond with the two envelopes on the left side. The 6 counters divided into 2 equal groups gives 3 counters in each group (since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d2e51ba9e45cf09b01000eea45a85ccf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#32;&#92;&#100;&#105;&#118;&#32;&#50;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"72\" style=\"vertical-align: -1px;\" \/>).<\/p>\n<p id=\"fs-id1168344620823\">What equation models the situation shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_02_02_002\">(Figure 2)<\/a>? There are two envelopes, and each contains <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;\" \/> counters. Together, the two envelopes must contain a total of 6 counters.<\/p>\n<div id=\"CNX_ElemAlg_Figure_02_02_002\" class=\"bc-figure figure\">\n<figure style=\"width: 211px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_02_002_img_new.jpg\" alt=\"Figure 2. Described in the previous paragraph.\" width=\"211\" height=\"193\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .2<\/figcaption><\/figure>\n<\/div>\n<table id=\"eip-id1169754148524\" class=\"unnumbered unstyled\" summary=\"This figure shows the steps for solving the equation 2x equals 6. The figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the equation 2 x equals 6. One line down on the left, the instructions say: \u201cIf we divide both sides of the equation by 2, as we did with the envelopes and counters, we get\u201d. To the right of this phrase is the same equation divided by 2 on both sides: 2 x over 2 equals 6 over 2, with divided by 2 written in red on both sides. Another line down to the right is the answer to the equation: x equals 3.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169751932125\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_02_003a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">If we divide both sides of the equation by 2, as we did with the envelopes and counters,<\/td>\n<td data-valign=\"top\"><span id=\"eip-id1169751896413\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_02_003b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">we get:<\/td>\n<td data-valign=\"top\"><span id=\"eip-id1169752207643\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_02_003c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168344314572\">We found that each envelope contains 3 counters. Does this check? We know <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e567c30e44c81c908cec3997266b038f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#116;&#105;&#109;&#101;&#115;&#51;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"72\" style=\"vertical-align: 0px;\" \/>, so it works! Three counters in each of two envelopes does equal six!<\/p>\n<p id=\"fs-id1168342996883\">This example leads to the Division Property of Equality.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Division and Multiplication Properties of Equality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166482132232\" data-type=\"note\">\n<p id=\"fs-id1470202\"><span class=\"no-emphasis\" data-type=\"term\">Division Property of Equality<\/span>: For all real numbers <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-58797fcd980ddcdad97f6b6f5260b5fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;&#44;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c540d76c127a15e856d4b530b506abdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf6c07a7e498d7cea19e596a04da4884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"41\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p id=\"fs-id1166491226917\"><span class=\"no-emphasis\" data-type=\"term\">Multiplication Property of Equality<\/span>: For all real numbers <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-58797fcd980ddcdad97f6b6f5260b5fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;&#44;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/>, if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3d764a87e80d22e0bd1d3004f678266a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#99;&#61;&#98;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<p id=\"fs-id1166497355943\">\n<\/div>\n<\/div>\n<p>When you divide or multiply both sides of an equation by the same quantity, you still have equality.<\/p>\n<p id=\"eip-742\">Let\u2019s review how these properties of equality can be applied in order to solve equations. Remember, the goal is to \u2018undo\u2019 the operation on the variable. In the example below the variable is multiplied by <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;\" \/>, so we will divide both sides by <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;\" \/> to \u2018undo\u2019 the multiplication.<\/p>\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-id1166490872658\" data-type=\"problem\">\n<p id=\"fs-id2048614\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-108bad35cde07fc7476f67450c04b2bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#61;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"75\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166491249070\" data-type=\"solution\">\n<p id=\"fs-id1166497438504\">We use the Division Property of Equality to divide both sides by <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;\" \/>.<\/p>\n<table id=\"eip-id1168469858566\" style=\"width: 100%;\" summary=\"The top line shows 4x equals negative 28. The next line says \u201cDivide both sides by 4 to undo the multiplication\u201d and shows 4x over a red 4 equals negative 28 over a red 4. The next step says \u201cSimplify\u201d and shows x equal negative seven. The next line says \u201cCheck your answer. Let x equal negative seven.\u201d and shows 4x equals negative 28. The next line shows four times negative seven may be equal to negative twenty-eight. The last line shows that negative twenty-eight equals negative twenty-eight with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468329066\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 4 to undo the multiplication.<\/td>\n<td><span id=\"eip-id1168469640578\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468462500\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48ebdcda08cf6d53794431f5b209e4f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168468413048\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168468512983\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168467108975\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_001_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166482394409\">Since this is a true statement, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48ebdcda08cf6d53794431f5b209e4f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: 0px;\" \/> is a solution to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-108bad35cde07fc7476f67450c04b2bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#61;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"75\" 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 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166497294315\" data-type=\"problem\">\n<p id=\"fs-id1166491296845\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3286b9cb5cc8d0544ca9982e5dcba695_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#121;&#61;&#45;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1856865\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1477744\"><em data-effect=\"italics\">y<\/em> = \u221216<\/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 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166494737904\" data-type=\"problem\">\n<p id=\"fs-id1166489098464\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-80099edad5c5b9c5753269495f5f4895_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#122;&#61;&#45;&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"73\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1215549\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166491297204\"><em data-effect=\"italics\">z<\/em> = \u221213<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166484167968\">In the previous example, to \u2018undo\u2019 multiplication, we divided. How do you think we \u2018undo\u2019 division?<\/p>\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-id1270894\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d136340ee4de11cd426e9677801124e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#125;&#123;&#45;&#55;&#125;&#61;&#45;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166484059715\" data-type=\"solution\">\n<p id=\"fs-id1166484082960\">Here <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;\" \/> is divided by <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;\" \/>. We can multiply both sides by <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;\" \/> to isolate <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;\" \/>.<\/p>\n<table id=\"eip-id1168468288515\" class=\"unnumbered unstyled\" summary=\"The top shows a over negative 7 equals negative 42. The next line says \u201cMultiply both sides by negative 7\u201d and shows a red negative 7 times a over negative 7 equals a red negative 7 times negative 42. The next step shows negative 7a over negative 7 equals 294. The next line says \u201cSimplify\u201d and shows a equals 294. The next line says \u201cCheck your answer. Let a equal 294.\u201d and shows a over negative 7 equals negative 42. The next line shows 294 over negative seven may be equal to negative 42. The last line shows that negative 42 equals negative 42 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469493043\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by <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;\" \/>.<\/td>\n<td><span id=\"eip-id1168469494749\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\n<span id=\"eip-id1168469803678\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168469473089\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c9be6eba432e28e73926e7e124d5949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#50;&#57;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"60\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469837940\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469546102\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168466076220\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_003_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/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 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1548304\" data-type=\"problem\">\n<p id=\"fs-id1166497442521\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-015baa983930a5df270b493ad3f05e91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;&#125;&#123;&#45;&#54;&#125;&#61;&#45;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1788930\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1337807\"><em data-effect=\"italics\">b<\/em> = 144<\/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 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1944777\" data-type=\"problem\">\n<p id=\"fs-id1166497327451\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2d2e3e648ba71e18e1b8cfd96b6f6a59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#125;&#123;&#45;&#56;&#125;&#61;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1388172\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166482443506\"><em data-effect=\"italics\">c<\/em> = 128<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1484125\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1481497\" data-type=\"exercise\">\n<div id=\"fs-id1548304\" data-type=\"problem\">\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-id829704\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5d6589f35289a8134d5dd85597903ecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#114;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"53\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1430634\" data-type=\"solution\">\n<p id=\"fs-id1166484083423\">Remember <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7f7ff69172baab999af3b13c7620635_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"21\" style=\"vertical-align: 0px;\" \/> is equivalent to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-279084ff2070ad2333e6f59d99e909a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<table id=\"eip-id1168469604717\" class=\"unnumbered unstyled\" summary=\"The first line says negative r equals 2. The next line says \u201cRewrite negative r as negative 1 times r\u201d and shows negative 1r equals 2. The next line says \u201cDivide both sides by negative 1\u201d and shows negative 1r over red negative 1 equals 2 over red negative 1. The next line says to divide and shows r equals negative 2. The next line says to check and shows negative r equals 2. It then says to substitute r equals negative 2 and shows negative red negative 2 followed by an equal sign with a question mark and then a 2. The last line says to simplify and shows that 2 equals 2, followed by a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168468268336\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Rewrite <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7f7ff69172baab999af3b13c7620635_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"21\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-279084ff2070ad2333e6f59d99e909a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><span id=\"eip-id1168468466657\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Divide both sides by <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;\" \/>.<\/td>\n<td><span id=\"eip-id1168467108096\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><span id=\"eip-id1168468270294\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check.<\/td>\n<td><span id=\"eip-id1168467243838\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d75e3ba8e2d2ab0451520a284f02520e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"54\" style=\"vertical-align: 0px;\" \/><\/td>\n<td><span id=\"eip-id1168468391711\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168468572983\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_015_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166486741570\">We see that there are two other ways to solve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5d6589f35289a8134d5dd85597903ecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#114;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"53\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id1499512\">We could multiply both sides by <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;\" \/>.<\/p>\n<p id=\"fs-id1525632\">We could take the opposite of both sides.<\/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 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1446828\" data-type=\"problem\">\n<p id=\"fs-id1555639\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c566c8d7074106ba2a760f8633bc4c54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#107;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166497278036\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><em data-effect=\"italics\">k<\/em> = \u22128<\/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-id1581535\" data-type=\"problem\">\n<p id=\"fs-id1525856\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1c88dde0d72f6d977f5c6c0abf9e9ecf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#103;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1537458\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1479537\"><em data-effect=\"italics\">g<\/em> = \u22123<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1439000\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1870080\" data-type=\"exercise\">\n<div id=\"fs-id1446828\" data-type=\"problem\">\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-id1166492357106\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ffdc0eb947b9d91e144c97675450b05f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1481662\" data-type=\"solution\">\n<p id=\"fs-id1358253\">Since the product of a number and its reciprocal is <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;\" \/>, our strategy will be to isolate <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;\" \/> by multiplying by the reciprocal of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e89c4f69688b0dd6ab75a55841059de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<table id=\"eip-id1168468646645\" style=\"width: 100%;\" summary=\"The first line shows two-thirds x equals 18. The next line says \u201cMultiply by the reciprocal of two-thirds\u201d and shows a red 3 over 2 times two-thirds x equals a red 3 over 2 times 18. The next line says \u201cReciprocals multiply to 1\u201d and shows 1x equals 3 over 2 times 18 over 1. The next line says \u201cMultiply\u201d and shows x equals 27. The next line says \u201cCheck your answer. Let x equal 27 and shows two-thirds x equals 18. The next line shows two-thirds times 27 may equal 18. The last line shows that 18 equals 18 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467105901\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply by the reciprocal of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e89c4f69688b0dd6ab75a55841059de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><span id=\"eip-id1168468293976\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Reciprocals multiply to one.<\/td>\n<td><span id=\"eip-id1168468384024\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168467173189\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24305e69c5fe2397471cc81e60d451f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: 0px;\" \/><\/td>\n<td><span id=\"eip-id1168468609890\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168468389040\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467391760\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_007_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166492770982\">Notice that we could have divided both sides of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ffdc0eb947b9d91e144c97675450b05f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e89c4f69688b0dd6ab75a55841059de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> to isolate <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;\" \/>. While this would work, multiplying by the reciprocal requires fewer steps.<\/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-id1517745\" data-type=\"problem\">\n<p id=\"fs-id1486445\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-33c3420d4a13df43679c052dc52aa8f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"63\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1297414\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1331214\"><em data-effect=\"italics\">n<\/em> = 35<\/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-id1448929\" data-type=\"problem\">\n<p id=\"fs-id1701200\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0d43fef04fc4c091905aa3849a4128ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"61\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166492694533\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1360078\"><em data-effect=\"italics\">y<\/em> = 18<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Solve Equations That Need to be Simplified<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166490756880\" class=\"bc-section section\" data-depth=\"1\">\n<p id=\"fs-id1166491281668\">Many equations start out more complicated than the ones we\u2019ve just solved. First, we need to simplify both sides of the equation as much as possible<\/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 id=\"fs-id1166497362242\" data-type=\"problem\">\n<p id=\"fs-id1438546\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1674920b8594fc5f2cf3c8e951714fae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#43;&#57;&#120;&#45;&#53;&#120;&#61;&#45;&#51;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"185\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166497454283\" data-type=\"solution\">\n<p id=\"fs-id1166488297763\">Start by combining like terms to simplify each side.<\/p>\n<table id=\"eip-id1168466098204\" class=\"unnumbered unstyled\" style=\"height: 220px;\" summary=\"The first line says \u201cGiven\u201d and shows 8x plus 9x minus 5x equals negative 3 plus 15. The next line says \u201cCombine like terms\u201d and shows 12x equals 12. The next line says \u201cDivide both sides by 12 to isolate x\u201d and shows 12x over a red 12 equals 12 over a red 12. The next line says \u201cSimplify\u201d and shows x equals 1. The next line says \u201cCheck your answer. Let x equal 1.\u201d and shows 8x plus 9x minus 5x equals negative 3 plus 15. The next line shows 8 times 1 plus 9 times 1 minus 5 times 1 may equal negative 3 plus 15. The next line shows 8 plus 9 minus 5 may equal negative 3 plus 15. The last line shows 12 equals 12 with a check mark.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 21px;\">\n<td style=\"height: 21px; width: 304.85px;\"><\/td>\n<td style=\"height: 21px; width: 305.15px;\"><span id=\"eip-id1168469437898\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 304.85px;\">Combine like terms.<\/td>\n<td style=\"height: 20px; width: 305.15px;\"><span id=\"eip-id1168469741226\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 42px;\">\n<td style=\"height: 42px; width: 304.85px;\">Divide both sides by 12 to isolate x.<\/td>\n<td style=\"height: 42px; width: 305.15px;\"><span id=\"eip-id1168466783373\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 304.85px;\">Simplify.<\/td>\n<td style=\"height: 19px; width: 305.15px;\"><span id=\"eip-id1168466094134\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 304.85px;\">Check your answer. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"height: 16px; width: 305.15px;\"><span id=\"eip-id1168469420018\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168469804185\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168469873842\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168469846182\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_009_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/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 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1166497359409\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8075c9a437dc22aff87eb207e9f32893_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#54;&#120;&#45;&#52;&#120;&#61;&#45;&#56;&#43;&#50;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"186\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166491249036\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166488294380\"><em data-effect=\"italics\">x<\/em> = 2<\/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-id1194556\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e9a3d6939878dd03c247fd10e34e8fa4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#110;&#45;&#51;&#110;&#45;&#54;&#110;&#61;&#55;&#45;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"182\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1287170\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id882539\"><em data-effect=\"italics\">n<\/em> = \u22125<\/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 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166494771813\" data-type=\"problem\">\n<p id=\"fs-id1482144\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d8bc2d63e55a1210c90521f3e48f9ad3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#45;&#50;&#48;&#61;&#49;&#55;&#121;&#45;&#56;&#121;&#45;&#54;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"186\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1166498049545\" data-type=\"solution\">\n<p id=\"fs-id1166491231401\">Simplify each side by combining like terms.<\/p>\n<table id=\"eip-id1168466111452\" class=\"unnumbered unstyled\" summary=\"The first line shows 11 minus 20 equals 17y minus 8y minus 6y. The next line says \u201cSimplify each side\u201d and shows negative 9 equals 3y. The next line says \u201cDivide both sides by 3 to isolate y\u201d and shows negative 9 over a red 3 equals 3y over a red 3. The next line shows negative 3 equals y. The next line says \u201cCheck your answer. Let y equal negative 3.\u201d and shows 11 minus 20 equals 17y minus 8y minus 6y. The next line shows that 11 minus 20 may equal 17 times negative 3 minus 8 times negative 3 minus six times negative 3. The next line shows that 11 minus 20 may equal negative 51 plus 24 plus 18. The last line shows negative 9 equals negative 9 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466275525\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify each side.<\/td>\n<td><span id=\"eip-id1168469468521\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 3 to isolate y.<\/td>\n<td><span id=\"eip-id1168469486411\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466644732\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-91f9ec631e44f3d108457c2f8adad27c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469490886\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469876517\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168466014831\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168466804792\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_011_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166497359226\">Notice that the variable ended up on the right side of the equal sign when we solved the equation. You may prefer to take one more step to write the solution with the variable on the left side of the equal sign.<\/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 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1483059\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a18413b5b92e128223903f7a9f08436b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#45;&#50;&#55;&#61;&#49;&#53;&#99;&#45;&#57;&#99;&#45;&#51;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"182\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166490789685\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166483071329\"><em data-effect=\"italics\">c<\/em> = \u22123<\/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-id1504324\" data-type=\"problem\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0eba2519559bbfc29c95acd676e73c81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#45;&#50;&#50;&#61;&#49;&#50;&#120;&#45;&#120;&#45;&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"180\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166494585908\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1487028\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3933fdb93c73f99fe9e37629fde4e546_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/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-id1166490920541\" data-type=\"problem\">\n<p id=\"fs-id1337655\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ea7c6145476dfee03d77830f7a2dfc8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#54;&#61;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1797147\" data-type=\"solution\">\n<p id=\"fs-id1166497370385\">Remember\u2014always simplify each side first.<\/p>\n<table id=\"eip-id1168468278405\" style=\"width: 100%;\" summary=\"The first line shows negative 3 times parentheses n minus 2 minus 6 equals 21. The next line says \u201cDistribute\u201d and shows negative 3n plus 6 minus 6 equals 21. The next line says \u201cSimplify\u201d and shows negative 3n equals 21. The next line says \u201cDivide both sides by negative 3 to isolate n\u201d and shows negative 3n over a red negative 3 equals 21 over a red negative 3. The next line says \u201cDivide\u201d and shows n equals negative 7. The next line says \u201cCheck your answer. Let n equal negative 7.\u201d and shows negative 3 times parentheses n minus 2 minus 6 equals 21. The next line shows negative 3 times parentheses negative 7 minus 2 minus 6 may equal 21. The next line shows negative 3 times negative 9 minus 6 may equal 21. The next line shows 27 minus 6 may equal 21. The last line shows 21 equals 21 with a check mark.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466025611\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-01-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168466335764\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-02-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168466131101\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-03-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by -3 to isolate n.<\/td>\n<td><span id=\"eip-id1168469668348\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-04-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\n<span id=\"eip-id1168469628218\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-05-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Check your answer. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-af059e4eec6ee001eed199259ef71744_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168465999518\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-06-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168469429073\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-07-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168469838157\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-08-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168469767068\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-09-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span id=\"eip-id1168466203164\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_08_02_013_img-10-1.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1314922\" data-type=\"exercise\">\n<div id=\"fs-id1166494585908\" data-type=\"solution\">\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-id1534798\" data-type=\"problem\">\n<p id=\"fs-id1166483061910\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0548dca6c67dcdac4c08b37a355e59d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#56;&#61;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1789275\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1536515\"><em data-effect=\"italics\">n<\/em> = \u22126<\/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-id1454602\" data-type=\"problem\">\n<p id=\"fs-id1430740\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01298d9f9b5ecfaf4470db2c87320fc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#50;&#61;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"161\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1407319\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1166490739724\"><em data-effect=\"italics\">n<\/em> = \u22125<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166483693638\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1534798\" data-type=\"problem\">\n<ul>\n<li><strong>Division and Multiplication Properties of Equality<\/strong>\n<ul id=\"eip-id1170323851320\">\n<li><strong>Division Property of Equality:<\/strong> For all real numbers <em data-effect=\"italics\">a, b, c,<\/em> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c540d76c127a15e856d4b530b506abdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3d764a87e80d22e0bd1d3004f678266a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#99;&#61;&#98;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li><strong>Multiplication Property of Equality:<\/strong> For all real numbers <em data-effect=\"italics\">a, b, c,<\/em> if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3d764a87e80d22e0bd1d3004f678266a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#99;&#61;&#98;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166479094172\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1407319\" data-type=\"solution\">\n<h1 id=\"fs-id1166490739724\">Practice Makes Perfect<\/h1>\n<div id=\"fs-id1230757\" class=\"practice-perfect\" data-depth=\"2\">\n<h2 id=\"fs-id1166492789212\">Solve Equations Using the Division and Multiplication Properties of Equality<\/h2>\n<p id=\"eip-743\">In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.<\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e8d4d5b1166fab2bc73dd369f5138d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#112;&#61;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8eb2515045487cd6c0c9f8c8e61b3f7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#61;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"60\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8bd71bf157eda9821a256a8c33d5d5a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#120;&#61;&#45;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b25ef3c1d02ab3193628f066db72f062_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#99;&#61;&#53;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2785b51cb2df510b5eeb414061ade896_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#50;&#61;&#49;&#50;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"81\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c51f498881f62f5665f37a9b9035c12c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#48;&#61;&#54;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-21c65c5d7b8a6ada7ba968beee4a431f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#109;&#61;&#45;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"93\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-67148e6b38922e64094f58d6d72659c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#112;&#61;&#45;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7bb4ed7cc2e7cd45391c173fb37cb4a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#55;&#53;&#97;&#61;&#49;&#49;&#46;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"105\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c823f9570a093f2bb00ae838e500474f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#50;&#53;&#122;&#61;&#51;&#46;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"95\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26cdc3e83065a7a85d7db920372ef277_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48957f697df3048d237c2077f769f8be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166478989761\">In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.<\/p>\n<table style=\"height: 126px; width: 100%;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3b184262272853fcc1aeb63795b42bc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#122;&#125;&#123;&#50;&#125;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"50\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"height: 18px; width: 444.717px;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-47cefab9b4558245329099798ec2c19f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#52;&#125;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"50\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3222d8f930b49bf1621b7bc45369570a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#125;&#123;&#45;&#51;&#125;&#61;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"height: 18px; width: 444.717px;\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-94c1d72b6dfc2695695841c628b319f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#48;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#113;&#125;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"74\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4305db42d3a7a99b679851c06f29a7c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#113;&#125;&#123;&#54;&#125;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"55\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"height: 18px; width: 444.717px;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23a9a14596038ac63e0b90ea093bceca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#57;&#125;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-706222dd1951652cfeb182fabdf0c894_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#112;&#125;&#123;&#45;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"height: 18px; width: 444.717px;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2605dc16997db649da2da628ccdf73df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#109;&#125;&#123;&#45;&#49;&#50;&#125;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-966b4e5c961976e3fad7c3ce5b1bdfd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#114;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"height: 18px; width: 444.717px;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e0ffca48ddaf2d40fcc73852b1582c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-752afe0fa6d4e843786fa629458d2502_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"78\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"height: 18px; width: 444.717px;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-db881dbf31a5f5f389f5430069be0e22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#119;&#61;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"80\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 442.867px;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-af0aadeb649b43d22cb91de5acbcbb62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#113;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"80\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"height: 18px; width: 444.717px;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f82d5bd701a3ceab4508dc652751ac5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"76\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Solve Equations That Need to be Simplified<\/h2>\n<p id=\"eip-78\">In the following exercises, solve the equation.<\/p>\n<table>\n<tbody>\n<tr>\n<td>27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-692caa38e923b415858d7a0b388dd481_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#121;&#45;&#51;&#121;&#43;&#49;&#50;&#121;&#61;&#45;&#52;&#51;&#43;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"202\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-385680dfe0e46e173cc27ec14a907f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#97;&#43;&#51;&#97;&#45;&#54;&#97;&#61;&#45;&#49;&#55;&#43;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"193\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e28643999bb99c758f4c5d2763aa5bfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#109;&#43;&#55;&#109;&#45;&#56;&#109;&#61;&#45;&#54;&#43;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"215\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17f02ebb9f5d45979274418c4325f1ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#120;&#45;&#57;&#120;&#43;&#50;&#120;&#61;&#53;&#48;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"184\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-37c53c131aa779ee535140e0755078e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;&#45;&#55;&#61;&#53;&#116;&#45;&#57;&#116;&#45;&#54;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"174\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-adabfc2999e016e28fdb72c615cae99e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;&#45;&#49;&#54;&#61;&#52;&#112;&#45;&#49;&#48;&#112;&#45;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"185\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-146e9f6796f47c77cb6ccd5c74ff0159_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#113;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#113;&#61;&#50;&#53;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"141\" style=\"vertical-align: -7px;\" \/><\/td>\n<td>34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e30d2fa012711fd808a36b1c2056a567_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#61;&#57;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-692edcc9c547c16726d41b3e0f298588_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#53;&#112;&#45;&#48;&#46;&#48;&#49;&#112;&#61;&#50;&#43;&#48;&#46;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"189\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b619f87372597ecc39b0a89441f5c81d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#50;&#53;&#100;&#43;&#48;&#46;&#49;&#48;&#100;&#61;&#54;&#45;&#48;&#46;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"188\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1166475101787\" class=\"writing\" data-depth=\"2\">\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table>\n<tbody>\n<tr>\n<td><strong data-effect=\"bold\">37. Teaching<\/strong> Connie\u2019s kindergarten class has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> children. She wants them to get into <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;\" \/> equal groups. Find the number of children in each group, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d208fd391fa57c168dc0f151de829fee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>, by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9ef2b8c56b25f6be0d715d40cc951826_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#103;&#61;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"60\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><strong data-effect=\"bold\">38. Balloons<\/strong> Ramona bought <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> balloons for a party. She wants to make <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;\" \/> equal bunches. Find the number of balloons in each bunch, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c07e91154d0d7c0fdbed0cb7f2ac7fb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#98;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"58\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">39. Unit price<\/strong> Nishant paid <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-58f1afc89a245a9fbf00dacaaa9786a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#49;&#50;&#46;&#57;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"50\" style=\"vertical-align: -1px;\" \/> for a pack of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> juice bottles. Find the price of each bottle, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ffe651ff13302402e0a522ee015d29a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#98;&#61;&#49;&#50;&#46;&#57;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"89\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><strong data-effect=\"bold\">40. Ticket price<\/strong> Daria paid <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bba4d27a068ce8fbbee4a3739311fb89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#92;&#36;&#51;&#54;&#46;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -1px;\" \/> for <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;\" \/> children\u2019s tickets at the ice skating rink. Find the price of each ticket, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/>, by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-05586dcc01783047b33f73e179075313_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#112;&#61;&#51;&#54;&#46;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"81\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">41. Fabric<\/strong> The drill team used <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;\" \/> yards of fabric to make flags for one-third of the members. Find how much fabric, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\" \/>, they would need to make flags for the whole team by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3be1717e537a138f9f8fe4ce90b9b508_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"63\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><strong data-effect=\"bold\">42. Fuel economy<\/strong> Tania\u2019s SUV gets half as many miles per gallon (mpg) as her husband\u2019s hybrid car. The SUV gets <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-44ccdaa61ed0aca7dcb2091d3efea59d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#32;&#109;&#112;&#103;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"57\" style=\"vertical-align: -4px;\" \/>. Find the miles per gallons, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/>, of the hybrid car, by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2aace6e69c3749a36e9f7472acd3b4f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#109;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1166475099267\" class=\"writing\" data-depth=\"2\">\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table>\n<tbody>\n<tr>\n<td>43. Emiliano thinks <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6738eb95899c39ce7f075218f4e46de4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/> is the solution to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1529e7978eace7bede791c193abe6ad6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#56;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/>. Explain why he is wrong.<\/td>\n<td>44. Frida started to solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f21dbc915ea63df63b7dd3fc23a81ce2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#120;&#61;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" style=\"vertical-align: 0px;\" \/> by adding <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;\" \/> to both sides. Explain why Frida\u2019s method will result in the correct solution.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 33%;\">1. 9<\/td>\n<td style=\"width: 33%;\">3. 3<\/td>\n<td style=\"width: 33%;\">5. \u22126<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">7. 7<\/td>\n<td style=\"width: 33%;\">9. 15<\/td>\n<td style=\"width: 33%;\">11. 0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">13. 28<\/td>\n<td style=\"width: 33%;\">15. 36<\/td>\n<td style=\"width: 33%;\">17. \u221248<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">19. 80<\/td>\n<td style=\"width: 33%;\">21. 25<\/td>\n<td style=\"width: 33%;\">23. \u221232<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">25. 5\/2<\/td>\n<td style=\"width: 33%;\">27. y = \u22121<\/td>\n<td style=\"width: 33%;\">29. m = \u22125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b568ce83ce815ec169dbf9495a18bbaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33%;\">33. q = 24<\/td>\n<td style=\"width: 33%;\">35. p = 56<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">37. 6 children<\/td>\n<td style=\"width: 33%;\">39. &#36;1.08<\/td>\n<td style=\"width: 33%;\">41. 42 yards<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33%;\">43. Answer will vary.<\/td>\n<td style=\"width: 33%;\"><\/td>\n<td style=\"width: 33%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cSolve Equations Using the Division and Multiplication Properties of Equality\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, 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","protected":false},"author":90,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-902","chapter","type-chapter","status-publish","hentry"],"part":767,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/902","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\/902\/revisions"}],"predecessor-version":[{"id":903,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/902\/revisions\/903"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/767"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/902\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=902"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=902"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=902"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=902"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}