{"id":368,"date":"2020-08-12T14:25:20","date_gmt":"2020-08-12T14:25:20","guid":{"rendered":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/solve-equations-using-the-subtraction-and-addition-properties-of-equality\/"},"modified":"2021-09-09T15:24:00","modified_gmt":"2021-09-09T15:24:00","slug":"solve-equations-using-the-subtraction-and-addition-properties-of-equality","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/solve-equations-using-the-subtraction-and-addition-properties-of-equality\/","title":{"raw":"2.1 Solve  Linear Equations","rendered":"2.1 Solve  Linear Equations"},"content":{"raw":"[latexpage]\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section it is expected that you will be able to:\r\n<ul>\r\n \t<li>Verify a solution of an equation<\/li>\r\n \t<li>Solve equations using the Subtraction and Addition Properties of Equality<\/li>\r\n \t<li>Solve equations using the Division and Multiplication Properties of Equality<\/li>\r\n \t<li>Solve an equation with variables and constants on both sides<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1>Verify a Solution of an Equation<\/h1>\r\n<p id=\"fs-id1168345252532\">Solving an equation is like discovering the answer to a puzzle. The purpose in solving an equation is to find the value or values of the variable that make each side of the equation the same \u2013 so that we end up with a true statement. Any value of the variable that makes the equation true is called a solution to the equation. It is the answer to the puzzle!<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Solution of an equation<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA <span data-type=\"term\"><strong>solution of an equation<\/strong><\/span> is a value of a variable that makes a true statement when substituted into the equation.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Determine whether a number is a solution to an equation<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1169750930815\" class=\"stepwise\" type=\"1\">\r\n \t<li>Substitute the number in for the variable in the equation.<\/li>\r\n \t<li>Simplify the expressions on both sides of the equation.<\/li>\r\n \t<li>Determine whether the resulting equation is true (the left side is equal to the right side).\r\n<ul id=\"fs-id1168345511300\" data-bullet-style=\"bullet\">\r\n \t<li>If it is true, the number is a solution.<\/li>\r\n \t<li>If it is not true, the number is not a solution.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345256645\" data-type=\"problem\">\r\n<p id=\"fs-id1168345302932\">Determine whether \\(x=-3\\) is a solution of \\(4x+5=-7\\).<\/p>\r\n<strong>Solution<\/strong>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345196931\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1168341917025\">Since a solution to an equation is a value of the variable that makes the equation true, begin by substituting the value of the solution for the variable.<\/p>\r\n\r\n<table id=\"eip-id1169740536663\" style=\"height: 94px; width: 100%;\" summary=\"This figure shows the steps for determining whether x equals 3\/2 is a solution to the algebraic equation 4 x minus 2 equals 2 x plus 1. The figure has two columns, with written instructions on the left and math on the right. At the top of the image in the right column is the equation 4 x minus 2 equals 2 x plus 1. One line down, the instructions on the left say \u201cSubstitute 3\/2 for x\u201d, with 3\/2 written in red. To the right of this instruction is the initial equation with 3\/2 substituted for x: 4, open parenthesis, 3\/2 written in red, close parenthesis, minus 3 may equal 2, open parenthesis, 3\/2 written in red, close parenthesis, plus 1. The next line down, the instructions on the left say \u201cMultiply\u201d. To the right of \u201cMultiply\u201d is the equation with the terms having been multiplied: 6 minus 2 may equal 3 plus 1. One more line down, the instructions on the left say: \u201cSubtract.\u201d To the right of \u201cSubtract\u201d is 4 equals 4, with a check mark next to it.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 35px;\">\r\n<td style=\"height: 35px; width: 50%;\">Substitute \\(x=-3\\) for x<\/td>\r\n<td style=\"height: 35px; width: 50%;\">\\(4(-3)+5=-7\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 26px;\">\r\n<td style=\"height: 26px; width: 50%;\">Multiply.<\/td>\r\n<td style=\"height: 26px; width: 50%;\">\u00a0\\(-12+5=-7\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"height: 17px; width: 50%;\">Simplify.<\/td>\r\n<td style=\"height: 17px; width: 50%;\" data-align=\"center\">\\(-7=-7\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1168345366859\">Since \\(x=-3\\) results in a true statement (-7 is in fact equal to -7), -3 is a solution to the equation \\(4x+5=-7\\).<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345399266\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345544118\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345250738\" data-type=\"problem\">\r\n<p id=\"fs-id1168345397818\">Is \\(y=2\\) a solution of \\(9y-2=6\\)?<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345211810\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345442278\">no<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1167836335358\">There are many types of equations. In this chapter we will focus on solving <span data-type=\"term\">linear equations.<\/span><\/p>\r\n\r\n<div id=\"fs-id1167836515647\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Linear Equation<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA <strong data-effect=\"bold\">linear equation<\/strong> is a first degree equation in one variable that can be written\u00a0as:\r\n<div id=\"fs-id1167829644900\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(ax+b=0\\), where <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em> are real numbers and \\(a\\ne 0,\\)<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1 data-type=\"title\">Solve Equations Using the Subtraction and Addition Properties of Equality<\/h1>\r\n<div id=\"CNX_ElemAlg_Figure_02_01_003_img_new\" class=\"bc-figure figure\">\r\n<p id=\"fs-id1168345374564\">Let us review all the properties that will help us to solve equations algebraically. The first one is the <strong>Subtraction Property of Equality<\/strong>.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Subtraction Property of Equality<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1168345346971\">For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>,<\/p>\r\n\r\n<div id=\"fs-id1168345360391\" class=\"unnumbered\" style=\"text-align: center;\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{ccccc}\\text{If}\\hfill &amp; &amp; \\hfill a&amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; &amp; \\hfill a-c&amp; =\\hfill &amp; b-c\\hfill \\end{array}\\)<\/div>\r\n<p id=\"fs-id1168345328049\">When you subtract the same quantity from both sides of an equation, you still have equality.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168345328756\">Let\u2019s see how to use this property to solve an equation. Remember, the goal is to isolate the variable on one side of the equation. And we check our solutions by substituting the value into the equation to make sure we have a true statement.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345197461\" data-type=\"problem\">\r\n<p id=\"fs-id1168345559741\">Solve: \\(y+37=-13.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345510395\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div class=\"hanging-indent\" data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1168345287978\">To get <em data-effect=\"italics\">y<\/em> by itself, we will undo the addition of 37 by using the Subtraction Property of Equality.<\/p>\r\n\r\n<table id=\"eip-id1169752878128\" style=\"height: 109px; width: 100%;\" summary=\"This 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 x plus 3 equals 8. One line down on the left, the instructions say: \u201cFirst, we took away three from each side.\u201d To the right of this sentence is the same equation with 3 being subtracted from both sides: x plus 3 minus 3 equals 8 minus 3, with minus 3 written in red on both sides. Another line down on the left, the instructions say: \u201cThen we were left with five.\u201d To the right of this sentence is the answer to the equation: x equals five.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"height: 17px; width: 63.7188%;\"><\/td>\r\n<td style=\"height: 17px; width: 36.0544%;\"><span id=\"eip-id1169752980473\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2020\/08\/CNX_ElemAlg_Figure_02_01_006d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 19px;\">\r\n<td style=\"height: 19px; width: 63.7188%;\">Subtract 37 from each side to \u2018undo\u2019 the addition.<\/td>\r\n<td style=\"height: 19px; width: 36.0544%;\"><span id=\"eip-id1169741763989\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_006e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 63.7188%;\">Simplify.<\/td>\r\n<td style=\"height: 18px; width: 36.0544%;\"><span id=\"eip-id1169752938273\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_006f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px; width: 63.7188%;\">Check:<\/td>\r\n<td style=\"height: 18px; width: 36.0544%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px; width: 63.7188%;\">Substitute \\(y=-50\\)<\/td>\r\n<td style=\"height: 15px; width: 36.0544%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px; width: 63.7188%;\"><\/td>\r\n<td style=\"height: 22px; width: 36.0544%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1168345539173\">Since \\(y=-50\\) makes \\(y+37=-13\\) a true statement, we have the solution to this equation.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345300888\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345441260\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345636236\" data-type=\"problem\">\r\n<p id=\"fs-id1168345337170\">Solve: \\(x+19=-27\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345375153\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168341852442\">\\(x=-46\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168345300888\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345441260\" data-type=\"exercise\">What happens when an equation has a number subtracted from the variable, as in the equation \\(x-5=8\\)? We use another property to solve equations when a number is subtracted from the variable. We want to isolate the variable, so to \u2018undo\u2019 the subtraction we will add the number to both sides. We use the <strong>Addition Property of Equality<\/strong>.<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Addition Property of Equality<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1168345274390\">For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>,<\/p>\r\n\r\n<div id=\"fs-id1168345384352\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{ccccc}\\text{If}\\hfill &amp; &amp; \\hfill a&amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; &amp; \\hfill a+c&amp; =\\hfill &amp; b+c\\hfill \\end{array}\\)<\/div>\r\n<p id=\"fs-id1168345287184\">When you add the same quantity to both sides of an equation, you still have equality.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168345550229\">In Example 2, 37 was added to the <em data-effect=\"italics\">y<\/em> and so we subtracted 37 to \u2018undo\u2019 the addition. In Example 3, we will need to \u2018undo\u2019 subtraction by using the <span class=\"no-emphasis\" data-type=\"term\">Addition Property of Equality<\/span>.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345425326\" data-type=\"problem\">\r\n<p id=\"fs-id1168345325321\">Solve: \\(a-28=-37.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345240578\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1169750584873\" style=\"height: 107px; width: 100%;\" summary=\"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 a minus 28 equals negative 37. One line down on the left, the instructions say: \u201cAdd 28 to each side to \u2018undo\u2019 the subtraction.\u201d To the right of this sentence is the same equation with 28 being added to both sides: a minus 28 plus 28 equals negative 37 plus 28, with plus 28 written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this sentence is the answer to the equation: a equals negative 9. Two lines down, the instructions say \u201cCheck\u201d. To the right of this word is the original equation again: a minus 28 equals negative 37. Then the instructions say to substitute negative 9 for a, and to the right is the equation with negative 9 substituted in for a: negative 9 (written in red) minus 28 equals negative 37. Below this is the equation negative 37 equals negative 37, with a check mark next to it.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 262.406px;\"><\/td>\r\n<td style=\"height: 14px; width: 221.406px;\"><span id=\"eip-id1169752949939\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px; width: 262.406px;\">Add 28 to each side to \u2018undo\u2019 the subtraction.<\/td>\r\n<td style=\"height: 15px; width: 221.406px;\"><span id=\"eip-id1169752907850\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 262.406px;\">Simplify.<\/td>\r\n<td style=\"height: 14px; width: 221.406px;\"><span id=\"eip-id1169753102934\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 262.406px;\">Check:<\/td>\r\n<td style=\"height: 14px; width: 221.406px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 262.406px;\">Substitute \\(a=-9\\)<\/td>\r\n<td style=\"height: 14px; width: 221.406px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px; width: 262.406px;\"><\/td>\r\n<td style=\"height: 22px; width: 221.406px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 262.406px;\">The solution to \\(a-28=-37\\) is \\(a=-9.\\)<\/td>\r\n<td style=\"height: 14px; width: 221.406px;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345404706\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345342475\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345302182\" data-type=\"problem\">\r\n<p id=\"fs-id1168345384195\">Solve: \\(n-61=-75.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345485609\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345531414\">\\(n=-14\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168345442219\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345250265\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345387536\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345293756\" data-type=\"problem\">\r\n<p id=\"fs-id1168345669119\">Solve: \\(x-\\frac{5}{8}=\\frac{3}{4}.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345667330\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1169752186691\" style=\"width: 100%;\" summary=\"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 x minus five eighths equals three quarters. One line down on the left, the instructions say: \u201cUse the Addition Property of Equality.\u201d To the right of this sentence is the same equation with five eighths being added to both sides: x minus five eighths plus five eighths equals three quarters plus five eighths, with plus five eighths written in red on both sides of the equal sign. The next line down on the left the instructions say: \u201cFind the LCD to add the fractions on the right.\u201d To the right of this sentence is the equation: x minus five eighths plus five eighths equals six eighths plus five eighths. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this sentence is the answer to the equation: x equals eleven eighths. Two lines down, the instructions say \u201cCheck\u201d. To the right of this instruction is the original equation again: x minus five eighths equals three quarters. Another line down, the instructions say to substitute 11 eighths for x, and to the right is the equation with 11 eighths substituted in for x: 11 eights (written in red) minus five eighths might equal three quarters. The instructions then say \u201cSubtract\u201d. To the right of this instruction is the equation: six eighths might equal three quarters. One more line down, the instructions say \u201cSimplify\u201d. To the right of that instruction is three quarters equals three quarters, with a check mark next to it.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 72.3356%;\"><\/td>\r\n<td style=\"width: 27.4376%;\"><span id=\"eip-id1169752197549\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 72.3356%;\">Use the Addition Property of Equality.<\/td>\r\n<td style=\"width: 27.4376%;\"><span id=\"eip-id1169751926086\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 72.3356%;\">Find the LCD to add the fractions on the right.<\/td>\r\n<td style=\"width: 27.4376%;\"><span id=\"eip-id1169745434963\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 72.3356%;\">Simplify.<\/td>\r\n<td style=\"width: 27.4376%;\"><span id=\"eip-id1169751866214\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 72.3356%;\">Check:<\/td>\r\n<td style=\"width: 27.4376%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 72.3356%;\">Substitute \\(x=\\frac{11}{8}.\\)<\/td>\r\n<td style=\"width: 27.4376%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 72.3356%;\">Subtract.<\/td>\r\n<td style=\"width: 27.4376%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 72.3356%;\">Simplify.<\/td>\r\n<td style=\"width: 27.4376%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 72.3356%;\">The solution to \\(x-\\frac{5}{8}=\\frac{3}{4}\\) is \\(x=\\frac{11}{8}.\\)<\/td>\r\n<td style=\"width: 27.4376%;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168345414504\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345239712\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345574727\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345414504\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345239712\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345574727\" data-type=\"problem\">\r\n<p id=\"fs-id1168345297557\">Solve: \\(p-\\frac{2}{3}\\phantom{\\rule{0.2em}{0ex}}=\\frac{5}{6}.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345414808\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345743306\">\\(p=\\frac{9}{6}\\phantom{\\rule{0.2em}{0ex}}p=\\frac{3}{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168341962891\">The next example will be an equation with decimals.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345217297\" data-type=\"problem\">\r\n<p id=\"fs-id1168341862678\">Solve: \\(n-0.63=-4.2.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345251888\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1169754089552\" style=\"height: 96px; width: 100%;\" summary=\"This 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 n minus 0.63 equals negative 4.2. One line down on the left, the instructions say: \u201cUse the Addition Property of Equality.\u201d To the right of this sentence is the same equation with 0.63 being added to both sides: n minus 0.63 plus 0.63 equals negative 4.2 plus 0.63, with plus 0.63 written in red on both sides. Another line down on the left, the instructions say: \u201cAdd.\u201d To the right of this sentence is the answer to the equation: n equals negative 3.57. Two lines down, the instructions say \u201cCheck\u201d. To the right of this word is the original equation again: n minus 0.63 equals negative 4.2. Then the instructions say \u201cLet n equal negative 3.57\u201d, and to the right is the equation with negative 3.57 substituted in for n: negative 3.57 (written in red) minus 0.63 might equal negative 4.2. Below this is the equation negative 4.2 equals negative 4.2 with a check mark next to it.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px; width: 348.406px;\"><\/td>\r\n<td style=\"height: 15px; width: 278.406px;\"><span id=\"eip-id1169745448207\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 348.406px;\">Use the Addition Property of Equality.<\/td>\r\n<td style=\"height: 14px; width: 278.406px;\"><span id=\"eip-id1169752211122\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px; width: 348.406px;\">Add.<\/td>\r\n<td style=\"height: 14px; width: 278.406px;\"><span id=\"eip-id1169754129874\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px; width: 348.406px;\">Check:<\/td>\r\n<td style=\"height: 15px; width: 278.406px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 23px;\">\r\n<td style=\"height: 23px; width: 348.406px;\">Let \\(n=-3.57\\).<\/td>\r\n<td style=\"height: 23px; width: 278.406px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px; width: 348.406px;\"><\/td>\r\n<td style=\"height: 15px; width: 278.406px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345409282\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345638730\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345293173\" data-type=\"problem\">\r\n<p id=\"fs-id1168345301399\">Solve: \\(b-0.47=-2.1.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345275306\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345293683\">\\(b=-1.63\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1 data-type=\"title\">Solve Equations Using the Division and Multiplication Properties of Equality<\/h1>\r\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.To solve those kind of equations we will use the <strong>Division Property of Equality<\/strong>.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">The Division Property of Equality<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1168344074804\">For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>, and \\(c\\ne 0\\),<\/p>\r\n\r\n<div id=\"fs-id1168344315866\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{ccccc}\\text{If}\\hfill &amp; &amp; \\hfill a&amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; &amp; \\hfill \\frac{a}{c}&amp; =\\hfill &amp; \\frac{b}{c}\\hfill \\end{array}\\)<\/div>\r\n<div data-type=\"equation\" data-label=\"\"><\/div>\r\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\">When you divide both sides of an equation by any non-zero number, you still have equality.<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168344149007\">The goal in solving an equation is to \u2018undo\u2019 the operation on the variable. In the next example, the variable is multiplied by 5, so we will divide both sides by 5 to \u2018undo\u2019 the multiplication.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168344214265\" data-type=\"problem\">\r\n<p id=\"fs-id1168344192993\">Solve: \\(5x=-27.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168344189039\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1169748428935\" style=\"height: 277px; width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the left, the instructions say: \u201cTo isolate x, \u2018undo\u2019 the multiplication by 5.\u201d To the right of this sentence is the equation 5 x equals negative 27. The next line down on the left, the instructions say: \u201cDivide to \u2018undo\u2019 the multiplication.\u201d To the right of this sentence is the same equation with both sides divided by 5: 5 x over 5 equals negative 27 over 5, with divided by 5 written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this sentence is the answer to the equation: x equals negative 27\/5. Another line down to the left, the instructions say: Check\u201d. To the right of this instruction is the original equation again: 5x equals negative 27. Another line down, the instructions say to substitute negative 27\/5 for x, and to the right is the equation with negative 27\/5 substituted for x: 5 times negative 27\/5, with negative 27\/5 in parentheses and written in red, equals negative 27. Below this is the equation negative 27 equals negative 27, with a check mark next to it. Another line down, in the right-hand column, is a sentence that reads \u201cSince this is a true statement x = -27\/5 is the solution to 5x = -27.\u201d\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 71.2018%;\">To isolate \\(x\\), \u201cundo\u201d the multiplication by 5.<\/td>\r\n<td style=\"width: 28.5714%;\"><span id=\"eip-id1169753966731\" data-type=\"media\" data-alt=\".\"><img class=\"alignleft\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 71.2018%;\">Divide to \u2018undo\u2019 the multiplication.<\/td>\r\n<td style=\"width: 28.5714%;\"><span id=\"eip-id1169753966753\" data-type=\"media\" data-alt=\".\"><img class=\"alignleft\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 71.2018%;\">Simplify.<\/td>\r\n<td style=\"width: 28.5714%;\"><span id=\"eip-id1169754099104\" data-type=\"media\" data-alt=\".\"><img class=\"alignleft\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 71.2018%;\">Check:<\/td>\r\n<td style=\"width: 28.5714%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 71.2018%;\">Substitute \\(-\\frac{27}{5}\\) for \\(x.\\)<\/td>\r\n<td style=\"width: 28.5714%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 71.2018%;\"><\/td>\r\n<td style=\"width: 28.5714%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 71.2018%;\">Since this is a true statement, \\(x=-\\frac{27}{5}\\)<span data-type=\"newline\">\r\n<\/span>is the solution to \\(5x=-27\\).<\/td>\r\n<td style=\"width: 28.5714%;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168344149474\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168344097238\" data-type=\"exercise\">\r\n<div id=\"fs-id1168344395192\" data-type=\"problem\">\r\n<p id=\"fs-id1168343187974\">Solve: \\(3y=-41.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168344193579\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168343188649\">\\(y=\\frac{-41}{3}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168344342565\">Consider the equation \\(\\frac{x}{4}=3\\). We want to know what number divided by 4 gives 3. So to \u201cundo\u201d the division, we will need to multiply by 4. The <strong>Multiplication Property of Equality<\/strong> will allow us to do this. This property says that if we start with two equal quantities and multiply both by the same number, the results are equal.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">The Multiplication Property of Equality<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1168344600409\">For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>,<\/p>\r\n\r\n<div id=\"fs-id1168344202393\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{ccccc}\\text{If}\\hfill &amp; &amp; \\hfill a&amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; &amp; \\hfill ac&amp; =\\hfill &amp; bc\\hfill \\end{array}\\)<\/div>\r\n<\/div>\r\n<\/div>\r\nIf you multiply both sides of an equation by the same number, you still have equality.\r\n<div id=\"fs-id1168343023900\" data-type=\"note\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168344229502\" data-type=\"problem\">\r\n<p id=\"fs-id1168343195079\">Solve: \\(\\frac{y}{-7}=-14.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168344374013\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1168344515851\">Here \\(y\\) is divided by \\(-7\\). We must multiply by \\(-7\\) to isolate \\(y\\).<\/p>\r\n\r\n<table style=\"border-collapse: collapse; width: 100%; height: 130px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 34px;\">\r\n<td style=\"width: 50%; height: 34px;\"><\/td>\r\n<td style=\"width: 50%; height: 34px;\"><span id=\"eip-id1169752958286\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\">Multiply both sides by \\(-7\\).<\/td>\r\n<td style=\"width: 50%; height: 16px;\"><span id=\"eip-id1169753238745\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\">Multiply.<\/td>\r\n<td style=\"width: 50%; height: 16px;\"><span id=\"eip-id1169750595124\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\">Simplify.<\/td>\r\n<td style=\"width: 50%; height: 16px;\"><span id=\"eip-id1169750876711\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\">Check.<\/td>\r\n<td style=\"width: 50%; height: 16px;\">\\(\\frac{y}{-7}=-14\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\">Substitute \\(y=98\\).<\/td>\r\n<td style=\"width: 50%; height: 16px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\">Divide<\/td>\r\n<td style=\"width: 50%; height: 16px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168344287502\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168343173477\" data-type=\"exercise\">\r\n<div id=\"fs-id1168344120375\" data-type=\"problem\">\r\n<p id=\"fs-id1168343024054\">Solve: \\(\\frac{a}{-7}=-42.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168343007643\" data-type=\"solution\"><details open=\"open\"><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168344312078\">\\(a=294\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168343160986\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168343174664\" data-type=\"exercise\">\r\n<div id=\"fs-id1168344449255\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168344115117\" data-type=\"problem\">\r\n<p id=\"fs-id1168344249917\">Solve: \\(\\frac{3}{4}x=12.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168344333366\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1168344440965\">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{3}{4}\\).<\/p>\r\n\r\n<table id=\"eip-id1169747451024\" class=\"grid\" style=\"width: 100%; height: 280px;\" summary=\"This 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 three-fourths x equals 12. One line down on the left, the instructions say: \u201cMultiply by the reciprocal of \u00be.\u201d To the right of this sentence is the same equation multiplied by 4\/3 on both sides: 4\/3 times three-fourths x equals 4\/3 times 12, with times 4\/3 written in red on both sides. Another line down on the left, the instructions say: \u201cReciprocals multiply to 1.\u201d To the right of this sentence is the equation 1x equals 4\/3 times 12. Another line down on the left, the instructions say: \u201cMultiply.\u201d To the right of this instruction is the answer to the equation: x equals 16. Below this is the text: \u201cNotice that we could have divided both sides of the equation three-fourths x equals 12 by \u00be to isolate x. While this would work, most people would find multiplying by the reciprocal easier.\u201d Two lines down, the instructions say: \u201cCheck\u201d. To the right of this word is the original equation again: three-fourths x equals 12. Then the instructions say: \u201cSubstitute x equals 16,\u201d and to the right is the equation with 16 substituted in for x: \u00be times 16 (written in red) might equal 12. Below this is the equation 12 equals 12, with a check mark next to it.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 31px;\">\r\n<td style=\"width: 68.7074%; height: 31px;\"><\/td>\r\n<td style=\"width: 31.0658%; height: 31px;\"><span id=\"eip-id1169750571487\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 31px;\">\r\n<td style=\"width: 68.7074%; height: 31px;\">Multiply by the reciprocal of \\(\\frac{3}{4}\\).<\/td>\r\n<td style=\"width: 31.0658%; height: 31px;\"><span id=\"eip-id1169753253515\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 31px;\">\r\n<td style=\"width: 68.7074%; height: 31px;\">Reciprocals multiply to 1.<\/td>\r\n<td style=\"width: 31.0658%; height: 31px;\"><span id=\"eip-id1169751034763\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 68.7074%; height: 14px;\">Multiply.<\/td>\r\n<td style=\"width: 31.0658%; height: 14px;\"><span id=\"eip-id1169750889650\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 62px;\">\r\n<td style=\"height: 62px; width: 68.7074%;\">Notice that we could have divided both sides of the equation \\(\\frac{3}{4}x=12\\) by \\(\\frac{3}{4}\\) to isolate \\(x\\). While this would work, most people would find multiplying by the reciprocal easier.<\/td>\r\n<td style=\"width: 31.0658%;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 32px;\">\r\n<td style=\"width: 68.7074%; height: 32px;\">Check:<\/td>\r\n<td style=\"width: 31.0658%; height: 32px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 79px;\">\r\n<td style=\"width: 68.7074%; height: 79px;\">Substitute \\(x=16\\).<\/td>\r\n<td style=\"width: 31.0658%; height: 79px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/>\r\n\r\n<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168344208698\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168344619809\" data-type=\"exercise\">\r\n<div id=\"fs-id1168343051295\" data-type=\"problem\">\r\n<p id=\"fs-id1168344323848\">Solve: \\(\\frac{2}{5}n=14.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168343030336\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168344316594\">\\(n=35\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168343128927\">Now we have covered all four properties of equality\u2014subtraction, addition, division, and multiplication. We\u2019ll list them all together here for easy reference.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Properties of Equality<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168343141934\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\r\n\r\n\\(\\begin{array}{ccc}\\mathbf{\\text{Subtraction Property of Equality}}\\hfill &amp; &amp; \\mathbf{\\text{Addition Property of Equality}}\\hfill \\\\ \\text{For any real numbers}\\phantom{\\rule{0.2em}{0ex}}a,b,\\text{and}\\phantom{\\rule{0.2em}{0ex}}c,\\hfill &amp; &amp; \\text{For any real numbers}\\phantom{\\rule{0.2em}{0ex}}a,b,\\text{and}\\phantom{\\rule{0.2em}{0ex}}c,\\hfill \\\\ \\phantom{\\rule{1em}{0ex}}\\begin{array}{cccc}\\text{if}\\hfill &amp; \\hfill a&amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; \\hfill a-c&amp; =\\hfill &amp; b-c.\\hfill \\end{array}\\hfill &amp; &amp; \\phantom{\\rule{1em}{0ex}}\\begin{array}{cccc}\\text{if}\\hfill &amp; \\hfill a&amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; \\hfill a+c&amp; =\\hfill &amp; b+c.\\hfill \\end{array}\\hfill \\\\ \\mathbf{\\text{Division Property of Equality}}\\hfill &amp; &amp; \\mathbf{\\text{Multiplication Property of Equality}}\\hfill \\\\ \\text{For any numbers}\\phantom{\\rule{0.2em}{0ex}}a,b,\\text{and}\\phantom{\\rule{0.2em}{0ex}}c,\\text{and}\\phantom{\\rule{0.2em}{0ex}}c\\ne 0,\\hfill &amp; &amp; \\text{For any numbers}\\phantom{\\rule{0.2em}{0ex}}a,b,\\text{and}\\phantom{\\rule{0.2em}{0ex}}c,\\hfill \\\\ \\phantom{\\rule{1em}{0ex}}\\begin{array}{cccc}\\text{if}\\hfill &amp; \\hfill a&amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; \\hfill \\frac{a}{c}&amp; =\\hfill &amp; \\frac{b}{c}.\\hfill \\end{array}\\hfill &amp; &amp; \\phantom{\\rule{1em}{0ex}}\\begin{array}{cccc}\\text{if}\\hfill &amp; \\hfill a&amp; =\\hfill &amp; b,\\hfill \\\\ \\text{then}\\hfill &amp; \\hfill ac&amp; =\\hfill &amp; bc.\\hfill \\end{array}\\hfill \\end{array}\\)\r\n\r\nWhen you add, subtract, multiply, or divide the same quantity from both sides of an equation, you still have equality.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\nNow we will use those properties to solve equations in which the variable terms, or constant terms, or both are on both sides of the equation.\r\n<h1 id=\"fs-id1168344108924\">Solve Equations with Variables and Constants on Both Sides<\/h1>\r\n<p id=\"fs-id1168344086598\">Our strategy will involve choosing one side of the equation to be the \u201cvariable side\u201d, and the other side of the equation to be the \u201cconstant side.\u201d Then, we will use the Subtraction and Addition Properties of Equality to get all the variable terms together on one side of the equation and the constant terms together on the other side.<\/p>\r\n<p id=\"fs-id1168344344951\">By doing this, we will transform the equation that began with variables and constants on both sides into the form \\(ax=b.\\) We already know how to solve equations of this form by using the Division or Multiplication Properties of Equality.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nSolve: \\(8y-9=31.\\)\r\n\r\n<strong>Solution<\/strong>\r\n\r\nIn this equation, the variable is found only on the left side. It makes sense to call the left side the \u201cvariable\u201d side. Therefore, the right side will be the \u201cconstant\u201d side. We will write the labels above the equation to help us remember what goes where. Since the left side is the \u201cvariable\u201d side, the 9 is out of place. It is subtracted from the \\(8y\\), so to \u201cundo\u201d subtraction, add 9 to both sides. Remember, whatever you do to the left, you must do to the right.\r\n<table style=\"border-collapse: collapse; width: 100%; height: 111px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 42px;\">\r\n<td style=\"width: 50%; height: 42px;\"><\/td>\r\n<td style=\"width: 50%; height: 42px;\"><span id=\"eip-id1168184743090\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 21px;\">\r\n<td style=\"width: 50%; height: 21px;\">Add 9 to both sides.<\/td>\r\n<td style=\"width: 50%; height: 21px;\"><span id=\"eip-id1168184743111\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\">Simplify.<\/td>\r\n<td style=\"width: 50%; height: 16px;\"><span id=\"eip-id1168184848828\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/> <\/span>\r\n\r\n<span id=\"eip-id1168184848828\" data-type=\"media\" data-alt=\".\">The variables are now on one side and the constants on the other. We continue from here as we did earlier.\r\n<\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\">Divide both sides by 8.<\/td>\r\n<td style=\"width: 50%; height: 16px;\"><span id=\"eip-id1168184848861\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 50%; height: 16px;\">Simplify.<\/td>\r\n<td style=\"width: 50%; height: 16px;\"><span id=\"eip-id1168184848881\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">Check.<\/td>\r\n<td style=\"width: 50%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">Let \\(y=5\\).<\/td>\r\n<td style=\"width: 50%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/>\r\n\r\n<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/>\r\n\r\n<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168344522317\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168344301536\" data-type=\"exercise\">\r\n<div id=\"fs-id1168343007231\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168344120441\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168343140153\" data-type=\"exercise\">\r\n<div id=\"fs-id1168344525168\" data-type=\"problem\">\r\n<p id=\"fs-id1168344285180\">Solve: \\(5y-9=16.\\)<\/p>\r\n\r\n<\/div>\r\n<details><summary class=\"answer\">Show answer<\/summary>\r\n<div id=\"fs-id1168344475410\" data-type=\"solution\">\r\n\r\n\\(y=5\\)\r\n\r\n<\/div>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\nWhat if there are variables on both sides of the equation? For equations like this, begin as we did above\u2014choose a \u201cvariable\u201d side and a \u201cconstant\u201d side, and then use the subtraction and addition properties of equality to collect all variables on one side and all constants on the other side.\r\n<div id=\"fs-id1168344071798\" class=\"bc-section section\" data-depth=\"1\">\r\n<div id=\"fs-id1168343024055\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168342980814\" data-type=\"exercise\">\r\n<div id=\"fs-id1168344505212\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168344198024\" data-type=\"problem\">\r\n<p id=\"fs-id1168344193531\">Solve: \\(5y-9=8y.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168344363684\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1168344523496\">The only constant is on the left and the \\(y\\)\u2019s are on both sides. Let\u2019s leave the constant on the left and get the variables to the right.<\/p>\r\n\r\n<table id=\"fs-id1167270176565\" style=\"width: 100%; height: 245px;\" summary=\"This 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 5 y minus 9 equals 8 y. The left side of the equation is labeled \u201cconstant\u201d, written in red, and the right side of the equation is labeled \u201cvariable\u201d, written in red. One line down on the left, the instructions say: \u201cSubtract 5y from both sides.\u201d To the right of this sentence is the same equation with 5 y subtracted from both sides: 5 y minus 5 y minus 9 equals 8 y minus 5 y, with minus 5 y written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the equation negative 9 equals 3y. Another line down on the left, the instructions say: \u201cWe have the y\u2019s on the right and the constants on the left. Divide both sides by 3.\u201d To the right of this instruction is the same equation divided by 3 on both sides: negative 9 over 3 equals 3y over 3, with the divided by 3 written in red on both sides. The next line down on the left, the instructions say: \u201cSimplify,\u201d and to the right of this instruction is the answer to the equation: negative 3 equals y. Another line down on the left, the instructions say: \u201cCheck\u201d. To the right of this word is the original equation again: 5 y minus 9 equals 8 y. Then the instructions say: \u201cLet y equal negative 3,\u201d and to the right is the equation with negative 3 substituted in for y: 5 times negative 3, with negative 3 written in red, minus 9 might equal 8 times negative 3, with negative 3 written in red. Below this is the equation negative 15 minus 9 might equal negative 24. Below this is the equation negative 24 equals negative 24, with a check mark next to it.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 39px;\">\r\n<td style=\"width: 64.1723%; height: 39px;\"><\/td>\r\n<td style=\"width: 35.6009%; height: 39px;\"><span id=\"fs-id1167270305902\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008e_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 21px;\">\r\n<td style=\"width: 64.1723%; height: 21px;\">Subtract \\(5y\\) from both sides.<\/td>\r\n<td style=\"width: 35.6009%; height: 21px;\"><span id=\"fs-id1167269944753\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008f_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 21px;\">\r\n<td style=\"width: 64.1723%; height: 21px;\">Simplify.<\/td>\r\n<td style=\"width: 35.6009%; height: 21px;\"><span id=\"fs-id1167269976413\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008g_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 38px;\">\r\n<td style=\"width: 64.1723%; height: 38px;\">We have the <em data-effect=\"italics\">y<\/em>\u2019s on the right and the<span data-type=\"newline\">\r\n<\/span>constants on the left. Divide both sides by 3.<\/td>\r\n<td style=\"width: 35.6009%; height: 38px;\"><span id=\"fs-id1167265560237\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008h_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 21px;\">\r\n<td style=\"width: 64.1723%; height: 21px;\">Simplify.<\/td>\r\n<td style=\"width: 35.6009%; height: 21px;\"><span id=\"fs-id1167270021089\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008i_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 21px;\">\r\n<td style=\"width: 64.1723%; height: 21px;\">Check:<\/td>\r\n<td style=\"width: 35.6009%; height: 21px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 28px;\">\r\n<td style=\"width: 64.1723%; height: 28px;\">Let \\(y=-3.\\)<\/td>\r\n<td style=\"width: 35.6009%; height: 28px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 24px;\">\r\n<td style=\"width: 64.1723%; height: 24px;\"><\/td>\r\n<td style=\"width: 35.6009%; height: 24px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 64.1723%; height: 16px;\"><\/td>\r\n<td style=\"width: 35.6009%; height: 32px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008d_img_new.jpg\" alt=\".\" width=\"143\" height=\"19\" data-media-type=\"image\/jpeg\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168344511607\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168343003381\" data-type=\"exercise\">\r\n<div id=\"fs-id1168344156204\" data-type=\"problem\">\r\n<p id=\"fs-id1168343046778\">Solve: \\(3p-14=5p.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168343054322\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168344120415\">\\(p=-7\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168344149630\">The next example will be the first to have variables and constants on both sides of the equation. It may take several steps to solve this equation, so we need a clear and organized strategy.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"title\">How to Solve Equations with Variables and Constants on Both Sides<\/div>\r\n<div data-type=\"exercise\">\r\n<div id=\"fs-id1168344198759\" data-type=\"problem\">\r\n<p id=\"fs-id1168344072753\">Solve: \\(7x+5=6x+2.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168344082079\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<span id=\"fs-id1168344202405\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads: \u201cStep 1. Choose which side will the \u201cvariable\u201d side\u2014the other side will be the \u201cconstant\u201d side.\u201d The text in the second cell reads: \u201cThe variable terms are 7 x and 6 x. Since 7 is greater than 6, we will make the left side the \u201cx\u201d side and so the right side will be the \u201cconstant\u201d side.\u201d The third cell contains the equation 7 x plus 5 equals 6 x plus 2, and the left side of the equation is labeled \u201cvariable\u201d written in red, and the right side of the equation is labeled \u201cconstant\u201d written in red.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_010a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads: \u201cStep 1. Choose which side will the \u201cvariable\u201d side\u2014the other side will be the \u201cconstant\u201d side.\u201d The text in the second cell reads: \u201cThe variable terms are 7 x and 6 x. Since 7 is greater than 6, we will make the left side the \u201cx\u201d side and so the right side will be the \u201cconstant\u201d side.\u201d The third cell contains the equation 7 x plus 5 equals 6 x plus 2, and the left side of the equation is labeled \u201cvariable\u201d written in red, and the right side of the equation is labeled \u201cconstant\u201d written in red.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168344074856\" data-type=\"media\" data-alt=\"In the second row of the table, the first cell says: \u201cStep 2. Collect the variable terms to the \u201cvariable\u201d side of the equation, using the addition or subtraction property of equality.\u201d In the second cell, the instructions say: \u201c With the right side as the \u201cconstant\u201d side, the 6x is out of place, so subtract 6x from both sides. Combine like terms. Now the variable is only on the left side!\u201d The third cell contains the original equation with 6x subtracted from both sides: 7 x minus 6 x plus 5 equals 6 x minus 6 x plus 2, with \u201cminus 6 x\u201d written in red on both sides. Below this is the same equation with like terms combined: x plus 5 equals 2.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_010b_img_new.jpg\" alt=\"In the second row of the table, the first cell says: \u201cStep 2. Collect the variable terms to the \u201cvariable\u201d side of the equation, using the addition or subtraction property of equality.\u201d In the second cell, the instructions say: \u201c With the right side as the \u201cconstant\u201d side, the 6x is out of place, so subtract 6x from both sides. Combine like terms. Now the variable is only on the left side!\u201d The third cell contains the original equation with 6x subtracted from both sides: 7 x minus 6 x plus 5 equals 6 x minus 6 x plus 2, with \u201cminus 6 x\u201d written in red on both sides. Below this is the same equation with like terms combined: x plus 5 equals 2.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168344349070\" data-type=\"media\" data-alt=\"In the third row of the table, the first cell says: \u201cStep 3. Collect all the constants to the other side of the equation, using the addition or subtraction property of equality.\u201d In the second cell, the instructions say: \u201cThe right side is the \u201cconstant\u201d side, so the 5 is out of place. Subtract 5 from both sides. Simplify.\u201d The third cell contains the equation x plus 5 minus 5 equals 2 minus 5, with \u201cminus 5\u201d written in red on both sides. Below this is the answer to the equation: x equals negative 3.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_010c_img_new.jpg\" alt=\"In the third row of the table, the first cell says: \u201cStep 3. Collect all the constants to the other side of the equation, using the addition or subtraction property of equality.\u201d In the second cell, the instructions say: \u201cThe right side is the \u201cconstant\u201d side, so the 5 is out of place. Subtract 5 from both sides. Simplify.\u201d The third cell contains the equation x plus 5 minus 5 equals 2 minus 5, with \u201cminus 5\u201d written in red on both sides. Below this is the answer to the equation: x equals negative 3.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168344504811\" data-type=\"media\" data-alt=\"In the fourth row of the table, the first cell says: \u201cStep 4. Make the coefficient of the variable equal 1, using the Multiplication or Division Property of Equality.\u201d In the second cell, the instructions say: \u201cThe coefficient of x is one. The equation is solved.\u201d The third cell is blank.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_010d_img_new.jpg\" alt=\"In the fourth row of the table, the first cell says: \u201cStep 4. Make the coefficient of the variable equal 1, using the Multiplication or Division Property of Equality.\u201d In the second cell, the instructions say: \u201cThe coefficient of x is one. The equation is solved.\u201d The third cell is blank.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168344149090\" data-type=\"media\" data-alt=\"In the fifth row of the table, the first cell says: \u201cStep 5. Check.\u201d The instructions in the second cell say: \u201cCheck. Let x equal negative 3. Simplify. Add.\u201d In the third cell is the original equation again: 7 x plus 5 equals 6x plus 2. Below this is the same equation with negative 3 substituted in for x: 7 times negative 3 (in paretheses) plus 5 might equal 6 times negative 3 (in parentheses) plus 2, with the \u201ctimes negative 3\u201d written in red on both sides of the equation. Below this is the equation negative 21 plus 5 might equal negative 18 plus 2. On the last line is the equation negative 16 equals negative 16, with a check mark next to it.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_010e_img_new.jpg\" alt=\"In the fifth row of the table, the first cell says: \u201cStep 5. Check.\u201d The instructions in the second cell say: \u201cCheck. Let x equal negative 3. Simplify. Add.\u201d In the third cell is the original equation again: 7 x plus 5 equals 6x plus 2. Below this is the same equation with negative 3 substituted in for x: 7 times negative 3 (in paretheses) plus 5 might equal 6 times negative 3 (in parentheses) plus 2, with the \u201ctimes negative 3\u201d written in red on both sides of the equation. Below this is the equation negative 21 plus 5 might equal negative 18 plus 2. On the last line is the equation negative 16 equals negative 16, with a check mark next to it.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168344514524\" data-type=\"exercise\">\r\n<div id=\"fs-id1168343007558\" data-type=\"problem\">\r\n<p id=\"fs-id1168343069772\">Solve: \\(12x+8=6x+2.\\)<\/p>\r\n\r\n<\/div>\r\n<details><summary class=\"answer\">Show answer<\/summary>\r\n<div id=\"fs-id1168344084568\" data-type=\"solution\">\r\n\r\n\\(x=-1\\)\r\n\r\n<\/div>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168344249495\">We\u2019ll list the steps below so you can easily refer to them. But we\u2019ll call this the \u2018Beginning Strategy\u2019 because we\u2019ll be adding some steps later in this chapter.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Equations with variables and constants on both sides of the equation (beginning strategy)<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1169750578662\" class=\"stepwise\" type=\"1\">\r\n \t<li>Choose which side will be the \u201cvariable\u201d side\u2014the other side will be the \u201cconstant\u201d side.<\/li>\r\n \t<li>Collect the variable terms to the \u201cvariable\u201d side of the equation, using the Addition or Subtraction Property of Equality.<\/li>\r\n \t<li>Collect all the constants to the other side of the equation, using the Addition or Subtraction Property of Equality.<\/li>\r\n \t<li>Make the coefficient of the variable equal 1, using the Multiplication or Division Property of Equality.<\/li>\r\n \t<li>Check the solution by substituting it into the original equation.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nIn Step 1, a helpful approach is to make the \u201cvariable\u201d side the side that has the variable with the larger coefficient. This usually makes the arithmetic easier.\r\n<div id=\"fs-id1168344115887\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168344227238\" data-type=\"exercise\">\r\n<div id=\"fs-id1168343061173\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168343008854\" data-type=\"problem\">\r\n<p id=\"fs-id1168344076393\">Solve: \\(7a-3=13a+7.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168344499016\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1168343237356\">In the first step, choose the variable side by comparing the coefficients of the variables on each side.<\/p>\r\n<p id=\"fs-id1168343131545\">Since \\(13\\) &gt; \\(7\\), make the right side the \u201cvariable\u201d side and the left side the \u201cconstant\u201d side.<\/p>\r\n\r\n<table id=\"eip-id1168184909198\" style=\"width: 100%;\" summary=\"This 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 7 a minus 3 equals 13 a plus 7, with the left side of the equation labeled \u201cconstant,\u201d written in red, and the right side of the equation labeled \u201cvariable,\u201d written in red. One line down on the left, the instructions say: \u201cSubtract 7 a from both sides to remove the variable term from the left.\u201d To the right of this sentence is the same equation with 7a subtracted from both sides: 7 a minus 7 a minus 3 equals 13 a minus 7 a plus 7, with \u201cminus 7 a\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the equation negative 3 equals 6 a plus 7. The next line down on the left, the instructions say: \u201cSubtract 7 from both sides to remove the constant from the right.\u201d To the right of this sentence is the same equation with 7 subtracted from both sides: negative 3 minus 7 equals 6 a plus 7 minus 7, with \u201cminus 7\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the equation negative 10 equals 6 a. One row down, the instructions say: \u201cDivide both sides by 6 to make 1 the coefficient of a,\u201d and to the right is the equation with both sides divided by 6: negative 10 over 6 equals 6a over 6, with \u201cdivided by 6\u201d written in red on both sides. One row down, the instructions say: \u201cSimplify,\u201d and to the right is the answer to the equation: negative 5\/3 equals a. One row down, the columns merge into one. The text says: \u201cCheck\u201d. To the right of this instruction is the original equation again: 7a minus 3 equals 13 a plus 7. Another row down, the instructions say: \u201cLet a equal negative 5\/3.\u201d To the right of this sentence is the original equation with negative 5\/3 substituted in for a: 7 times negative 5\/3 minus 3 might equal 13 times negative 5\/3 plus 7, with negative 5\/3 written in red on both sides. Below that is the equation negative 35\/3 minus 9\/3 might equal 65\/3 plus 21\/3. Below that is the equation negative 54\/3 equals negative 54\/3, with a check mark next to it.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 67.8005%;\"><\/td>\r\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877266\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 67.8005%;\">Subtract \\(7a\\) from both sides to remove the variable term from the left.<\/td>\r\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877293\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 67.8005%;\">Combine like terms.<\/td>\r\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877314\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 67.8005%;\">Subtract \\(7\\) from both sides to remove the constant from the right.<\/td>\r\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877339\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 67.8005%;\">Simplify.<\/td>\r\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877360\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 67.8005%;\" data-valign=\"bottom\">Divide both sides by \\(6\\) to make \\(1\\) the coefficient of \\(a\\).<\/td>\r\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877394\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 67.8005%;\">Simplify.<\/td>\r\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184833888\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 67.8005%;\">Check:<\/td>\r\n<td style=\"width: 31.9728%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 67.8005%;\">Let \\(a=-\\frac{5}{3}\\).<\/td>\r\n<td style=\"width: 31.9728%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 67.8005%;\"><\/td>\r\n<td style=\"width: 31.9728%;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 67.8005%;\"><\/td>\r\n<td style=\"width: 31.9728%;\">\\(-\\frac{44}{3}=-\\frac{44}{3}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168343131452\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168344192020\" data-type=\"exercise\">\r\n<div id=\"fs-id1168344509721\" data-type=\"problem\">\r\n<p id=\"fs-id1168344502381\">Solve: \\(2a-2=6a+18.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168344215124\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168344315440\">\\(a=-5\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168343131452\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168344192020\" data-type=\"exercise\">\r\n<div id=\"fs-id1168344509721\" data-type=\"problem\">In the last example, we could have made the left side the \u201cvariable\u201d side, but it would have led to a negative coefficient on the variable term. (Try it!) While we could work with the negative, there is less chance of errors when working with positives. The strategy outlined above helps avoid the negatives!<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168344297464\">To solve an equation with fractions, we just follow the steps of our strategy to get the solution!<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168342992147\" data-type=\"problem\">\r\n<p id=\"fs-id1168344250068\">Solve: \\(\\frac{5}{4}x+6=\\frac{1}{4}x-2.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168344504486\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1168344156941\">Since \\(\\frac{5}{4}\\) &gt; \\(\\frac{1}{4}\\), make the left side the \u201cvariable\u201d side and the right side the \u201cconstant\u201d side.<\/p>\r\n\r\n<table id=\"eip-id1168186270303\" style=\"width: 100%;\" summary=\"This 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 five-fourths x plus 6 equals one-fourth x minus 2, with the left side of the equation labeled \u201cvariable,\u201d written in red, and the right side of the equation labeled \u201cconstant,\u201d written in red. One line down on the left, the instructions say: \u201cSubtract one-fourth x from both sides.\u201d To the right of this instruction is the same equation with one-fourth x subtracted from both sides: five-fourths x minus one-fourth x plus 6 equals one-fourth x minus one-fourth x minus 2, with \u201cminus one-fourth x\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cCombine like terms,\u201d and to the right of this instruction is the equation x plus 6 equals negative 2. Then the next line down on the left, the instructions say: \u201cSubtract 6 from both sides.\u201d To the right of this instruction is the same equation with 6 subtracted from both sides: x plus 6 minus 6 equals negative 2 minus 6, with \u201cminus 6\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the answer to the equation: x equals negative 8. One row down, the columns merge into one. The instructions say: \u201cCheck,\u201d and to the right is the original equation again: five-fourths x plus 6 equals one-fourth x minus 2. Another line down on the left, the instructions say: \u201cLet x equal negative 8,\u201d and to the right is the original equation with negative 8 substituted in for x: 5\/4 times negative 8 plus 6 might equal \u00bc times negative 8 minus 2, with \u201ctimes negative 8\u201d written in red on both sides. Below this is the equation negative 10 plus 6 might equal negative 2 minus 2. Below this is the equation negative 4 equals negative 4, with a check mark next to it.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 399.406px;\" colspan=\"2\"><\/td>\r\n<td style=\"width: 253.406px;\"><span id=\"eip-id1168186270365\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 399.406px;\" colspan=\"2\">Subtract \\(\\frac{1}{4}x\\) from both sides.<\/td>\r\n<td style=\"width: 253.406px;\"><span id=\"eip-id1168186270396\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 399.406px;\" colspan=\"2\">Combine like terms.<\/td>\r\n<td style=\"width: 253.406px;\"><span id=\"eip-id1168186252297\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_013c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 399.406px;\" colspan=\"2\">Subtract \\(6\\) from both sides.<\/td>\r\n<td style=\"width: 253.406px;\"><span id=\"eip-id1168186252322\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_013d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 399.406px;\" colspan=\"2\">Simplify.<\/td>\r\n<td style=\"width: 253.406px;\"><span id=\"eip-id1168186252343\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_013e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span>\r\n\r\n<span id=\"eip-id1168186252343\" data-type=\"media\" data-alt=\".\">\\(\\begin{array}{cccccc}\\text{Check:}\\hfill &amp; &amp; &amp; \\hfill \\frac{5}{4}x+6&amp; =\\hfill &amp; \\frac{1}{4}x-2\\hfill \\\\ \\text{Let}\\phantom{\\rule{0.2em}{0ex}}x=-8.\\hfill &amp; &amp; &amp; \\hfill \\frac{5}{4}\\left(-8\\right)+6&amp; \\stackrel{?}{=}\\hfill &amp; \\frac{1}{4}\\left(-8\\right)-2\\hfill \\\\ &amp; &amp; &amp; \\hfill -10+6&amp; \\stackrel{?}{=}\\hfill &amp; -2-2\\hfill \\\\ &amp; &amp; &amp; \\hfill -4&amp; =\\hfill &amp; -4\u2713\\hfill \\end{array}\\)<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 13<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168343159196\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168344285089\" data-type=\"exercise\">\r\n<div id=\"fs-id1168343001184\" data-type=\"problem\">\r\n<p id=\"fs-id1168344367951\">Solve: \\(\\frac{7}{8}x-12=-\\frac{1}{8}x-2.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168343186830\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168343079905\">\\(x=10\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168344187424\">We will use the same strategy to find the solution for an equation with decimals.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168343021370\" data-type=\"problem\">\r\n<p id=\"fs-id1168342967652\">Solve: \\(7.8x+4=5.4x-8.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168343001168\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1168344620464\">Since \\(7.8\\) &gt; \\(5.4\\), make the left side the \u201cvariable\u201d side and the right side the \u201cconstant\u201d side.<\/p>\r\n\r\n<table id=\"eip-id1168181949602\" style=\"height: 181px; width: 100%;\" summary=\"This 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 7.8 x plus 4 equals 5.4 x minus 8, with the left side of the equation labeled \u201cvariable side,\u201d written in red, and the right side of the equation labeled \u201cconstant side,\u201d written in red. One line down on the left, the instructions say: Subtract 5.4 x from both sides. To the right is the same equation with 5.4 x subtracted from both sides: 7.8 x minus 5.4 x plus 4 equals 5.4 x minus 5.4 x minus 8, with \u201cminus 5.4x\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the equation 2.4 x plus 4 equals negative 8. Another line down on the left, the instructions say: \u201cSubtract 4 from both sides.\u201d To the right of this sentence is the equation 2.4x plus 4 minus 4 equals negative 8 minus 4, with \u201cminus 4\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right of this instruction is the equation 2.4 x equals negative 12. One more line down on the left, the instructions say: \u201cUse the division property of equality.\u201d To the right of this instruction is the same equation divided by 2.4 on both sides: 2.4 x over 2.4 equals negative 12 over 2.4, with \u201cdivided by 2.4\u201d written in red on both sides. One more line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the answer to the equation: x equals negative 5. One more line down, the columns merge into one, and the instructions say: \u201cCheck.\u201d To the right of this instruction is the original equation again: 7.8 x plus 4 equals 5.4 x minus 5. Another line down to the left, the instructions say: \u201cLet x equal negative 5.\u201d To the right is the original equation with negative 5 substituted in for x: 7.8 times negative 5 plus 4 equals 5.4 times negative 5 minus 8, with \u201ctimes negative 5\u201d written in red on both sides. Below that is the equation negative 39 plus 4 might equal negative 27 minus 8. Below that is the equation negative 35 equals negative 35, with a check mark next to it.\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 27px;\">\r\n<td style=\"width: 59.1837%; height: 27px;\"><\/td>\r\n<td style=\"width: 40.5896%; height: 27px;\"><span id=\"eip-id1168181949667\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 59.1837%; height: 14px;\">Subtract \\(5.4x\\) from both sides.<\/td>\r\n<td style=\"width: 40.5896%; height: 14px;\"><span id=\"eip-id1168181949695\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 59.1837%; height: 14px;\">Combine like terms.<\/td>\r\n<td style=\"width: 40.5896%; height: 14px;\"><span id=\"eip-id1168181949716\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 59.1837%; height: 14px;\">Subtract \\(4\\) from both sides.<\/td>\r\n<td style=\"width: 40.5896%; height: 14px;\"><span id=\"eip-id1168181949742\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 59.1837%; height: 14px;\">Simplify.<\/td>\r\n<td style=\"width: 40.5896%; height: 14px;\"><span id=\"eip-id1168181949763\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 26px;\">\r\n<td style=\"width: 59.1837%; height: 26px;\">Use the Division Propery of Equality.<\/td>\r\n<td style=\"width: 40.5896%; height: 26px;\"><span id=\"eip-id1168181949784\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 59.1837%; height: 14px;\">Simplify.<\/td>\r\n<td style=\"width: 40.5896%; height: 14px;\"><span id=\"eip-id1168181949805\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 59.1837%; height: 14px;\">Check:<\/td>\r\n<td style=\"width: 40.5896%; height: 14px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 59.1837%; height: 14px;\">Let \\(x=-5\\).<\/td>\r\n<td style=\"width: 40.5896%; height: 14px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 59.1837%; height: 16px;\"><\/td>\r\n<td style=\"width: 40.5896%; height: 16px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 59.1837%; height: 14px;\"><\/td>\r\n<td style=\"width: 40.5896%; height: 14px;\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 14<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168344115607\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168344219079\" data-type=\"exercise\">\r\n<div id=\"fs-id1168344600521\" data-type=\"problem\">\r\n<p id=\"fs-id1168343046083\">Solve: \\(2.8x+12=-1.4x-9.\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168344124234\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168344080762\">\\(x=-5\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1 style=\"text-align: left;\" data-type=\"title\">Key Concepts<\/h1>\r\n<ul>\r\n \t<li><strong data-effect=\"bold\">To determine whether a number is a solution to an equation<\/strong>\r\n<ol id=\"fs-id1168345387608\" type=\"1\">\r\n \t<li>Substitute the number in for the variable in the equation.<\/li>\r\n \t<li>Simplify the expressions on both sides of the equation.<\/li>\r\n \t<li>Determine whether the resulting statement is true.\r\n<ul id=\"fs-id1168345449988\">\r\n \t<li>If it is true, the number is a solution.<\/li>\r\n \t<li>If it is not true, the number is not a solution.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">The addition property of equality<\/strong>\r\n<ul id=\"fs-id1168345417795\" data-bullet-style=\"open-circle\">\r\n \t<li>For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>, if \\(a=b\\), then \\(a+c=b+c\\).<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">The subtraction property of equality<\/strong>\r\n<ul id=\"fs-id1168345560039\" data-bullet-style=\"open-circle\">\r\n \t<li>For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>, if \\(a=b\\), then \\(a-c=b-c\\).<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">The division property of equality<\/strong>\r\n<ul>\r\n \t<li>For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>, and \\(c\\ne 0\\), if \\(a=b\\), then \\(\\frac{a}{c}=\\frac{b}{c}\\).<span data-type=\"newline\">\r\n<\/span> When you divide both sides of an equation by any non-zero number, you still have equality.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>The multiplication property of equality<\/strong>\r\n<ul>\r\n \t<li>For any numbers <em>a<\/em>, <em>b<\/em>, and <em>c<\/em>, if <em>a<\/em> = <em>b <\/em>then <em>ac<\/em> = <em>bc<\/em>.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h1>Glossary<\/h1>\r\n<div class=\"textbox shaded\">\r\n\r\n<strong>solution of an equation<\/strong>\r\n\r\nA value of a variable that makes a true statement when substituted into the equation.\r\n\r\n<\/div>\r\n<h1 data-type=\"title\">2.1 Exercise Set<\/h1>\r\n<p id=\"fs-id1169752935790\">In the following exercises, determine whether the given value is a solution to the equation.<\/p>\r\n\r\n<ol>\r\n \t<li>Is \\(y=-4\\) a solution of \\(6y+30=6\\)?<\/li>\r\n \t<li>Is \\(u=3\\) a solution of \\(8u-4=18\\)?<\/li>\r\n<\/ol>\r\n<div id=\"fs-id1168345526003\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345255518\" data-type=\"solution\">\r\n\r\nIn the following exercises, solve each equation using the Subtraction and Addition Properties of Equality.\r\n<ol class=\"twocolumn\" start=\"3\">\r\n \t<li>\\(x+24=35\\)<\/li>\r\n \t<li>\\(y+45=-66\\)<\/li>\r\n \t<li>\\(b+\\frac{1}{4}=\\frac{3}{4}\\)<\/li>\r\n \t<li>\\(p+2.4=-9.3\\)<\/li>\r\n \t<li>\\(a-45=76\\)<\/li>\r\n \t<li>\\(m-18=-200\\)<\/li>\r\n \t<li>\\(x-\\frac{1}{3}=2\\)<\/li>\r\n \t<li>\\(y-3.8=10\\)<\/li>\r\n \t<li>\\(x-165=-420\\)<\/li>\r\n \t<li>\\(z+0.52=-8.5\\)<\/li>\r\n \t<li>\\(q+\\frac{3}{4}=\\frac{1}{2}\\)<\/li>\r\n \t<li>\\(p-\\frac{2}{5}=\\frac{2}{3}\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169749821619\">In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution.<\/p>\r\n\r\n<ol class=\"twocolumn\" start=\"15\">\r\n \t<li>\\(8x=56\\)<\/li>\r\n \t<li>\\(-5c=55\\)<\/li>\r\n \t<li>\\(-809=15y\\)<\/li>\r\n \t<li>\\(-37p=-541\\)<\/li>\r\n \t<li>\\(0.25z=3.25\\)<\/li>\r\n \t<li>\\(-13x=0\\)<\/li>\r\n \t<li>\\(\\frac{x}{4}=35\\)<\/li>\r\n \t<li>\\(-20=\\frac{q}{-5}\\)<\/li>\r\n \t<li>\\(\\frac{y}{9}=-16\\)<\/li>\r\n \t<li>\\(\\frac{m}{-12}=45\\)<\/li>\r\n \t<li>\\(-y=6\\)<\/li>\r\n \t<li>\\(-v=-72\\)<\/li>\r\n \t<li>\\(\\frac{2}{3}y=48\\)<\/li>\r\n \t<li>\\(-\\frac{5}{8}w=40\\)<\/li>\r\n \t<li>\\(-\\frac{2}{5}=\\frac{1}{10}a\\)<\/li>\r\n \t<li>\\(-\\frac{7}{10}x=-\\frac{14}{3}\\)<\/li>\r\n \t<li>\\(\\frac{7}{12}=-\\frac{3}{4}p\\)<\/li>\r\n \t<li>\\(-\\frac{5}{18}=-\\frac{10}{9}u\\)<\/li>\r\n<\/ol>\r\n<p id=\"fs-id1169752884228\">In the following exercises, solve the following equations with constants on both sides.<\/p>\r\n\r\n<ol class=\"twocolumn\" start=\"33\">\r\n \t<li>\\(21k=20k-11\\)<\/li>\r\n \t<li>\\(8x+27=11x\\)<\/li>\r\n \t<li>\\(5z=39-8z\\)<\/li>\r\n \t<li>\\(4x+\\frac{3}{4}=3x\\)<\/li>\r\n \t<li>\\(-11r-8=-7r\\)<\/li>\r\n \t<li>\\(6x-17=5x+2\\)<\/li>\r\n \t<li>\\(21+18f=19f+14\\)<\/li>\r\n \t<li>\\(12q-5=9q-20\\)<\/li>\r\n \t<li>\\(8c+7=-3c-37\\)<\/li>\r\n \t<li>\\(7x-17=-8x+13\\)<\/li>\r\n \t<li>\\(9p+14=6+4p\\)<\/li>\r\n \t<li>\\(3y-4=12-y\\)<\/li>\r\n \t<li>\\(\\frac{7}{4}m-7=\\frac{3}{4}m-13\\)<\/li>\r\n \t<li>\\(11-\\frac{1}{5}a=\\frac{4}{5}a+4\\)<\/li>\r\n \t<li>\\(\\frac{5}{4}a+15=\\frac{3}{4}a-5\\)<\/li>\r\n \t<li>\\(\\frac{3}{5}p+2=\\frac{4}{5}p-1\\)<\/li>\r\n \t<li>\\(13z+6.45=8z+23.75\\)<\/li>\r\n \t<li>\\(6.6x-18.9=3.4x+54.7\\)<\/li>\r\n<\/ol>\r\n<h1 style=\"text-align: left;\">Answers<\/h1>\r\n<ol class=\"threecolumn\">\r\n \t<li>\\(yes\\)<\/li>\r\n \t<li>\\(no\\)<\/li>\r\n \t<li>\\(x = 11\\)<\/li>\r\n \t<li>\\(y = -111\\)<\/li>\r\n \t<li>\\(b = \\frac{1}{2}\\)<\/li>\r\n \t<li>\\(p = -11.7\\)<\/li>\r\n \t<li>\\(a = 121\\)<\/li>\r\n \t<li>\\(m = -182\\)<\/li>\r\n \t<li>\\(x = \\frac{7}{3}\\)<\/li>\r\n \t<li>\\(y = 13.8\\)<\/li>\r\n \t<li>\\(x = -255\\)<\/li>\r\n \t<li>\\(z = -9.02\\)<\/li>\r\n \t<li>\\(q = -1\/4\\)<\/li>\r\n \t<li>\\(p = \\frac{16}{15}\\)<\/li>\r\n \t<li>\\(x=7\\)<\/li>\r\n \t<li>\\(c=-11\\)<\/li>\r\n \t<li>\\(y=-\\frac{809}{15}\\)<\/li>\r\n \t<li>\\(p=\\frac{541}{37}\\)<\/li>\r\n \t<li>\\(z=13\\)<\/li>\r\n \t<li>\\(x=0\\)<\/li>\r\n \t<li>\\(x=140\\)<\/li>\r\n \t<li>\\(q=100\\)<\/li>\r\n \t<li>\\(y=-144\\)<\/li>\r\n \t<li>\\(m=-540\\)<\/li>\r\n \t<li>\\(y=-6\\)<\/li>\r\n \t<li>\\(v=72\\)<\/li>\r\n \t<li>\\(y=72\\)<\/li>\r\n \t<li>\\(w=-64\\)<\/li>\r\n \t<li>\\(a=-4\\)<\/li>\r\n \t<li>\\(x=\\frac{20}{3}\\)<\/li>\r\n \t<li>\\(p=-\\frac{7}{9}\\)<\/li>\r\n \t<li>\\(u=\\frac{1}{4}\\)<\/li>\r\n \t<li>\\(k=-11\\)<\/li>\r\n \t<li>\\(x=9\\)<\/li>\r\n \t<li>\\(z=3\\)<\/li>\r\n \t<li>\\(x=-\\frac{3}{4}\\)<\/li>\r\n \t<li>\\(r=-2\\)<\/li>\r\n \t<li>\\(x=19\\)<\/li>\r\n \t<li>\\(f=7\\)<\/li>\r\n \t<li>\\(q=-5\\)<\/li>\r\n \t<li>\\(c=-4\\)<\/li>\r\n \t<li>\\(x=2\\)<\/li>\r\n \t<li>\\(p=-\\frac{8}{5}\\)<\/li>\r\n \t<li>\\(y=4\\)<\/li>\r\n \t<li>\\(m=-6\\)<\/li>\r\n \t<li>\\(a=7\\)<\/li>\r\n \t<li>\\(a=-40\\)<\/li>\r\n \t<li>\\(p=15\\)<\/li>\r\n \t<li>\\(z=3.46\\)<\/li>\r\n \t<li>\\(x=23\\)<\/li>\r\n<\/ol>\r\n<h1>Attributions<\/h1>\r\nThis chapter has been adapted from \"Solve Equations Using the Subtraction and Addition Properties of Equality\" in\u00a0<a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Adaptation Statement 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 it is expected that you will be able to:<\/p>\n<ul>\n<li>Verify a solution of an equation<\/li>\n<li>Solve equations using the Subtraction and Addition Properties of Equality<\/li>\n<li>Solve equations using the Division and Multiplication Properties of Equality<\/li>\n<li>Solve an equation with variables and constants on both sides<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Verify a Solution of an Equation<\/h1>\n<p id=\"fs-id1168345252532\">Solving an equation is like discovering the answer to a puzzle. The purpose in solving an equation is to find the value or values of the variable that make each side of the equation the same \u2013 so that we end up with a true statement. Any value of the variable that makes the equation true is called a solution to the equation. It is the answer to the puzzle!<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Solution of an equation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A <span data-type=\"term\"><strong>solution of an equation<\/strong><\/span> is a value of a variable that makes a true statement when substituted into the equation.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Determine whether a number is a solution to an equation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169750930815\" class=\"stepwise\" type=\"1\">\n<li>Substitute the number in for the variable in the equation.<\/li>\n<li>Simplify the expressions on both sides of the equation.<\/li>\n<li>Determine whether the resulting equation is true (the left side is equal to the right side).\n<ul id=\"fs-id1168345511300\" data-bullet-style=\"bullet\">\n<li>If it is true, the number is a solution.<\/li>\n<li>If it is not true, the number is not a solution.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\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-id1168345256645\" data-type=\"problem\">\n<p id=\"fs-id1168345302932\">Determine whether <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7e135cd6350a4c21195c621240f7aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/> is a solution of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e9613e6307ac98886ed874d0220ea918_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#53;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"96\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<\/div>\n<div id=\"fs-id1168345196931\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168341917025\">Since a solution to an equation is a value of the variable that makes the equation true, begin by substituting the value of the solution for the variable.<\/p>\n<table id=\"eip-id1169740536663\" style=\"height: 94px; width: 100%;\" summary=\"This figure shows the steps for determining whether x equals 3\/2 is a solution to the algebraic equation 4 x minus 2 equals 2 x plus 1. The figure has two columns, with written instructions on the left and math on the right. At the top of the image in the right column is the equation 4 x minus 2 equals 2 x plus 1. One line down, the instructions on the left say \u201cSubstitute 3\/2 for x\u201d, with 3\/2 written in red. To the right of this instruction is the initial equation with 3\/2 substituted for x: 4, open parenthesis, 3\/2 written in red, close parenthesis, minus 3 may equal 2, open parenthesis, 3\/2 written in red, close parenthesis, plus 1. The next line down, the instructions on the left say \u201cMultiply\u201d. To the right of \u201cMultiply\u201d is the equation with the terms having been multiplied: 6 minus 2 may equal 3 plus 1. One more line down, the instructions on the left say: \u201cSubtract.\u201d To the right of \u201cSubtract\u201d is 4 equals 4, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 35px;\">\n<td style=\"height: 35px; width: 50%;\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7e135cd6350a4c21195c621240f7aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/> for x<\/td>\n<td style=\"height: 35px; width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-da89c2e1f3eb7a3d11b7cfbf8ab4e9d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#40;&#45;&#51;&#41;&#43;&#53;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"122\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"height: 26px; width: 50%;\">Multiply.<\/td>\n<td style=\"height: 26px; width: 50%;\">\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3a783b7ea2fa59d6436179b971a36fd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#43;&#53;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"108\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"height: 17px; width: 50%;\">Simplify.<\/td>\n<td style=\"height: 17px; width: 50%;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3e084d1c79989c1da5066a68902d7079_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"68\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168345366859\">Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7e135cd6350a4c21195c621240f7aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/> results in a true statement (-7 is in fact equal to -7), -3 is a solution to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e9613e6307ac98886ed874d0220ea918_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#53;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"96\" style=\"vertical-align: -2px;\" \/>.<\/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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345399266\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345544118\" data-type=\"exercise\">\n<div id=\"fs-id1168345250738\" data-type=\"problem\">\n<p id=\"fs-id1168345397818\">Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-552d8ed773e160e229551b39aff39445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/> a solution of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fc68b4bb00cfaf8a6fd07dc1e4a733b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#121;&#45;&#50;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -4px;\" \/>?<\/p>\n<\/div>\n<div id=\"fs-id1168345211810\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345442278\">no<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836335358\">There are many types of equations. In this chapter we will focus on solving <span data-type=\"term\">linear equations.<\/span><\/p>\n<div id=\"fs-id1167836515647\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Linear Equation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A <strong data-effect=\"bold\">linear equation<\/strong> is a first degree equation in one variable that can be written\u00a0as:<\/p>\n<div id=\"fs-id1167829644900\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b2c5a97201db17cfbef7b7550aa81e23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#120;&#43;&#98;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" style=\"vertical-align: -2px;\" \/>, where <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em> are real numbers and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6d28cb478bd8b6abe7d9573551313d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"46\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Solve Equations Using the Subtraction and Addition Properties of Equality<\/h1>\n<div id=\"CNX_ElemAlg_Figure_02_01_003_img_new\" class=\"bc-figure figure\">\n<p id=\"fs-id1168345374564\">Let us review all the properties that will help us to solve equations algebraically. The first one is the <strong>Subtraction Property of Equality<\/strong>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Subtraction Property of Equality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1168345346971\">For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>,<\/p>\n<div id=\"fs-id1168345360391\" class=\"unnumbered\" style=\"text-align: center;\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bd48deec7bb6516786f529c7c18ce828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#45;&#99;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#45;&#99;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"189\" style=\"vertical-align: -11px;\" \/><\/div>\n<p id=\"fs-id1168345328049\">When you subtract the same quantity from both sides of an equation, you still have equality.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345328756\">Let\u2019s see how to use this property to solve an equation. Remember, the goal is to isolate the variable on one side of the equation. And we check our solutions by substituting the value into the equation to make sure we have a true statement.<\/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-id1168345197461\" data-type=\"problem\">\n<p id=\"fs-id1168345559741\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6b79a0c5aec365510dba265bfc3b5271_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#51;&#55;&#61;&#45;&#49;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"108\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345510395\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div class=\"hanging-indent\" data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168345287978\">To get <em data-effect=\"italics\">y<\/em> by itself, we will undo the addition of 37 by using the Subtraction Property of Equality.<\/p>\n<table id=\"eip-id1169752878128\" style=\"height: 109px; width: 100%;\" summary=\"This 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 x plus 3 equals 8. One line down on the left, the instructions say: \u201cFirst, we took away three from each side.\u201d To the right of this sentence is the same equation with 3 being subtracted from both sides: x plus 3 minus 3 equals 8 minus 3, with minus 3 written in red on both sides. Another line down on the left, the instructions say: \u201cThen we were left with five.\u201d To the right of this sentence is the answer to the equation: x equals five.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"height: 17px; width: 63.7188%;\"><\/td>\n<td style=\"height: 17px; width: 36.0544%;\"><span id=\"eip-id1169752980473\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2020\/08\/CNX_ElemAlg_Figure_02_01_006d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 19px;\">\n<td style=\"height: 19px; width: 63.7188%;\">Subtract 37 from each side to \u2018undo\u2019 the addition.<\/td>\n<td style=\"height: 19px; width: 36.0544%;\"><span id=\"eip-id1169741763989\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_006e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 63.7188%;\">Simplify.<\/td>\n<td style=\"height: 18px; width: 36.0544%;\"><span id=\"eip-id1169752938273\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_006f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 63.7188%;\">Check:<\/td>\n<td style=\"height: 18px; width: 36.0544%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 63.7188%;\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bcd3281dc9745ad53b5f048b5a6a4423_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"height: 15px; width: 36.0544%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 63.7188%;\"><\/td>\n<td style=\"height: 22px; width: 36.0544%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168345539173\">Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bcd3281dc9745ad53b5f048b5a6a4423_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"65\" style=\"vertical-align: -4px;\" \/> makes <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-30ffcdc7c755a8d8fa0d11a002cac839_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#51;&#55;&#61;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -4px;\" \/> a true statement, we have the solution to this equation.<\/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 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345300888\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345441260\" data-type=\"exercise\">\n<div id=\"fs-id1168345636236\" data-type=\"problem\">\n<p id=\"fs-id1168345337170\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0eac7d92db3824efbed0f8506d84be7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#49;&#57;&#61;&#45;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"105\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345375153\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168341852442\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cf5de9a3f6e561fad3cb9a9e2fafa308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#52;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345300888\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345441260\" data-type=\"exercise\">What happens when an equation has a number subtracted from the variable, as in the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cfe518e9ce6c1f5cedf6325bef7a1459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#53;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"73\" style=\"vertical-align: 0px;\" \/>? We use another property to solve equations when a number is subtracted from the variable. We want to isolate the variable, so to \u2018undo\u2019 the subtraction we will add the number to both sides. We use the <strong>Addition Property of Equality<\/strong>.<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Addition Property of Equality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1168345274390\">For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>,<\/p>\n<div id=\"fs-id1168345384352\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-76bde772fe605f3de14b2b20583a5f76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#43;&#99;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#43;&#99;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"189\" style=\"vertical-align: -13px;\" \/><\/div>\n<p id=\"fs-id1168345287184\">When you add the same quantity to both sides of an equation, you still have equality.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345550229\">In Example 2, 37 was added to the <em data-effect=\"italics\">y<\/em> and so we subtracted 37 to \u2018undo\u2019 the addition. In Example 3, we will need to \u2018undo\u2019 subtraction by using the <span class=\"no-emphasis\" data-type=\"term\">Addition Property of Equality<\/span>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345425326\" data-type=\"problem\">\n<p id=\"fs-id1168345325321\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c6eea7c18eb51c08c35f43040d1c55c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#50;&#56;&#61;&#45;&#51;&#55;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"108\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345240578\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169750584873\" style=\"height: 107px; width: 100%;\" summary=\"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 a minus 28 equals negative 37. One line down on the left, the instructions say: \u201cAdd 28 to each side to \u2018undo\u2019 the subtraction.\u201d To the right of this sentence is the same equation with 28 being added to both sides: a minus 28 plus 28 equals negative 37 plus 28, with plus 28 written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this sentence is the answer to the equation: a equals negative 9. Two lines down, the instructions say \u201cCheck\u201d. To the right of this word is the original equation again: a minus 28 equals negative 37. Then the instructions say to substitute negative 9 for a, and to the right is the equation with negative 9 substituted in for a: negative 9 (written in red) minus 28 equals negative 37. Below this is the equation negative 37 equals negative 37, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 262.406px;\"><\/td>\n<td style=\"height: 14px; width: 221.406px;\"><span id=\"eip-id1169752949939\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 262.406px;\">Add 28 to each side to \u2018undo\u2019 the subtraction.<\/td>\n<td style=\"height: 15px; width: 221.406px;\"><span id=\"eip-id1169752907850\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 262.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 221.406px;\"><span id=\"eip-id1169753102934\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 262.406px;\">Check:<\/td>\n<td style=\"height: 14px; width: 221.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 262.406px;\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5e6e9dbd895daf6ba8c33c66f79229d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 14px; width: 221.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 262.406px;\"><\/td>\n<td style=\"height: 22px; width: 221.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 262.406px;\">The solution to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-630b651483666db2f1f5e3100f4f214f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#50;&#56;&#61;&#45;&#51;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"104\" style=\"vertical-align: 0px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-741fe18dbc4eeacaa38b0ba8779ed623_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#57;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"60\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"height: 14px; width: 221.406px;\"><\/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 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345404706\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345342475\" data-type=\"exercise\">\n<div id=\"fs-id1168345302182\" data-type=\"problem\">\n<p id=\"fs-id1168345384195\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bc0eda3ad6480f979c04b08e83da9787_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#54;&#49;&#61;&#45;&#55;&#53;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"110\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345485609\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345531414\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b31862f44b7e4626ab3b87190f2bc646_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345442219\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345250265\" data-type=\"exercise\">\n<div id=\"fs-id1168345387536\" data-type=\"solution\">\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-id1168345293756\" data-type=\"problem\">\n<p id=\"fs-id1168345669119\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5b82f8f44c932f735f6c16ed92d47232_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"81\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345667330\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169752186691\" style=\"width: 100%;\" summary=\"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 x minus five eighths equals three quarters. One line down on the left, the instructions say: \u201cUse the Addition Property of Equality.\u201d To the right of this sentence is the same equation with five eighths being added to both sides: x minus five eighths plus five eighths equals three quarters plus five eighths, with plus five eighths written in red on both sides of the equal sign. The next line down on the left the instructions say: \u201cFind the LCD to add the fractions on the right.\u201d To the right of this sentence is the equation: x minus five eighths plus five eighths equals six eighths plus five eighths. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this sentence is the answer to the equation: x equals eleven eighths. Two lines down, the instructions say \u201cCheck\u201d. To the right of this instruction is the original equation again: x minus five eighths equals three quarters. Another line down, the instructions say to substitute 11 eighths for x, and to the right is the equation with 11 eighths substituted in for x: 11 eights (written in red) minus five eighths might equal three quarters. The instructions then say \u201cSubtract\u201d. To the right of this instruction is the equation: six eighths might equal three quarters. One more line down, the instructions say \u201cSimplify\u201d. To the right of that instruction is three quarters equals three quarters, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 72.3356%;\"><\/td>\n<td style=\"width: 27.4376%;\"><span id=\"eip-id1169752197549\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 72.3356%;\">Use the Addition Property of Equality.<\/td>\n<td style=\"width: 27.4376%;\"><span id=\"eip-id1169751926086\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 72.3356%;\">Find the LCD to add the fractions on the right.<\/td>\n<td style=\"width: 27.4376%;\"><span id=\"eip-id1169745434963\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 72.3356%;\">Simplify.<\/td>\n<td style=\"width: 27.4376%;\"><span id=\"eip-id1169751866214\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 72.3356%;\">Check:<\/td>\n<td style=\"width: 27.4376%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 72.3356%;\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a277a2138c989786937b523a1877a396_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#56;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"55\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 27.4376%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 72.3356%;\">Subtract.<\/td>\n<td style=\"width: 27.4376%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 72.3356%;\">Simplify.<\/td>\n<td style=\"width: 27.4376%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_008h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 72.3356%;\">The solution to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7dce3bebdb5f5fd23cf76d45fb209808_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a277a2138c989786937b523a1877a396_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#56;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"55\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 27.4376%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345414504\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345239712\" data-type=\"exercise\">\n<div id=\"fs-id1168345574727\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345414504\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345239712\" data-type=\"exercise\">\n<div id=\"fs-id1168345574727\" data-type=\"problem\">\n<p id=\"fs-id1168345297557\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7070130208245c3997f4fb6fe131e062_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#45;&#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;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345414808\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345743306\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a3624f71df136c080f9533a77d3929da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#112;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"89\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168341962891\">The next example will be an equation with decimals.<\/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-id1168345217297\" data-type=\"problem\">\n<p id=\"fs-id1168341862678\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a418d08feef75ac7a5716a14afa0019c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#48;&#46;&#54;&#51;&#61;&#45;&#52;&#46;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"128\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345251888\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169754089552\" style=\"height: 96px; width: 100%;\" summary=\"This 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 n minus 0.63 equals negative 4.2. One line down on the left, the instructions say: \u201cUse the Addition Property of Equality.\u201d To the right of this sentence is the same equation with 0.63 being added to both sides: n minus 0.63 plus 0.63 equals negative 4.2 plus 0.63, with plus 0.63 written in red on both sides. Another line down on the left, the instructions say: \u201cAdd.\u201d To the right of this sentence is the answer to the equation: n equals negative 3.57. Two lines down, the instructions say \u201cCheck\u201d. To the right of this word is the original equation again: n minus 0.63 equals negative 4.2. Then the instructions say \u201cLet n equal negative 3.57\u201d, and to the right is the equation with negative 3.57 substituted in for n: negative 3.57 (written in red) minus 0.63 might equal negative 4.2. Below this is the equation negative 4.2 equals negative 4.2 with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 348.406px;\"><\/td>\n<td style=\"height: 15px; width: 278.406px;\"><span id=\"eip-id1169745448207\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 348.406px;\">Use the Addition Property of Equality.<\/td>\n<td style=\"height: 14px; width: 278.406px;\"><span id=\"eip-id1169752211122\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 348.406px;\">Add.<\/td>\n<td style=\"height: 14px; width: 278.406px;\"><span id=\"eip-id1169754129874\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 348.406px;\">Check:<\/td>\n<td style=\"height: 15px; width: 278.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 348.406px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c671fc719ef3366f1a7171f6cbcddfc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#45;&#51;&#46;&#53;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"80\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"height: 23px; width: 278.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 348.406px;\"><\/td>\n<td style=\"height: 15px; width: 278.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_01_009c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/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<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345409282\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345638730\" data-type=\"exercise\">\n<div id=\"fs-id1168345293173\" data-type=\"problem\">\n<p id=\"fs-id1168345301399\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8b2de3d11fe3101ec50601be1d7d5fdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#45;&#48;&#46;&#52;&#55;&#61;&#45;&#50;&#46;&#49;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"125\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168345275306\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345293683\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8b3bc3914f461cc4246bd4db4a16de4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#45;&#49;&#46;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"77\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\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\/businesstechnicalmath\/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\/businesstechnicalmath\/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.To solve those kind of equations we will use the <strong>Division Property of Equality<\/strong>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">The Division Property of Equality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1168344074804\">For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>,<\/p>\n<div id=\"fs-id1168344315866\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-28f98db39674ce9fd3d77897ea876432_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"136\" style=\"vertical-align: -17px;\" \/><\/div>\n<div data-type=\"equation\" data-label=\"\"><\/div>\n<div class=\"unnumbered\" data-type=\"equation\" data-label=\"\">When you divide both sides of an equation by any non-zero number, you still have equality.<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344149007\">The goal in solving an equation is to \u2018undo\u2019 the operation on the variable. In the next example, the variable is multiplied by 5, so we will divide both sides by 5 to \u2018undo\u2019 the multiplication.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344214265\" data-type=\"problem\">\n<p id=\"fs-id1168344192993\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6fee90772b35ad62689cfb52fac5ef61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#61;&#45;&#50;&#55;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"79\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168344189039\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169748428935\" style=\"height: 277px; width: 100%; width: 100%;\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the left, the instructions say: \u201cTo isolate x, \u2018undo\u2019 the multiplication by 5.\u201d To the right of this sentence is the equation 5 x equals negative 27. The next line down on the left, the instructions say: \u201cDivide to \u2018undo\u2019 the multiplication.\u201d To the right of this sentence is the same equation with both sides divided by 5: 5 x over 5 equals negative 27 over 5, with divided by 5 written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this sentence is the answer to the equation: x equals negative 27\/5. Another line down to the left, the instructions say: Check\u201d. To the right of this instruction is the original equation again: 5x equals negative 27. Another line down, the instructions say to substitute negative 27\/5 for x, and to the right is the equation with negative 27\/5 substituted for x: 5 times negative 27\/5, with negative 27\/5 in parentheses and written in red, equals negative 27. Below this is the equation negative 27 equals negative 27, with a check mark next to it. Another line down, in the right-hand column, is a sentence that reads \u201cSince this is a true statement x = -27\/5 is the solution to 5x = -27.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 71.2018%;\">To isolate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>, \u201cundo\u201d the multiplication by 5.<\/td>\n<td style=\"width: 28.5714%;\"><span id=\"eip-id1169753966731\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" class=\"alignleft\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.2018%;\">Divide to \u2018undo\u2019 the multiplication.<\/td>\n<td style=\"width: 28.5714%;\"><span id=\"eip-id1169753966753\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" class=\"alignleft\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.2018%;\">Simplify.<\/td>\n<td style=\"width: 28.5714%;\"><span id=\"eip-id1169754099104\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" class=\"alignleft\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.2018%;\">Check:<\/td>\n<td style=\"width: 28.5714%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.2018%;\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7f8a75b7068a4d546f3438fbeea9a547_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"29\" style=\"vertical-align: -6px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a9cc293b28f198c32e0356b52e2e23bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"14\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 28.5714%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.2018%;\"><\/td>\n<td style=\"width: 28.5714%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.2018%;\">Since this is a true statement, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-846e539951819c1253664399c2a9f090_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"63\" style=\"vertical-align: -6px;\" \/><span data-type=\"newline\"><br \/>\n<\/span>is the solution to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c756b10b3cc5ec3237dc0eea613ca904_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#61;&#45;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"75\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 28.5714%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344149474\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344097238\" data-type=\"exercise\">\n<div id=\"fs-id1168344395192\" data-type=\"problem\">\n<p id=\"fs-id1168343187974\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-651adb2dbe0420507ce71ccba00bf28e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#121;&#61;&#45;&#52;&#49;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168344193579\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168343188649\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cec94b673ca63de503baae5a0626eaa7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#52;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344342565\">Consider the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-53e1b8d3f97fbf1f54fab0f8c9b3213a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#52;&#125;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -6px;\" \/>. We want to know what number divided by 4 gives 3. So to \u201cundo\u201d the division, we will need to multiply by 4. The <strong>Multiplication Property of Equality<\/strong> will allow us to do this. This property says that if we start with two equal quantities and multiply both by the same number, the results are equal.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">The Multiplication Property of Equality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1168344600409\">For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>,<\/p>\n<div id=\"fs-id1168344202393\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-acb7d218283a3941e357e5cf2bfb6d5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#99;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#99;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"146\" style=\"vertical-align: -11px;\" \/><\/div>\n<\/div>\n<\/div>\n<p>If you multiply both sides of an equation by the same number, you still have equality.<\/p>\n<div id=\"fs-id1168343023900\" data-type=\"note\">\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-id1168344229502\" data-type=\"problem\">\n<p id=\"fs-id1168343195079\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-61b679aaf66442680a4ad2acc3780b18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#45;&#55;&#125;&#61;&#45;&#49;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"79\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168344374013\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168344515851\">Here <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> is divided by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 must multiply by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 130px;\">\n<tbody>\n<tr style=\"height: 34px;\">\n<td style=\"width: 50%; height: 34px;\"><\/td>\n<td style=\"width: 50%; height: 34px;\"><span id=\"eip-id1169752958286\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">Multiply both sides by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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 style=\"width: 50%; height: 16px;\"><span id=\"eip-id1169753238745\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">Multiply.<\/td>\n<td style=\"width: 50%; height: 16px;\"><span id=\"eip-id1169750595124\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">Simplify.<\/td>\n<td style=\"width: 50%; height: 16px;\"><span id=\"eip-id1169750876711\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">Check.<\/td>\n<td style=\"width: 50%; height: 16px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bf663674bbaa08459dcf603c24995c8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#45;&#55;&#125;&#61;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-80da698073565757625bb4cd70b13fd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#57;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td style=\"width: 50%; height: 16px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">Divide<\/td>\n<td style=\"width: 50%; height: 16px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_005b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344287502\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343173477\" data-type=\"exercise\">\n<div id=\"fs-id1168344120375\" data-type=\"problem\">\n<p id=\"fs-id1168343024054\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7a93c792643a2ea080ad04ee6d305c56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#45;&#55;&#125;&#61;&#45;&#52;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168343007643\" data-type=\"solution\">\n<details open=\"open\">\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344312078\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168343160986\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343174664\" data-type=\"exercise\">\n<div id=\"fs-id1168344449255\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344115117\" data-type=\"problem\">\n<p id=\"fs-id1168344249917\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11a6973f5920de4ea9ca051967d9e133_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#61;&#49;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"65\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168344333366\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168344440965\">Since the product of a number and its reciprocal is 1, our strategy will be to isolate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-469181e98c8ec4b1bce8f57ea4ba4e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<table id=\"eip-id1169747451024\" class=\"grid\" style=\"width: 100%; height: 280px;\" summary=\"This 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 three-fourths x equals 12. One line down on the left, the instructions say: \u201cMultiply by the reciprocal of \u00be.\u201d To the right of this sentence is the same equation multiplied by 4\/3 on both sides: 4\/3 times three-fourths x equals 4\/3 times 12, with times 4\/3 written in red on both sides. Another line down on the left, the instructions say: \u201cReciprocals multiply to 1.\u201d To the right of this sentence is the equation 1x equals 4\/3 times 12. Another line down on the left, the instructions say: \u201cMultiply.\u201d To the right of this instruction is the answer to the equation: x equals 16. Below this is the text: \u201cNotice that we could have divided both sides of the equation three-fourths x equals 12 by \u00be to isolate x. While this would work, most people would find multiplying by the reciprocal easier.\u201d Two lines down, the instructions say: \u201cCheck\u201d. To the right of this word is the original equation again: three-fourths x equals 12. Then the instructions say: \u201cSubstitute x equals 16,\u201d and to the right is the equation with 16 substituted in for x: \u00be times 16 (written in red) might equal 12. Below this is the equation 12 equals 12, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 31px;\">\n<td style=\"width: 68.7074%; height: 31px;\"><\/td>\n<td style=\"width: 31.0658%; height: 31px;\"><span id=\"eip-id1169750571487\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 31px;\">\n<td style=\"width: 68.7074%; height: 31px;\">Multiply by the reciprocal of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-469181e98c8ec4b1bce8f57ea4ba4e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td style=\"width: 31.0658%; height: 31px;\"><span id=\"eip-id1169753253515\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 31px;\">\n<td style=\"width: 68.7074%; height: 31px;\">Reciprocals multiply to 1.<\/td>\n<td style=\"width: 31.0658%; height: 31px;\"><span id=\"eip-id1169751034763\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 68.7074%; height: 14px;\">Multiply.<\/td>\n<td style=\"width: 31.0658%; height: 14px;\"><span id=\"eip-id1169750889650\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"height: 62px; width: 68.7074%;\">Notice that we could have divided both sides of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-51b21b75a5bb362ec5be43e45f397f88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-469181e98c8ec4b1bce8f57ea4ba4e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#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\/businesstechnicalmath\/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, most people would find multiplying by the reciprocal easier.<\/td>\n<td style=\"width: 31.0658%;\"><\/td>\n<\/tr>\n<tr style=\"height: 32px;\">\n<td style=\"width: 68.7074%; height: 32px;\">Check:<\/td>\n<td style=\"width: 31.0658%; height: 32px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 79px;\">\n<td style=\"width: 68.7074%; height: 79px;\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d64a5cf83814d9888bfab8bf27403b02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td style=\"width: 31.0658%; height: 79px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_02_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/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 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344208698\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344619809\" data-type=\"exercise\">\n<div id=\"fs-id1168343051295\" data-type=\"problem\">\n<p id=\"fs-id1168344323848\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7d0f6d5eb8e749d1b0bbca592450b11f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#110;&#61;&#49;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"65\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168343030336\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344316594\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e1fe4ad9268dc2da36d4d8ef725691d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"51\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168343128927\">Now we have covered all four properties of equality\u2014subtraction, addition, division, and multiplication. We\u2019ll list them all together here for easy reference.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Equality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343141934\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-28a669e985737cb1d56a402e401da07d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#117;&#98;&#116;&#114;&#97;&#99;&#116;&#105;&#111;&#110;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#32;&#111;&#102;&#32;&#69;&#113;&#117;&#97;&#108;&#105;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#100;&#100;&#105;&#116;&#105;&#111;&#110;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#32;&#111;&#102;&#32;&#69;&#113;&#117;&#97;&#108;&#105;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#111;&#114;&#32;&#97;&#110;&#121;&#32;&#114;&#101;&#97;&#108;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#111;&#114;&#32;&#97;&#110;&#121;&#32;&#114;&#101;&#97;&#108;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#45;&#99;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#45;&#99;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#43;&#99;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#43;&#99;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#105;&#118;&#105;&#115;&#105;&#111;&#110;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#32;&#111;&#102;&#32;&#69;&#113;&#117;&#97;&#108;&#105;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#117;&#108;&#116;&#105;&#112;&#108;&#105;&#99;&#97;&#116;&#105;&#111;&#110;&#32;&#80;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#32;&#111;&#102;&#32;&#69;&#113;&#117;&#97;&#108;&#105;&#116;&#121;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#111;&#114;&#32;&#97;&#110;&#121;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#92;&#110;&#101;&#32;&#48;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#111;&#114;&#32;&#97;&#110;&#121;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#102;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#44;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#99;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#99;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"173\" width=\"601\" style=\"vertical-align: -83px;\" \/><\/p>\n<p>When you add, subtract, multiply, or divide the same quantity from both sides of an equation, you still have equality.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Now we will use those properties to solve equations in which the variable terms, or constant terms, or both are on both sides of the equation.<\/p>\n<h1 id=\"fs-id1168344108924\">Solve Equations with Variables and Constants on Both Sides<\/h1>\n<p id=\"fs-id1168344086598\">Our strategy will involve choosing one side of the equation to be the \u201cvariable side\u201d, and the other side of the equation to be the \u201cconstant side.\u201d Then, we will use the Subtraction and Addition Properties of Equality to get all the variable terms together on one side of the equation and the constant terms together on the other side.<\/p>\n<p id=\"fs-id1168344344951\">By doing this, we will transform the equation that began with variables and constants on both sides into the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dda3fba1a3da1b11dea742ec9cd5015c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#120;&#61;&#98;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: 0px;\" \/> We already know how to solve equations of this form by using the Division or Multiplication Properties of Equality.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-492f0006debc2a6b593df2a074ea2246_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#121;&#45;&#57;&#61;&#51;&#49;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"94\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>In this equation, the variable is found only on the left side. It makes sense to call the left side the \u201cvariable\u201d side. Therefore, the right side will be the \u201cconstant\u201d side. We will write the labels above the equation to help us remember what goes where. Since the left side is the \u201cvariable\u201d side, the 9 is out of place. It is subtracted from the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6f2cb48f7e495efa9bdaa8ee706ed1d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"18\" style=\"vertical-align: -4px;\" \/>, so to \u201cundo\u201d subtraction, add 9 to both sides. Remember, whatever you do to the left, you must do to the right.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 111px;\">\n<tbody>\n<tr style=\"height: 42px;\">\n<td style=\"width: 50%; height: 42px;\"><\/td>\n<td style=\"width: 50%; height: 42px;\"><span id=\"eip-id1168184743090\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 21px;\">\n<td style=\"width: 50%; height: 21px;\">Add 9 to both sides.<\/td>\n<td style=\"width: 50%; height: 21px;\"><span id=\"eip-id1168184743111\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">Simplify.<\/td>\n<td style=\"width: 50%; height: 16px;\"><span id=\"eip-id1168184848828\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/> <\/span><\/p>\n<p><span id=\"eip-id1168184848828\" data-type=\"media\" data-alt=\".\">The variables are now on one side and the constants on the other. We continue from here as we did earlier.<br \/>\n<\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">Divide both sides by 8.<\/td>\n<td style=\"width: 50%; height: 16px;\"><span id=\"eip-id1168184848861\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 50%; height: 16px;\">Simplify.<\/td>\n<td style=\"width: 50%; height: 16px;\"><span id=\"eip-id1168184848881\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Check.<\/td>\n<td style=\"width: 50%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-39af43abd99adaf051fde7775af522c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td style=\"width: 50%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_004d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div id=\"fs-id1168344522317\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344301536\" data-type=\"exercise\">\n<div id=\"fs-id1168343007231\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344120441\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343140153\" data-type=\"exercise\">\n<div id=\"fs-id1168344525168\" data-type=\"problem\">\n<p id=\"fs-id1168344285180\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4de92ec91d09f6953343044c70d3f4bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;&#45;&#57;&#61;&#49;&#54;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"94\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1168344475410\" data-type=\"solution\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-39af43abd99adaf051fde7775af522c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>What if there are variables on both sides of the equation? For equations like this, begin as we did above\u2014choose a \u201cvariable\u201d side and a \u201cconstant\u201d side, and then use the subtraction and addition properties of equality to collect all variables on one side and all constants on the other side.<\/p>\n<div id=\"fs-id1168344071798\" class=\"bc-section section\" data-depth=\"1\">\n<div id=\"fs-id1168343024055\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168342980814\" data-type=\"exercise\">\n<div id=\"fs-id1168344505212\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344198024\" data-type=\"problem\">\n<p id=\"fs-id1168344193531\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3c29331fb62171ae987334f19f7e6365_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;&#45;&#57;&#61;&#56;&#121;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168344363684\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168344523496\">The only constant is on the left and the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>\u2019s are on both sides. Let\u2019s leave the constant on the left and get the variables to the right.<\/p>\n<table id=\"fs-id1167270176565\" style=\"width: 100%; height: 245px;\" summary=\"This 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 5 y minus 9 equals 8 y. The left side of the equation is labeled \u201cconstant\u201d, written in red, and the right side of the equation is labeled \u201cvariable\u201d, written in red. One line down on the left, the instructions say: \u201cSubtract 5y from both sides.\u201d To the right of this sentence is the same equation with 5 y subtracted from both sides: 5 y minus 5 y minus 9 equals 8 y minus 5 y, with minus 5 y written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the equation negative 9 equals 3y. Another line down on the left, the instructions say: \u201cWe have the y\u2019s on the right and the constants on the left. Divide both sides by 3.\u201d To the right of this instruction is the same equation divided by 3 on both sides: negative 9 over 3 equals 3y over 3, with the divided by 3 written in red on both sides. The next line down on the left, the instructions say: \u201cSimplify,\u201d and to the right of this instruction is the answer to the equation: negative 3 equals y. Another line down on the left, the instructions say: \u201cCheck\u201d. To the right of this word is the original equation again: 5 y minus 9 equals 8 y. Then the instructions say: \u201cLet y equal negative 3,\u201d and to the right is the equation with negative 3 substituted in for y: 5 times negative 3, with negative 3 written in red, minus 9 might equal 8 times negative 3, with negative 3 written in red. Below this is the equation negative 15 minus 9 might equal negative 24. Below this is the equation negative 24 equals negative 24, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 39px;\">\n<td style=\"width: 64.1723%; height: 39px;\"><\/td>\n<td style=\"width: 35.6009%; height: 39px;\"><span id=\"fs-id1167270305902\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008e_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 21px;\">\n<td style=\"width: 64.1723%; height: 21px;\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ced6e13bb9f8c850f4b8c91f46ef4889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"18\" style=\"vertical-align: -4px;\" \/> from both sides.<\/td>\n<td style=\"width: 35.6009%; height: 21px;\"><span id=\"fs-id1167269944753\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008f_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 21px;\">\n<td style=\"width: 64.1723%; height: 21px;\">Simplify.<\/td>\n<td style=\"width: 35.6009%; height: 21px;\"><span id=\"fs-id1167269976413\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008g_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 38px;\">\n<td style=\"width: 64.1723%; height: 38px;\">We have the <em data-effect=\"italics\">y<\/em>\u2019s on the right and the<span data-type=\"newline\"><br \/>\n<\/span>constants on the left. Divide both sides by 3.<\/td>\n<td style=\"width: 35.6009%; height: 38px;\"><span id=\"fs-id1167265560237\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008h_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 21px;\">\n<td style=\"width: 64.1723%; height: 21px;\">Simplify.<\/td>\n<td style=\"width: 35.6009%; height: 21px;\"><span id=\"fs-id1167270021089\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008i_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 21px;\">\n<td style=\"width: 64.1723%; height: 21px;\">Check:<\/td>\n<td style=\"width: 35.6009%; height: 21px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 64.1723%; height: 28px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c969882b6218a3357058a4f00796c77f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 35.6009%; height: 28px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 64.1723%; height: 24px;\"><\/td>\n<td style=\"width: 35.6009%; height: 24px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 64.1723%; height: 16px;\"><\/td>\n<td style=\"width: 35.6009%; height: 32px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_008d_img_new.jpg\" alt=\".\" width=\"143\" height=\"19\" data-media-type=\"image\/jpeg\" \/><\/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 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344511607\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168343003381\" data-type=\"exercise\">\n<div id=\"fs-id1168344156204\" data-type=\"problem\">\n<p id=\"fs-id1168343046778\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-82367867e758ad745b74a582d6e0af91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#112;&#45;&#49;&#52;&#61;&#53;&#112;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"103\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168343054322\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344120415\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-99a7b42f8c8ecd0d95f5eaf3d506913b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344149630\">The next example will be the first to have variables and constants on both sides of the equation. It may take several steps to solve this equation, so we need a clear and organized strategy.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Solve Equations with Variables and Constants on Both Sides<\/div>\n<div data-type=\"exercise\">\n<div id=\"fs-id1168344198759\" data-type=\"problem\">\n<p id=\"fs-id1168344072753\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-65af5b40c25bd00cc92a6dd1d6a8dffb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#53;&#61;&#54;&#120;&#43;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"127\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168344082079\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p><span id=\"fs-id1168344202405\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads: \u201cStep 1. Choose which side will the \u201cvariable\u201d side\u2014the other side will be the \u201cconstant\u201d side.\u201d The text in the second cell reads: \u201cThe variable terms are 7 x and 6 x. Since 7 is greater than 6, we will make the left side the \u201cx\u201d side and so the right side will be the \u201cconstant\u201d side.\u201d The third cell contains the equation 7 x plus 5 equals 6 x plus 2, and the left side of the equation is labeled \u201cvariable\u201d written in red, and the right side of the equation is labeled \u201cconstant\u201d written in red.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_010a_img_new.jpg\" alt=\"This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. On the top row of the table, the first cell on the left reads: \u201cStep 1. Choose which side will the \u201cvariable\u201d side\u2014the other side will be the \u201cconstant\u201d side.\u201d The text in the second cell reads: \u201cThe variable terms are 7 x and 6 x. Since 7 is greater than 6, we will make the left side the \u201cx\u201d side and so the right side will be the \u201cconstant\u201d side.\u201d The third cell contains the equation 7 x plus 5 equals 6 x plus 2, and the left side of the equation is labeled \u201cvariable\u201d written in red, and the right side of the equation is labeled \u201cconstant\u201d written in red.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168344074856\" data-type=\"media\" data-alt=\"In the second row of the table, the first cell says: \u201cStep 2. Collect the variable terms to the \u201cvariable\u201d side of the equation, using the addition or subtraction property of equality.\u201d In the second cell, the instructions say: \u201c With the right side as the \u201cconstant\u201d side, the 6x is out of place, so subtract 6x from both sides. Combine like terms. Now the variable is only on the left side!\u201d The third cell contains the original equation with 6x subtracted from both sides: 7 x minus 6 x plus 5 equals 6 x minus 6 x plus 2, with \u201cminus 6 x\u201d written in red on both sides. Below this is the same equation with like terms combined: x plus 5 equals 2.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_010b_img_new.jpg\" alt=\"In the second row of the table, the first cell says: \u201cStep 2. Collect the variable terms to the \u201cvariable\u201d side of the equation, using the addition or subtraction property of equality.\u201d In the second cell, the instructions say: \u201c With the right side as the \u201cconstant\u201d side, the 6x is out of place, so subtract 6x from both sides. Combine like terms. Now the variable is only on the left side!\u201d The third cell contains the original equation with 6x subtracted from both sides: 7 x minus 6 x plus 5 equals 6 x minus 6 x plus 2, with \u201cminus 6 x\u201d written in red on both sides. Below this is the same equation with like terms combined: x plus 5 equals 2.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168344349070\" data-type=\"media\" data-alt=\"In the third row of the table, the first cell says: \u201cStep 3. Collect all the constants to the other side of the equation, using the addition or subtraction property of equality.\u201d In the second cell, the instructions say: \u201cThe right side is the \u201cconstant\u201d side, so the 5 is out of place. Subtract 5 from both sides. Simplify.\u201d The third cell contains the equation x plus 5 minus 5 equals 2 minus 5, with \u201cminus 5\u201d written in red on both sides. Below this is the answer to the equation: x equals negative 3.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_010c_img_new.jpg\" alt=\"In the third row of the table, the first cell says: \u201cStep 3. Collect all the constants to the other side of the equation, using the addition or subtraction property of equality.\u201d In the second cell, the instructions say: \u201cThe right side is the \u201cconstant\u201d side, so the 5 is out of place. Subtract 5 from both sides. Simplify.\u201d The third cell contains the equation x plus 5 minus 5 equals 2 minus 5, with \u201cminus 5\u201d written in red on both sides. Below this is the answer to the equation: x equals negative 3.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168344504811\" data-type=\"media\" data-alt=\"In the fourth row of the table, the first cell says: \u201cStep 4. Make the coefficient of the variable equal 1, using the Multiplication or Division Property of Equality.\u201d In the second cell, the instructions say: \u201cThe coefficient of x is one. The equation is solved.\u201d The third cell is blank.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_010d_img_new.jpg\" alt=\"In the fourth row of the table, the first cell says: \u201cStep 4. Make the coefficient of the variable equal 1, using the Multiplication or Division Property of Equality.\u201d In the second cell, the instructions say: \u201cThe coefficient of x is one. The equation is solved.\u201d The third cell is blank.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1168344149090\" data-type=\"media\" data-alt=\"In the fifth row of the table, the first cell says: \u201cStep 5. Check.\u201d The instructions in the second cell say: \u201cCheck. Let x equal negative 3. Simplify. Add.\u201d In the third cell is the original equation again: 7 x plus 5 equals 6x plus 2. Below this is the same equation with negative 3 substituted in for x: 7 times negative 3 (in paretheses) plus 5 might equal 6 times negative 3 (in parentheses) plus 2, with the \u201ctimes negative 3\u201d written in red on both sides of the equation. Below this is the equation negative 21 plus 5 might equal negative 18 plus 2. On the last line is the equation negative 16 equals negative 16, with a check mark next to it.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_010e_img_new.jpg\" alt=\"In the fifth row of the table, the first cell says: \u201cStep 5. Check.\u201d The instructions in the second cell say: \u201cCheck. Let x equal negative 3. Simplify. Add.\u201d In the third cell is the original equation again: 7 x plus 5 equals 6x plus 2. Below this is the same equation with negative 3 substituted in for x: 7 times negative 3 (in paretheses) plus 5 might equal 6 times negative 3 (in parentheses) plus 2, with the \u201ctimes negative 3\u201d written in red on both sides of the equation. Below this is the equation negative 21 plus 5 might equal negative 18 plus 2. On the last line is the equation negative 16 equals negative 16, with a check mark next to it.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344514524\" data-type=\"exercise\">\n<div id=\"fs-id1168343007558\" data-type=\"problem\">\n<p id=\"fs-id1168343069772\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b75dad251161bb380c36c69fbf0998df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#120;&#43;&#56;&#61;&#54;&#120;&#43;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"135\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<div id=\"fs-id1168344084568\" data-type=\"solution\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ad143a0d979362a51b48a48c9ca9f59e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344249495\">We\u2019ll list the steps below so you can easily refer to them. But we\u2019ll call this the \u2018Beginning Strategy\u2019 because we\u2019ll be adding some steps later in this chapter.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Equations with variables and constants on both sides of the equation (beginning strategy)<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169750578662\" class=\"stepwise\" type=\"1\">\n<li>Choose which side will be the \u201cvariable\u201d side\u2014the other side will be the \u201cconstant\u201d side.<\/li>\n<li>Collect the variable terms to the \u201cvariable\u201d side of the equation, using the Addition or Subtraction Property of Equality.<\/li>\n<li>Collect all the constants to the other side of the equation, using the Addition or Subtraction Property of Equality.<\/li>\n<li>Make the coefficient of the variable equal 1, using the Multiplication or Division Property of Equality.<\/li>\n<li>Check the solution by substituting it into the original equation.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>In Step 1, a helpful approach is to make the \u201cvariable\u201d side the side that has the variable with the larger coefficient. This usually makes the arithmetic easier.<\/p>\n<div id=\"fs-id1168344115887\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344227238\" data-type=\"exercise\">\n<div id=\"fs-id1168343061173\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343008854\" data-type=\"problem\">\n<p id=\"fs-id1168344076393\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-87cf7ed28b45f1360ae16c6a3557fac8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#97;&#45;&#51;&#61;&#49;&#51;&#97;&#43;&#55;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"134\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168344499016\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168343237356\">In the first step, choose the variable side by comparing the coefficients of the variables on each side.<\/p>\n<p id=\"fs-id1168343131545\">Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-837d0d6b05c238eddf106b68ec9dcfd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/>, make the right side the \u201cvariable\u201d side and the left side the \u201cconstant\u201d side.<\/p>\n<table id=\"eip-id1168184909198\" style=\"width: 100%;\" summary=\"This 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 7 a minus 3 equals 13 a plus 7, with the left side of the equation labeled \u201cconstant,\u201d written in red, and the right side of the equation labeled \u201cvariable,\u201d written in red. One line down on the left, the instructions say: \u201cSubtract 7 a from both sides to remove the variable term from the left.\u201d To the right of this sentence is the same equation with 7a subtracted from both sides: 7 a minus 7 a minus 3 equals 13 a minus 7 a plus 7, with \u201cminus 7 a\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the equation negative 3 equals 6 a plus 7. The next line down on the left, the instructions say: \u201cSubtract 7 from both sides to remove the constant from the right.\u201d To the right of this sentence is the same equation with 7 subtracted from both sides: negative 3 minus 7 equals 6 a plus 7 minus 7, with \u201cminus 7\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the equation negative 10 equals 6 a. One row down, the instructions say: \u201cDivide both sides by 6 to make 1 the coefficient of a,\u201d and to the right is the equation with both sides divided by 6: negative 10 over 6 equals 6a over 6, with \u201cdivided by 6\u201d written in red on both sides. One row down, the instructions say: \u201cSimplify,\u201d and to the right is the answer to the equation: negative 5\/3 equals a. One row down, the columns merge into one. The text says: \u201cCheck\u201d. To the right of this instruction is the original equation again: 7a minus 3 equals 13 a plus 7. Another row down, the instructions say: \u201cLet a equal negative 5\/3.\u201d To the right of this sentence is the original equation with negative 5\/3 substituted in for a: 7 times negative 5\/3 minus 3 might equal 13 times negative 5\/3 plus 7, with negative 5\/3 written in red on both sides. Below that is the equation negative 35\/3 minus 9\/3 might equal 65\/3 plus 21\/3. Below that is the equation negative 54\/3 equals negative 54\/3, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 67.8005%;\"><\/td>\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877266\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 67.8005%;\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-57444a17a512a6be97a4dfabc5c69f84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> from both sides to remove the variable term from the left.<\/td>\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877293\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 67.8005%;\">Combine like terms.<\/td>\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877314\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 67.8005%;\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> from both sides to remove the constant from the right.<\/td>\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877339\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 67.8005%;\">Simplify.<\/td>\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877360\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 67.8005%;\" data-valign=\"bottom\">Divide both sides by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> to make <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> the coefficient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/>.<\/td>\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184877394\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 67.8005%;\">Simplify.<\/td>\n<td style=\"width: 31.9728%;\"><span id=\"eip-id1168184833888\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 67.8005%;\">Check:<\/td>\n<td style=\"width: 31.9728%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 67.8005%;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-be8ed391ecdaaa64efd3fc4b57bd3187_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td style=\"width: 31.9728%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 67.8005%;\"><\/td>\n<td style=\"width: 31.9728%;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_012c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 67.8005%;\"><\/td>\n<td style=\"width: 31.9728%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-eb230e7869fcae3cb6b5eec88874ce37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#52;&#125;&#123;&#51;&#125;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343131452\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344192020\" data-type=\"exercise\">\n<div id=\"fs-id1168344509721\" data-type=\"problem\">\n<p id=\"fs-id1168344502381\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-412169d999f38e082734de9971997dae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#97;&#45;&#50;&#61;&#54;&#97;&#43;&#49;&#56;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"134\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168344215124\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344315440\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f0a1ebc3825fb7a3acd97d2c5ebf8b41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168343131452\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344192020\" data-type=\"exercise\">\n<div id=\"fs-id1168344509721\" data-type=\"problem\">In the last example, we could have made the left side the \u201cvariable\u201d side, but it would have led to a negative coefficient on the variable term. (Try it!) While we could work with the negative, there is less chance of errors when working with positives. The strategy outlined above helps avoid the negatives!<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344297464\">To solve an equation with fractions, we just follow the steps of our strategy to get the solution!<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342992147\" data-type=\"problem\">\n<p id=\"fs-id1168344250068\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0d61ef81c7ac997685d6b621e4340841_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;&#120;&#43;&#54;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#120;&#45;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"129\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168344504486\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168344156941\">Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-27f26f48f049d16d7bf76d51e1f91cef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-83dc4a903812856a369855508d0b2637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>, make the left side the \u201cvariable\u201d side and the right side the \u201cconstant\u201d side.<\/p>\n<table id=\"eip-id1168186270303\" style=\"width: 100%;\" summary=\"This 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 five-fourths x plus 6 equals one-fourth x minus 2, with the left side of the equation labeled \u201cvariable,\u201d written in red, and the right side of the equation labeled \u201cconstant,\u201d written in red. One line down on the left, the instructions say: \u201cSubtract one-fourth x from both sides.\u201d To the right of this instruction is the same equation with one-fourth x subtracted from both sides: five-fourths x minus one-fourth x plus 6 equals one-fourth x minus one-fourth x minus 2, with \u201cminus one-fourth x\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cCombine like terms,\u201d and to the right of this instruction is the equation x plus 6 equals negative 2. Then the next line down on the left, the instructions say: \u201cSubtract 6 from both sides.\u201d To the right of this instruction is the same equation with 6 subtracted from both sides: x plus 6 minus 6 equals negative 2 minus 6, with \u201cminus 6\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the answer to the equation: x equals negative 8. One row down, the columns merge into one. The instructions say: \u201cCheck,\u201d and to the right is the original equation again: five-fourths x plus 6 equals one-fourth x minus 2. Another line down on the left, the instructions say: \u201cLet x equal negative 8,\u201d and to the right is the original equation with negative 8 substituted in for x: 5\/4 times negative 8 plus 6 might equal \u00bc times negative 8 minus 2, with \u201ctimes negative 8\u201d written in red on both sides. Below this is the equation negative 10 plus 6 might equal negative 2 minus 2. Below this is the equation negative 4 equals negative 4, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 399.406px;\" colspan=\"2\"><\/td>\n<td style=\"width: 253.406px;\"><span id=\"eip-id1168186270365\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_013a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 399.406px;\" colspan=\"2\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-88e4289cbc3095732e5796cf1f724188_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"19\" style=\"vertical-align: -6px;\" \/> from both sides.<\/td>\n<td style=\"width: 253.406px;\"><span id=\"eip-id1168186270396\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_013b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 399.406px;\" colspan=\"2\">Combine like terms.<\/td>\n<td style=\"width: 253.406px;\"><span id=\"eip-id1168186252297\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_013c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 399.406px;\" colspan=\"2\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> from both sides.<\/td>\n<td style=\"width: 253.406px;\"><span id=\"eip-id1168186252322\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_013d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 399.406px;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 253.406px;\"><span id=\"eip-id1168186252343\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_013e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/p>\n<p><span id=\"eip-id1168186252343\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2fe5922567e3200fde6a2854481c6f02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#104;&#101;&#99;&#107;&#58;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;&#120;&#43;&#54;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#120;&#45;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#76;&#101;&#116;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#45;&#56;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#54;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#48;&#43;&#54;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#50;&#45;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#52;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#52;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"93\" width=\"346\" style=\"vertical-align: -39px;\" \/><\/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 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343159196\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344285089\" data-type=\"exercise\">\n<div id=\"fs-id1168343001184\" data-type=\"problem\">\n<p id=\"fs-id1168344367951\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e0655d723b4f9651490320e49e7659a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;&#120;&#45;&#49;&#50;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;&#120;&#45;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"151\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168343186830\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168343079905\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6adca822887415d6f9a00ba1a1d97657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168344187424\">We will use the same strategy to find the solution for an equation with decimals.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168343021370\" data-type=\"problem\">\n<p id=\"fs-id1168342967652\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-908eb9125700162c9299e50bde12c3a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#56;&#120;&#43;&#52;&#61;&#53;&#46;&#52;&#120;&#45;&#56;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"154\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168343001168\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168344620464\">Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f6578adc4c7ff8a4a5147446911541c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e9bccec1720559a0b8ad2ea334eb78a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: 0px;\" \/>, make the left side the \u201cvariable\u201d side and the right side the \u201cconstant\u201d side.<\/p>\n<table id=\"eip-id1168181949602\" style=\"height: 181px; width: 100%; width: 100%;\" summary=\"This 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 7.8 x plus 4 equals 5.4 x minus 8, with the left side of the equation labeled \u201cvariable side,\u201d written in red, and the right side of the equation labeled \u201cconstant side,\u201d written in red. One line down on the left, the instructions say: Subtract 5.4 x from both sides. To the right is the same equation with 5.4 x subtracted from both sides: 7.8 x minus 5.4 x plus 4 equals 5.4 x minus 5.4 x minus 8, with \u201cminus 5.4x\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the equation 2.4 x plus 4 equals negative 8. Another line down on the left, the instructions say: \u201cSubtract 4 from both sides.\u201d To the right of this sentence is the equation 2.4x plus 4 minus 4 equals negative 8 minus 4, with \u201cminus 4\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right of this instruction is the equation 2.4 x equals negative 12. One more line down on the left, the instructions say: \u201cUse the division property of equality.\u201d To the right of this instruction is the same equation divided by 2.4 on both sides: 2.4 x over 2.4 equals negative 12 over 2.4, with \u201cdivided by 2.4\u201d written in red on both sides. One more line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the answer to the equation: x equals negative 5. One more line down, the columns merge into one, and the instructions say: \u201cCheck.\u201d To the right of this instruction is the original equation again: 7.8 x plus 4 equals 5.4 x minus 5. Another line down to the left, the instructions say: \u201cLet x equal negative 5.\u201d To the right is the original equation with negative 5 substituted in for x: 7.8 times negative 5 plus 4 equals 5.4 times negative 5 minus 8, with \u201ctimes negative 5\u201d written in red on both sides. Below that is the equation negative 39 plus 4 might equal negative 27 minus 8. Below that is the equation negative 35 equals negative 35, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 27px;\">\n<td style=\"width: 59.1837%; height: 27px;\"><\/td>\n<td style=\"width: 40.5896%; height: 27px;\"><span id=\"eip-id1168181949667\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 59.1837%; height: 14px;\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ba2c9c2cc7d23df472d5e1d4c8849061_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"33\" style=\"vertical-align: -1px;\" \/> from both sides.<\/td>\n<td style=\"width: 40.5896%; height: 14px;\"><span id=\"eip-id1168181949695\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 59.1837%; height: 14px;\">Combine like terms.<\/td>\n<td style=\"width: 40.5896%; height: 14px;\"><span id=\"eip-id1168181949716\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 59.1837%; height: 14px;\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/> from both sides.<\/td>\n<td style=\"width: 40.5896%; height: 14px;\"><span id=\"eip-id1168181949742\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 59.1837%; height: 14px;\">Simplify.<\/td>\n<td style=\"width: 40.5896%; height: 14px;\"><span id=\"eip-id1168181949763\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 26px;\">\n<td style=\"width: 59.1837%; height: 26px;\">Use the Division Propery of Equality.<\/td>\n<td style=\"width: 40.5896%; height: 26px;\"><span id=\"eip-id1168181949784\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 59.1837%; height: 14px;\">Simplify.<\/td>\n<td style=\"width: 40.5896%; height: 14px;\"><span id=\"eip-id1168181949805\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 59.1837%; height: 14px;\">Check:<\/td>\n<td style=\"width: 40.5896%; height: 14px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 59.1837%; height: 14px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d3e213d8d687e32831c24e16c432b60e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 40.5896%; height: 14px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 59.1837%; height: 16px;\"><\/td>\n<td style=\"width: 40.5896%; height: 16px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 59.1837%; height: 14px;\"><\/td>\n<td style=\"width: 40.5896%; height: 14px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_02_03_014d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168344115607\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168344219079\" data-type=\"exercise\">\n<div id=\"fs-id1168344600521\" data-type=\"problem\">\n<p id=\"fs-id1168343046083\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cf058457bf95e5c7eda27315312bd0f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#56;&#120;&#43;&#49;&#50;&#61;&#45;&#49;&#46;&#52;&#120;&#45;&#57;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"177\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1168344124234\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168344080762\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d3e213d8d687e32831c24e16c432b60e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 style=\"text-align: left;\" data-type=\"title\">Key Concepts<\/h1>\n<ul>\n<li><strong data-effect=\"bold\">To determine whether a number is a solution to an equation<\/strong>\n<ol id=\"fs-id1168345387608\" type=\"1\">\n<li>Substitute the number in for the variable in the equation.<\/li>\n<li>Simplify the expressions on both sides of the equation.<\/li>\n<li>Determine whether the resulting statement is true.\n<ul id=\"fs-id1168345449988\">\n<li>If it is true, the number is a solution.<\/li>\n<li>If it is not true, the number is not a solution.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">The addition property of equality<\/strong>\n<ul id=\"fs-id1168345417795\" data-bullet-style=\"open-circle\">\n<li>For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>, if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fb3e831fa117e5f6ffe14a23913c265e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#99;&#61;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"100\" style=\"vertical-align: -2px;\" \/>.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">The subtraction property of equality<\/strong>\n<ul id=\"fs-id1168345560039\" data-bullet-style=\"open-circle\">\n<li>For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>, if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-092c2c215b89a565a36b73ba234b32c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#99;&#61;&#98;&#45;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"100\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">The division property of equality<\/strong>\n<ul>\n<li>For any numbers <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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\/businesstechnicalmath\/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\/businesstechnicalmath\/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;\" \/>.<span data-type=\"newline\"><br \/>\n<\/span> When you divide both sides of an equation by any non-zero number, you still have equality.<\/li>\n<\/ul>\n<\/li>\n<li><strong>The multiplication property of equality<\/strong>\n<ul>\n<li>For any numbers <em>a<\/em>, <em>b<\/em>, and <em>c<\/em>, if <em>a<\/em> = <em>b <\/em>then <em>ac<\/em> = <em>bc<\/em>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<p><strong>solution of an equation<\/strong><\/p>\n<p>A value of a variable that makes a true statement when substituted into the equation.<\/p>\n<\/div>\n<h1 data-type=\"title\">2.1 Exercise Set<\/h1>\n<p id=\"fs-id1169752935790\">In the following exercises, determine whether the given value is a solution to the equation.<\/p>\n<ol>\n<li>Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-53923be0c534e9cf06b453317eed3f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/> a solution of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4b45a646249580ba74b7e5e5a85f80d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#121;&#43;&#51;&#48;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\" \/>?<\/li>\n<li>Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4c9362b4d3f1e72137a095026128b158_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> a solution of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e31d236a91f82aa1a18f74c100f76d80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#117;&#45;&#52;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"91\" style=\"vertical-align: 0px;\" \/>?<\/li>\n<\/ol>\n<div id=\"fs-id1168345526003\" data-type=\"exercise\">\n<div id=\"fs-id1168345255518\" data-type=\"solution\">\n<p>In the following exercises, solve each equation using the Subtraction and Addition Properties of Equality.<\/p>\n<ol class=\"twocolumn\" start=\"3\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f60aea6e72353ed774b5aed08892e086_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#50;&#52;&#61;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"90\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ba82054f962cdc6b60d2ef921b9dae68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#52;&#53;&#61;&#45;&#54;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-50b3f1347e30336afed86e9bede3984d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"73\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c5a7efd37629922e6445880b98891a76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#43;&#50;&#46;&#52;&#61;&#45;&#57;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-42789c0f642d8542e636097f5691790e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#52;&#53;&#61;&#55;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"90\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a3a9e06ac8f4f1ff50343f1bda262ed6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#45;&#49;&#56;&#61;&#45;&#50;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"120\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-865fcfe43dde968558a5d4b8f70dc0cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"74\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-77b821bb979aa8ff0c70cde91c60006d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#51;&#46;&#56;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-60e7eae90b5c536b7c5063af524c157d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#49;&#54;&#53;&#61;&#45;&#52;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"123\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ecc37f7fb7463f50b68a44e8a60bf285_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#43;&#48;&#46;&#53;&#50;&#61;&#45;&#56;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"122\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-659ed02d05d144180f1fbfce0479b19b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"74\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7a9a865c36bab680b8de14e7e60a88a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p id=\"fs-id1169749821619\">In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution.<\/p>\n<ol class=\"twocolumn\" start=\"15\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fd298319a3ef9ef8a217860df6990075_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#61;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e8bfe0259ba46f43769bae879749407e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#48;&#57;&#61;&#49;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8f7206b9b120a0be2ec83e04a03f1384_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#55;&#112;&#61;&#45;&#53;&#52;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"103\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7baed25138a3f0ada08819d52d803e3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#51;&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"73\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5b3667181b497be150b94ddc3e39744f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#52;&#125;&#61;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"50\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-23fe3822a775e05caa1deb3d40d8f59e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#48;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#113;&#125;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"74\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3e2e994c5cc38ef3dedd4be2cd0ee344_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#57;&#125;&#61;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"65\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fe96fcf53134e9cc6aaf934507694ab3_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;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"67\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e8e7602f370fac51ea7d1ec1994773b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ae9427f6f16d16727867cdb65c253239_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#118;&#61;&#45;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"77\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2ce923c5d147628413b77447c7c10fc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#121;&#61;&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cc4afaf8fdd30f3d8bb34c09abb8dd00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#119;&#61;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"78\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-529702492f5b244a96864097ce6767bf_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;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"74\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6dadec09f5bff148f5a54cb0e7dd3b1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#48;&#125;&#120;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"94\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2860fb050c674e4ae2dc7d9f6b750e8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"73\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dc35c02d364638dfd9ddcd8e523e9bd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#56;&#125;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#57;&#125;&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"96\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<p id=\"fs-id1169752884228\">In the following exercises, solve the following equations with constants on both sides.<\/p>\n<ol class=\"twocolumn\" start=\"33\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-873aba3ba9b3b07a635db62fff8a58c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#107;&#61;&#50;&#48;&#107;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"117\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1da915892244dd6b14b303d77b369b87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#43;&#50;&#55;&#61;&#49;&#49;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"110\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ff03bc4447c3d3464fb5e74409731904_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#122;&#61;&#51;&#57;&#45;&#56;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"99\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-111640870060d4684fa2e3b57a5a61d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#61;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"94\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3882196b7ca06319959389e371a58274_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#114;&#45;&#56;&#61;&#45;&#55;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"124\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8ca2a2ccc40c83eb9484fa39661d8388_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#45;&#49;&#55;&#61;&#53;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"131\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ef7ab43cfaae06666011a673479b58bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#43;&#49;&#56;&#102;&#61;&#49;&#57;&#102;&#43;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"159\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2bf28b1a5e285f1d6b318e2d88c4cc1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#113;&#45;&#53;&#61;&#57;&#113;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"137\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-69270041f75647e960846f92bf0aae02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#99;&#43;&#55;&#61;&#45;&#51;&#99;&#45;&#51;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"141\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d04f352eb7eaa2fcf13763da2e3d8013_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#45;&#49;&#55;&#61;&#45;&#56;&#120;&#43;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"154\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b7029371ce3db8f16a72ce397b05814d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#112;&#43;&#49;&#52;&#61;&#54;&#43;&#52;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"129\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2763f0622bdfb89fee3df8efc062404b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#121;&#45;&#52;&#61;&#49;&#50;&#45;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-985fdbb369d5ab28aed995e403db9e99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#52;&#125;&#109;&#45;&#55;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#109;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"144\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9f63de3e9bed04f4566de880f3d803e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#97;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#97;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"133\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-73c2b15059e75d6675bd336ba6d86e4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;&#97;&#43;&#49;&#53;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#97;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"131\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6f5ab07b47e18a0775e1884beae61ecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#112;&#43;&#50;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#112;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"121\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9a4485db25de3eee5af075a9145c94f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#122;&#43;&#54;&#46;&#52;&#53;&#61;&#56;&#122;&#43;&#50;&#51;&#46;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"182\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2838bd03f4a07cf50335672543a59162_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#54;&#120;&#45;&#49;&#56;&#46;&#57;&#61;&#51;&#46;&#52;&#120;&#43;&#53;&#52;&#46;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"196\" style=\"vertical-align: -2px;\" \/><\/li>\n<\/ol>\n<h1 style=\"text-align: left;\">Answers<\/h1>\n<ol class=\"threecolumn\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b045359757320ec6d0731806bd6696d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"25\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8801e2282b857205cf27907b7ad6d579_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#111;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"20\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d0b789492438c2462e97a2daa962e43e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#32;&#61;&#32;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-171db53df64b698560d785a3b839db58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#32;&#61;&#32;&#45;&#49;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9f46f169b823e1ce12c27d73348ad45b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6d63572b1dfe54d863fee3ce97453746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#32;&#61;&#32;&#45;&#49;&#49;&#46;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"80\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-716fb20d86ba0c3a76df7da56ef535c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#61;&#32;&#49;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"59\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2b9f32e6155ce77f0ec4945a3723c71c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#32;&#61;&#32;&#45;&#49;&#56;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"79\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-103b0c0613e6a546e1f356b244b3f58f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a43123bec22bab5dc14d5c608a9981d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#32;&#61;&#32;&#49;&#51;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2220061c1d773137e147e1decd54bba1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#32;&#61;&#32;&#45;&#50;&#53;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"74\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c5054bf696cc0cd976ef9d7bbff03ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#32;&#61;&#32;&#45;&#57;&#46;&#48;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"78\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-292a2afdeb4ebcd353bcb42bc65c3e9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#32;&#61;&#32;&#45;&#49;&#47;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c43fc2c390d7f18c7492bb1d820f8a0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"49\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-49af7f686347e06977fd3a18757933db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c19da6c663a7fb5a1795a8537c93b0df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#61;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-02cb9f99c915bfdaa1b7e9a67b52e659_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#48;&#57;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"70\" style=\"vertical-align: -7px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c22a8b45c73a45294a1d3e642fb31d45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#52;&#49;&#125;&#123;&#51;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-18008e8e8505dedc84e363edf1cd2e37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#61;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"51\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fcf4478d3f34f8a62c3c6131285604f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-03034331ababeaf1863e4efc063ddff4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#61;&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7a5a806e3481b34a36fc14f88dae74d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#49;&#52;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-81244c816312fd90d78830a30a046b33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#53;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"80\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a9ec985c3bc0aa35a95da9940e4def8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6bf73d23bc5e7b97fc278993200315b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;&#61;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-edca48ab560517659afdf61efbc55f56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"50\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-52326327e80557408a1c20f5a6688efb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#61;&#45;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"69\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-774e72b4d598f46773bd391dc297c842_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-da92c22f3368e9175e5eec206315afc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#48;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"50\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d403fe0b9c2e7baefeb0b4bec285a656_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-795914c2d55097504e8716c6ce4436e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-051c28e1447654a79f77fe713388fb71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#61;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"64\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-300a345ef7b973d34879ac8e90555390_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8d5ca556614763b247419777fffcf49b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-df1706d253fb58689c9e0f54253f4801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7c81767aa02e58d86ba02f26eeeb2acd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5e35fbc61fc47fdb6a046faa96ae387b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-86bd8ec7bdac916173cb830884d5151b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fc2df6832c4b35231873132e3ca5233a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"54\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b2e94803bdca8b76219eaeb6d137c0a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0621c4f761e7864714642fcc62d4c42f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-47e30ec3a4ab07de584d750916543a6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"62\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5596251aa16299b0cd103934866fbde5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e4883b5fbd41a9d9186c6f49f8c32cc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"65\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-71745d8db6496f45e724d38fc0563e87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e04a0cdee59c0b26c61b9bbdeee1a75b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#61;&#51;&#46;&#52;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"65\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4b14a9731377a579bb0e684b9cc6dcca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from &#8220;Solve Equations Using the Subtraction and Addition Properties of Equality&#8221; in\u00a0<a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Adaptation Statement for more information.<\/p>\n","protected":false},"author":125,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["izabela-mazur","lynn-marecek","maryanne-anthony-smith"],"pb_section_license":""},"chapter-type":[],"contributor":[60,63,64],"license":[],"class_list":["post-368","chapter","type-chapter","status-publish","hentry","contributor-izabela-mazur","contributor-lynn-marecek","contributor-maryanne-anthony-smith"],"part":272,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/368","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/users\/125"}],"version-history":[{"count":5,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/368\/revisions"}],"predecessor-version":[{"id":1902,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/368\/revisions\/1902"}],"part":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/parts\/272"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/368\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/media?parent=368"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapter-type?post=368"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/contributor?post=368"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/license?post=368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}