{"id":1247,"date":"2020-07-31T20:33:56","date_gmt":"2020-08-01T00:33:56","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-a-general-strategy-to-solve-linear-equations\/"},"modified":"2021-03-24T10:56:33","modified_gmt":"2021-03-24T14:56:33","slug":"use-a-general-strategy-to-solve-linear-equations","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-a-general-strategy-to-solve-linear-equations\/","title":{"raw":"5.5 Use a General Strategy to Solve Linear Equations","rendered":"5.5 Use a General Strategy to Solve Linear Equations"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Solve equations using a general strategy<\/li>\n \t<li>Classify equations<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Solve Equations Using the General Strategy<\/h1>\n<p id=\"fs-id1166503235300\">Until now we have dealt with solving one specific form of a linear equation. It is time now to lay out one overall strategy that can be used to solve any linear equation. Some equations we solve will not require all these steps to solve, but many will.<\/p>\n<p id=\"fs-id1166503225036\">Beginning by simplifying each side of the equation makes the remaining steps easier.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1. How to Solve Linear Equations Using the General Strategy<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">Solve: \\(-6\\left(x+3\\right)=24\\).<\/div>\n<div id=\"fs-id1166503439330\" data-type=\"exercise\">\n<div id=\"fs-id1166503414798\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><\/div>\n<span id=\"fs-id1166503550871\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and five 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. Simplify each side of the equation as much as possible.\u201d The text in the second cell reads: \u201cUse the Distributive Property. Notice that each side of the equation is simplified as much as possible.\u201d The third cell contains the equation negative 6 times x plus 3, where x plus 3 is in parentheses, equals 24. Below this is the same equation with the negative 6 distributed across the parentheses: negative 6x minus 18 equals 24.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_02_04_001a_img_new.jpg\" alt=\"This figure is a table that has three columns and five 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. Simplify each side of the equation as much as possible.\u201d The text in the second cell reads: \u201cUse the Distributive Property. Notice that each side of the equation is simplified as much as possible.\u201d The third cell contains the equation negative 6 times x plus 3, where x plus 3 is in parentheses, equals 24. Below this is the same equation with the negative 6 distributed across the parentheses: negative 6x minus 18 equals 24.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1166503588359\" data-type=\"media\" data-alt=\"In the second row of the table, the first cell says: \u201cStep 2. Collect all variable terms on one side of the equation.\u201d In the second cell, the instructions say: \u201cNothing to do\u2014all x\u2019s are on the left side. The third cell is blank.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_001b_img_new.jpg\" alt=\"In the second row of the table, the first cell says: \u201cStep 2. Collect all variable terms on one side of the equation.\u201d In the second cell, the instructions say: \u201cNothing to do\u2014all x\u2019s are on the left side. The third cell is blank.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1166503595352\" data-type=\"media\" data-alt=\"In the third row of the table, the first cell says: \u201cStep 3. Collect constant terms on the other side of the equation. In the second cell, the instructions say: \u201cTo get constants only on the right, add 18 to each side. Simplify.\u201d The third cell contains the same equation with 18 added to both sides: negative 6x minus 18 plus 18 equals 24 plus 18. Below this is the equation negative 6x equals 42.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_001c_img_new.jpg\" alt=\"In the third row of the table, the first cell says: \u201cStep 3. Collect constant terms on the other side of the equation. In the second cell, the instructions say: \u201cTo get constants only on the right, add 18 to each side. Simplify.\u201d The third cell contains the same equation with 18 added to both sides: negative 6x minus 18 plus 18 equals 24 plus 18. Below this is the equation negative 6x equals 42.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1166503436790\" data-type=\"media\" data-alt=\"In the fourth row of the table, the first cell says: \u201cStep 4. Make the coefficient of the variable term equal to 1.\u201d In the second cell, the instructions say: \u201cDivide each side by negative 6. Simplify. The third cell contains the same equation divided by negative 6 on both sides: negative 6x over negative 6 equals 42 over negative 6, with \u201cdivided by negative 6\u201d written in red on both sides. Below this is the answer to the equation: x equals negative 7.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_001d_img_new.jpg\" alt=\"In the fourth row of the table, the first cell says: \u201cStep 4. Make the coefficient of the variable term equal to 1.\u201d In the second cell, the instructions say: \u201cDivide each side by negative 6. Simplify. The third cell contains the same equation divided by negative 6 on both sides: negative 6x over negative 6 equals 42 over negative 6, with \u201cdivided by negative 6\u201d written in red on both sides. Below this is the answer to the equation: x equals negative 7.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1166503410270\" data-type=\"media\" data-alt=\"In the fifth row of the table, the first cell says: \u201cStep 5. Check the solution.\u201d In the second cell, the instructions say: \u201cLet x equal negative 7. Simplify. Multiply.\u201d In the third cell, there is the instruction: \u201cCheck,\u201d and to the right of this is the original equation again: negative 6 times x plus 3, with x plus 3 in parentheses, equal 24. Below this is the same equation with negative 7 substituted in for x: negative 6 times negative 7 plus 3, with negative 7 plus 3 in parentheses, might equal 24. Below this is the equation negative 6 times negative 4 might equal 24. Below this is the equation 24 equals 24, with a check mark next to it.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_001e_img_new.jpg\" alt=\"In the fifth row of the table, the first cell says: \u201cStep 5. Check the solution.\u201d In the second cell, the instructions say: \u201cLet x equal negative 7. Simplify. Multiply.\u201d In the third cell, there is the instruction: \u201cCheck,\u201d and to the right of this is the original equation again: negative 6 times x plus 3, with x plus 3 in parentheses, equal 24. Below this is the same equation with negative 7 substituted in for x: negative 6 times negative 7 plus 3, with negative 7 plus 3 in parentheses, might equal 24. Below this is the equation negative 6 times negative 4 might equal 24. Below this is the equation 24 equals 24, with a check mark next to it.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503445017\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503509611\" data-type=\"exercise\">\n<div id=\"fs-id1166503215410\" data-type=\"problem\">\n<p id=\"fs-id1166503362084\">Solve: \\(5\\left(x+3\\right)=35\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503415875\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503193709\">\\(x=4\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503605525\" data-type=\"problem\">\n<p id=\"fs-id1166503252098\">Solve: \\(6\\left(y-4\\right)=-18\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503229225\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503246990\">\\(y=1\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503156030\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503186090\" data-type=\"exercise\">\n<div id=\"fs-id1166503229225\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">General strategy for solving linear equations.<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169750704770\" class=\"stepwise\" type=\"1\">\n \t<li><strong data-effect=\"bold\">Simplify each side of the equation as much as possible.<\/strong>\nUse the Distributive Property to remove any parentheses.\nCombine like terms.<\/li>\n \t<li><strong data-effect=\"bold\">Collect all the variable terms on one side of the equation.<\/strong>\nUse the Addition or Subtraction Property of Equality.<\/li>\n \t<li><strong data-effect=\"bold\">Collect all the constant terms on the other side of the equation.<\/strong>\nUse the Addition or Subtraction Property of Equality.<\/li>\n \t<li><strong data-effect=\"bold\">Make the coefficient of the variable term to equal to 1.<\/strong>\nUse the Multiplication or Division Property of Equality.\nState the solution to the equation.<\/li>\n \t<li><strong data-effect=\"bold\">Check the solution.<\/strong> Substitute the solution into the original equation to make sure the result is a true statement.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503317199\" class=\"howto\" data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503130441\" data-type=\"problem\">\n<p id=\"fs-id1166503227410\">Solve: \\(-\\left(y+9\\right)=8\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503286200\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168186270143\" class=\"unnumbered unstyled can-break\" 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 negative y plus 9, with y plus 9 in parentheses, equals 8. One line down on the left, the instructions say: \u201cSimplify each side of the equation as much as possible by distributing.\u201d To the right of this sentence is the equation with the negative 1 distributed across the parentheses: negative y minus 9 equals 8. Another line down on the left, the instructions say: \u201cThe only y term is on the left side, so all variable terms are on the left side of the equation.\u201d Another line down on the left, the instructions say: \u201cAdd 9 to both sides to get all constant terms on the right side of the equation.\u201d To the right of this sentence is the same equation with 9 added to both sides: negative y minus 9 plus 9 equals 8 plus 9, with the \u201cplus 9\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation negative y equals 17. The next line down on the left, the instructions say: \u201cRewrite negative y as negative 1y.\u201d To the right of this sentence is the equation negative 1y equals 17. Another line down on the left, the instructions say: \u201cMake the coefficient of the variable term equal to 1 by dividing both sides by negative 1.\u201d To the right of this sentence is the same equation divided by negative 1 on both sides: negative 1y over negative 1 equals 17 over negative 1, with \u201cdivided by negative 1\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: y equals negative 17. One more line down, the two columns merge into one. The instructions say: \u201cCheck,\u201d and to the right is the original equation again: negative y plus 9, with y plus 9 in parentheses, equals 8. Another line down on the left, the instructions say: \u201cLet y equal negative 17.\u201d To the right of this sentence is the original equation with negative 17 substituted in for y: negative negative 17 plus 9, with negative 17 (written in red) plus 9 in parentheses, might equal 8. Below this is the equation negative negative 8, with negative 8 in parentheses, might equal 8. Below this is the equation 8 equals 8, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\"><\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168182926599\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Simplify each side of the equation as much as possible by distributing.<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168182925961\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">The only \\(y\\) term is on the left side, so all variable terms are on the left side of the equation.<\/td>\n<td style=\"width: 190.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Add \\(9\\) to both sides to get all constant terms on the right side of the equation.<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168182479309\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168183617621\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Rewrite \\(-y\\) as \\(-1y\\).<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168186319838\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Make the coefficient of the variable term to equal to \\(1\\) by dividing both sides by \\(-1\\).<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168183711455\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168186255231\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\" rowspan=\"4\">Check:\nLet \\(y=-17\\).<\/td>\n<td style=\"width: 190.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 190.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 190.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 190.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002d_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\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503134908\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503071906\" data-type=\"exercise\">\n<div id=\"fs-id1166503598697\" data-type=\"problem\">\n<p id=\"fs-id1166503410124\">Solve: \\(-\\left(y+8\\right)=-2\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503105719\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503552701\">\\(y=-6\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503250323\" data-type=\"problem\">\n<p id=\"fs-id1166503135907\">Solve: \\(-\\left(z+4\\right)=-12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503151758\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503151452\">\\(z=8\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503129226\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503085255\" data-type=\"exercise\">\n<div id=\"fs-id1166503151758\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503112659\" data-type=\"problem\">\n<p id=\"fs-id1166503129418\">Solve: \\(5\\left(a-3\\right)+5=-10\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503095216\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168183921388\" class=\"unnumbered unstyled can-break\" style=\"width: 652px;\" 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 times a minus 3, with a minus 3 in parentheses, plus 5 equals negative 10. One line down on the left, the instructions say: \u201cSimplify each side of the equation as much as possible.\u201d Below this is the instruction: \u201cDistribute.\u201d To the right of this sentence is the equation with the 5 distributed across the parentheses: 5a minus 15 plus 5 equals negative 10. Another line down to the left, the instructions say: \u201cCombine like terms,\u201d and to the right is the equation 5a minus 10 equals negative 10. Another line down on the left, the instructions say: \u201cThe only a term is on the left side, so all variable terms are on one side of the equation.\u201d Another line down on the left, the instructions say, \u201cAdd 10 to both sides to get all constant terms on the other side of the equation.\u201d To the right of this sentence is the same equation with 10 added to both sides: 5a minus 10 plus 10 equals negative 10 plus 10, with \u201cplus 10\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation 5a equals 0. Then the next line down on the left, the instructions say: \u201cMake the coefficient of the variable term equal to 1 by dividing both sides by 5.\u201d To the right of this instruction is the same equation divided by 5 on both sides: 5a over 5 equals 0 over 5, with \u201cdivided by 5\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: a equals 0. Another line down, the two columns merge into one, and the instructions say: \u201cCheck\u201d. To the right of this instruction is the original equation again: 5 times a minus 3, with a minus 3 in parentheses, plus 5 equals negative 10. Another line down on the left, the instructions say: \u201cLet a equal 0,\u201d and to the right is the original equation with 0 substituted in for a: 5 times 0 minus 3, with 0 minus 3 in parentheses, plus 5 might equal negative 10. Below this is the equation 5 times negative 3, with negative 3 in parentheses, plus 5 might equal negative 10. Below this is the equation negative 15 plus 5 might equal negative 10. Below this is the equation negative 10 equals negative 10, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 411.406px;\"><\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168183700800\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Simplify each side of the equation as much as possible.<\/td>\n<td style=\"width: 210.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Distribute.<\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168186310229\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Combine like terms.<\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168186310250\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">The only \\(a\\) term is on the left side, so all variable terms are on one side of the equation.<\/td>\n<td style=\"width: 210.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Add \\(10\\) to both sides to get all constant terms on the other side of the equation.<\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168180438670\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Simplify.<\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168180438691\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Make the coefficient of the variable term to equal to \\(1\\) by dividing both sides by \\(5\\).<\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168183706781\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Simplify.<\/td>\n<td style=\"width: 210.406px;\"><span id=\"fs-id1169148972308\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Check:<\/td>\n<td style=\"width: 210.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Let \\(a=0\\).<\/td>\n<td style=\"width: 210.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\"><\/td>\n<td style=\"width: 210.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\"><\/td>\n<td style=\"width: 210.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\"><\/td>\n<td style=\"width: 210.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004e_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\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503171465\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503111561\" data-type=\"exercise\">\n<div id=\"fs-id1166503415945\" data-type=\"problem\">\n<p id=\"fs-id1166503595258\">Solve: \\(2\\left(m-4\\right)+3=-1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503589379\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503203687\">\\(m=2\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503414548\" data-type=\"problem\">\n<p id=\"fs-id1166503107223\">Solve: \\(7\\left(n-3\\right)-8=-15\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503130262\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503210362\">\\(n=2\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503131879\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503102000\" data-type=\"exercise\">\n<div id=\"fs-id1166503130262\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503096427\" data-type=\"problem\">\n<p id=\"fs-id1166503250994\">Solve: \\(\\frac{2}{3}\\left(6m-3\\right)=8-m\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503182988\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168183634185\" class=\"unnumbered unstyled can-break\" style=\"height: 470px; width: 621px;\" 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 two thirds times 6 m minus 3, with 6 m minus 3 in parentheses, equals 8 minus m. One line down on the left, the instructions say: \u201cDistribute.\u201d To the right of this instruction is the equation with the two thirds distributed across the parentheses: 4 m minus 2 equals 8 minus m. Another line down to the left, the instructions say: \u201cAdd m to get the variables only on the left.\u201d To the right of this sentence is the equation with m added to both sides: 4 m plus m minus 2 equals 8 minus m plus m, with \u201cplus m\u201d written in red on both sides. One more line down to the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation 5 m minus 2 equals 8. Another line down to the left, the instructions say: \u201cAdd 2 to get constants only on the right.\u201d To the right of this sentence is the equation 5m minus 2 plus 2 equals 8 plus 2, with \u201cplus 2\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation 5m equals 10. Another line down on the left, the instructions say: \u201cDivide by 5,\u201d and to the right of this instruction is the equation divided by 5 on both sides: 5m over 5 equals 10 over 5, with \u201cdivided by 5\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: m equals 2. The next line down, the two columns merge into one. The instructions say: \u201cCheck,\u201d and to the right of this is the original equation: two thirds times 6 m minus 3, with 6m minus 3 in parentheses, equals 8 minus m. The next line down on the left, the instructions say: \u201cLet m equal 2,\u201d and to the right of this is the original equation with 2 substituted in for m: two thirds times 6 times 2 minus 3, with 6 times 2 minus 3 in parentheses, might equal 8 minus 2. The 2 on both sides is written in red. Below this is the equation two thirds times 12 minus 3, with 12 minus 3 in parentheses, might equal 6. Below this is the equation two thirds times 9 might equal 6. Below this is the equation 6 equals 6, with a check mark next to it.\" width=\"651\" data-label=\"\">\n<tbody>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 379.406px;\"><\/td>\n<td style=\"height: 34px; width: 211.406px;\"><span id=\"eip-id1168186258867\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 379.406px;\">Distribute.<\/td>\n<td style=\"height: 15px; width: 211.406px;\"><span id=\"eip-id1168186258904\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 379.406px;\">Add \\(m\\) to get the variables only to the left.<\/td>\n<td style=\"height: 16px; width: 211.406px;\"><span id=\"eip-id1168186258926\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 379.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 211.406px;\"><span id=\"eip-id1168186258951\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 379.406px;\">Add \\(2\\) to get constants only on the right.<\/td>\n<td style=\"height: 14px; width: 211.406px;\"><span id=\"eip-id1168182090489\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 379.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 211.406px;\"><span id=\"eip-id1168182090515\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 35px;\">\n<td style=\"height: 35px; width: 379.406px;\">Divide by \\(5\\).<\/td>\n<td style=\"height: 35px; width: 211.406px;\"><span id=\"eip-id1168182090536\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 379.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 211.406px;\"><span id=\"eip-id1168181361933\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 379.406px;\">Check:<\/td>\n<td style=\"height: 34px; width: 211.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 379.406px;\">Let \\(m=2\\).<\/td>\n<td style=\"height: 34px; width: 211.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 379.406px;\"><\/td>\n<td style=\"height: 34px; width: 211.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 379.406px;\"><\/td>\n<td style=\"height: 34px; width: 211.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 379.406px;\"><\/td>\n<td style=\"height: 14px; width: 211.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006e_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\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503065666\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503438703\" data-type=\"exercise\">\n<div id=\"fs-id1166503509060\" data-type=\"problem\">\n<p id=\"fs-id1166503290734\">Solve: \\(\\frac{1}{3}\\left(6u+3\\right)=7-u\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503474602\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503363073\">\\(u=2\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503241695\" data-type=\"problem\">\n<p id=\"fs-id1166503220607\">Solve: \\(\\frac{2}{3}\\left(9x-12\\right)=8+2x\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503251979\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503205461\">\\(x=4\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503239723\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503072103\" data-type=\"exercise\">\n<div id=\"fs-id1166503251979\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503598333\" data-type=\"problem\">\n<p id=\"fs-id1166503120009\">Solve: \\(8-2\\left(3y+5\\right)=0\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503062316\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168181353799\" class=\"unnumbered unstyled can-break\" style=\"height: 543px;\" 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 8 minus 2 times 3y plus 5, with 3y plus 5 in parentheses, equals 0. One line down on the left, the instructions say: \u201cSimplify\u2014use the Distributive Property.\u201d To the right of this instruction is the same equation with the negative 2 distributed through the parentheses: 8 minus 6y minus 10 equals 0. Another line down to the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the equation negative 6y minus 2 equals 0. Another line down to the left, the instructions say: \u201cAdd 2 to both sides to collect constants on the right.\u201d To the right of this instruction is the equation with 2 added to both sides: negative 6y minus 2 plus 2 equals 0 plus 2. Another line down to the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation negative 6y equals 2. Another line down to the left, the instructions say: \u201cDivide both sides by negative 6.\u201d To the right is the equation divided by negative 6 on both sides: negative 6y over negative 6 equals 2 over negative 6. The next line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the answer to the equation: y equals negative 1\/3. Another line down, the two columns merge into one, and the instructions say: \u201cCheck: Let y equal negative 1\/3.\u201d Below this is the original equation again: 8 minus 2 times 3y plus 5, with 3y plus 5 in parentheses, equals 0. Below this is the original equation with negative 1\/3 substituted in for y: 8 minus 2 times 3 times negative 1\/3 plus 5, with 3 times negative 1\/3 plus 5 in brackets, equals 0. Below this is the equation 8 minus 2 times negative 1 plus 5, with negative 1 plus 5 in parentheses, might equal 0. Below this is the equation 8 minus 2 times 4 might equal 0. Below this is the equation 8 minus 8 might equal 0. Below this is the equation 0 equals 0, with a check mark next to it.\" width=\"613\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 374.406px;\"><\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168181353818\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Simplify\u2014use the Distributive Property.<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168184849050\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Combine like terms.<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168184849067\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Add \\(2\\) to both sides to collect constants on the right.<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168181427139\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Simplify.<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168181427156\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Divide both sides by \\(-6\\).<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168185239692\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Simplify.<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168185239709\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Check: Let \\(y=-\\frac{1}{3}\\).<\/td>\n<td style=\"width: 209.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008a_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\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503203417\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503241592\" data-type=\"exercise\">\n<div id=\"fs-id1166503123493\" data-type=\"problem\">\n<p id=\"fs-id1166503326742\">Solve: \\(12-3\\left(4j+3\\right)=-17\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503285200\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503207949\">\\(j=\\frac{5}{3}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503083669\" data-type=\"problem\">\n<p id=\"fs-id1166503406468\">Solve: \\(-6-8\\left(k-2\\right)=-10\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503589411\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503111804\">\\(k=\\frac{5}{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503258808\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503129268\" data-type=\"exercise\">\n<div id=\"fs-id1166503589411\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503052806\" data-type=\"problem\">\n<p id=\"fs-id1166503414130\">Solve: \\(4\\left(x-1\\right)-2=5\\left(2x+3\\right)+6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503131392\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168183715192\" class=\"unnumbered unstyled can-break\" style=\"height: 343px; width: 652px;\" 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 4 times x minus 1, with x minus 1 in parentheses, minus 2 equals 5 times 2 x plus 3, with 2 x plus 3 in parentheses, plus 6. One line down on the left, the instructions say: \u201cDistribute.\u201d To the right is the same equation with the 4 distributed through the parentheses on the left, and with the 5 distributed through the parentheses on the right: 4 x minus 4 minus 2 equals 10 x plus 15 plus 6. Another line down on the left, the instructions say: \u201cCombine like terms,\u201d and to the right is the equation 4x minus 6 equals 10 x plus 21. Another line down on the left, the instructions say: \u201cSubtract 4 x to get the variables only on the right since 10 is greater than 4.\u201d To the right of this instruction is the equation with 4 x subtracted from both sides: 4 x minus 4 x minus 6 equals 10 x minus 4x plus 21, with \u201cminus 4 x\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation negative 6 equals 6 x plus 21. The next line down on the left, the instructions say: \u201cSubtract 21 to get the constants on the left.\u201d To the right of this sentence is the equation with 21 subtracted from both sides: negative 6 minus 21 equals 6 x plus 21 minus 21, with \u201cminus 21\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation negative 27 equals 6 x. Another line down on the left, the instructions say: \u201c Divide by 6.\u201d To the right is the same equation divided by 6 on both sides: negative 27 over 6 equals 6x over 6, with \u201cdivided by 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: negative 9\/2 equals x. The next line down, the two columns merge into one. The instructions say: \u201cCheck,\u201d and to the right is the original equation again: 4 times x minus 1, with x minus 1 in parentheses, minus 2 equals 5 times 2 x plus 3, with 2 x plus 3 in parentheses, plus 6. Another line down on the left, the instructions say: \u201cLet x equal negative 9\/2,\u201d and to the right is the original equation with negative 9\/2 substituted in for x: 4 times negative 9\/2 (written in red) minus 1, with negative 9\/2 minus 1 in parentheses, minus 2 might equal 5 times 2 times negative 9\/2 (written in red) plus 2, with 2 times negative 9\/2 plus 3 in parentheses, plus 6. Below this is the equation 4 times negative 11\/2 minus 2 might equal 5 times negative 9 plus 3, with negative 9 plus 3 in parentheses, plus 6. Below this is the equation negative 22 minus 2 might equal 5 times negative 6 plus 6. Below this is the equation negative 24 might equal negative 30 plus 6. 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: 16px;\">\n<td style=\"height: 16px; width: 393.406px;\"><\/td>\n<td style=\"height: 16px; width: 228.406px;\"><span id=\"eip-id1168186221884\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 393.406px;\">Distribute.<\/td>\n<td style=\"height: 14px; width: 228.406px;\"><span id=\"eip-id1168186221905\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 393.406px;\">Combine like terms.<\/td>\n<td style=\"height: 15px; width: 228.406px;\"><span id=\"eip-id1168186221926\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 393.406px;\">Subtract \\(4x\\) to get the variables only on the right side since \\(10\\) &gt; \\(4\\).<\/td>\n<td style=\"height: 30px; width: 228.406px;\"><span id=\"eip-id1168186221962\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 393.406px;\">Simplify.<\/td>\n<td style=\"height: 15px; width: 228.406px;\"><span id=\"eip-id1168186221983\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 393.406px;\">Subtract \\(21\\) to get the constants on left.<\/td>\n<td style=\"height: 15px; width: 228.406px;\"><span id=\"eip-id1168186222009\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 393.406px;\">Simplify.<\/td>\n<td style=\"height: 15px; width: 228.406px;\"><span id=\"eip-id1168186222030\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 393.406px;\">Divide by 6.<\/td>\n<td style=\"height: 34px; width: 228.406px;\"><span id=\"eip-id1168186222051\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010n_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 33px;\">\n<td style=\"height: 33px; width: 393.406px;\">Simplify.<\/td>\n<td style=\"height: 33px; width: 228.406px;\"><span id=\"eip-id1168186222072\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010o_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"height: 17px; width: 393.406px;\">Check:<\/td>\n<td style=\"height: 17px; width: 228.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 43px;\">\n<td style=\"height: 43px; width: 393.406px;\">Let \\(x=-\\frac{9}{2}\\).<\/td>\n<td style=\"height: 43px; width: 228.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"height: 36px; width: 393.406px;\"><\/td>\n<td style=\"height: 36px; width: 228.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px; width: 393.406px;\"><\/td>\n<td style=\"height: 24px; width: 228.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 393.406px;\"><\/td>\n<td style=\"height: 22px; width: 228.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 393.406px;\"><\/td>\n<td style=\"height: 14px; width: 228.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503596018\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503508080\" data-type=\"exercise\">\n<div id=\"fs-id1166503203543\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503596018\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503508080\" data-type=\"exercise\">\n<div id=\"fs-id1166503203543\" data-type=\"problem\">\n<p id=\"fs-id1166503539599\">Solve: \\(6\\left(p-3\\right)-7=5\\left(4p+3\\right)-12\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503472126\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503474200\">\\(p=-2\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503053175\" data-type=\"problem\">\n<p id=\"fs-id1166503437786\">Solve: \\(8\\left(q+1\\right)-5=3\\left(2q-4\\right)-1\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503472134\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503362137\">\\(q=-8\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503471538\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503251554\" data-type=\"exercise\">\n<div id=\"fs-id1166503472134\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503080422\" data-type=\"problem\">\n<p id=\"fs-id1166503106025\">Solve: \\(10\\left[3-8\\left(2s-5\\right)\\right]=15\\left(40-5s\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503168241\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168182924453\" class=\"unnumbered unstyled can-break\" style=\"width: 648px; height: 563px;\" 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 10 times 3 minus 8 times 2 s minus 5, with 2 s minus 5 in parentheses, and with 3 minus 8 times 2 s minus 5 in brackets, equals 15 times 40 minus 5 s, with 40 minus 5s in parentheses. One line down on the left, the instructions say: \u201cSimplify from the innermost parentheses first.\u201d To the right of this instruction is the equation with the 8 distributed through the innermost parentheses on the left: 10 times 3 minus 16 s plus 40, with 3 minus 16 s plus 40 in brackets, equals 15 times 40 minus 5 s, with 40 minus 5s in parentheses. Another line down on the left, the instructions say: \u201cCombine like terms in the brackets.\u201d To the right of this sentence is the equation 10 times 43 minus 16 s, with 43 minus 16 s in brackets, equals 15 times 40 minus 5 s, with 40 minus 5 s in parentheses. Another line down on the left, the instructions say: \u201cDistribute.\u201d To the right of this instruction is the equation with the 10 distributed through the brackets on the left, and the 15 distributed through the parentheses on the right: 430 minus 160s equals 600 minus 75 s. Another line down on the left, the instructions say: \u201cAdd 160 s to get the s\u2019s to the right.\u201d To the right of this instruction is the equation with 160 s added to both sides: 430 minus 160 s plus 160 s equals 600 minus 75 s plus 160 s, with \u201cplus 160 s\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation 430 equals 600 plus 85s. The next line down on the left, the instructions say: \u201cSubtract 600 to get the constants on the left.\u201d To the right of this sentence is the same equation with 600 subtracted from both sides: 430 minus 600 equals 600 plus 85 s minus 600. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right of this instruction is the equation negative 170 equals 85 s. Next line down on the left, the instructions say: \u201cDivide,\u201d and to the right of this instruction is the same equation divided by 85 on both sides: negative 170 over 85 equals 85 s over 85, with \u201cdivided by 85\u201d written in red on both sides. One more line down, the instructions say: \u201cSimplify,\u201d and to the right of this word is the answer to the equation: negative 2 equals s. Below this, the two columns merge into one. The instructions say: \u201cCheck,\u201d and to the right of this is the original equation again: 10 times 3 minus 8 times 2s minus 5, with 2 s minus 5 in parentheses, and with 3 minus 8 times 2s minus 5 in brackets, equals 15 times 40 minus 5 s, with 40 minus 5 s in parentheses. Another line down on the left, the instructions say: \u201cSubstitute negative 2 for s,\u201d and to the right is the original equation with negative 2 substituted in for s: 10 times 3 minus 8 times 2 times negative 2 (written in red) minus 5, with 2 times negative 2 minus 5 in parentheses, and with 3 minus 8 times 2 times negative 2 minus 5 in brackets, might equal 15 times 40 minus 5 times negative 2 (written in red), with 40 minus 5 times negative 2 in parentheses. Below this is the equation 10 times 3 minus 8 times negative 4 minus 5, with negative 4 minus 5 in parentheses, and with 3 minus 8 times negative 4 minus 5 in brackets, might equal 15 times 40 plus 10, with 40 plus 10 in parentheses. Below this is the equation 10 times 3 minus 8 times negative 9, with 3 minus 8 times negative 9 in brackets, might equal 15 times 50. Below this is the equation 10 times 3 plus 72, with 3 plus 72 in brackets, might equal 750. Below this is the equation 10 times 75 might equal 750. Below this is the equation 750 equals 750, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"width: 313.406px; height: 17px;\"><\/td>\n<td style=\"width: 304.406px; height: 17px;\"><span id=\"eip-id1168182924494\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 313.406px; height: 16px;\">Simplify from the innermost parentheses first.<\/td>\n<td style=\"width: 304.406px; height: 16px;\"><span id=\"eip-id1168182924552\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 313.406px; height: 17px;\">Combine like terms in the brackets.<\/td>\n<td style=\"width: 304.406px; height: 17px;\"><span id=\"eip-id1168182924574\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 313.406px; height: 15px;\">Distribute.<\/td>\n<td style=\"width: 304.406px; height: 15px;\"><span id=\"eip-id1168182924595\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 313.406px; height: 16px;\">Add \\(160s\\) to get the s\u2019s to the right.<\/td>\n<td style=\"width: 304.406px; height: 16px;\"><span id=\"eip-id1168182924623\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 313.406px; height: 15px;\">Simplify.<\/td>\n<td style=\"width: 304.406px; height: 15px;\"><span id=\"eip-id1168182924644\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 313.406px; height: 17px;\">Subtract 600 to get the constants to the left.<\/td>\n<td style=\"width: 304.406px; height: 17px;\"><span id=\"eip-id1168182924665\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012n_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 313.406px; height: 15px;\">Simplify.<\/td>\n<td style=\"width: 304.406px; height: 15px;\"><span id=\"eip-id1168182924686\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012o_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"width: 313.406px; height: 34px;\">Divide.<\/td>\n<td style=\"width: 304.406px; height: 34px;\"><span id=\"eip-id1168182924707\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012p_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 313.406px; height: 14px;\">Simplify.<\/td>\n<td style=\"width: 304.406px; height: 14px;\"><span id=\"eip-id1168183693287\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012q_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 313.406px; height: 17px;\">Check:<\/td>\n<td style=\"width: 304.406px; height: 17px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 25px;\">\n<td style=\"width: 313.406px; height: 25px;\">Substitute \\(s=-2\\).<\/td>\n<td style=\"width: 304.406px; height: 25px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 313.406px; height: 23px;\"><\/td>\n<td style=\"width: 304.406px; height: 23px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 313.406px; height: 24px;\"><\/td>\n<td style=\"width: 304.406px; height: 24px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 313.406px; height: 24px;\"><\/td>\n<td style=\"width: 304.406px; height: 24px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 313.406px; height: 24px;\"><\/td>\n<td style=\"width: 304.406px; height: 24px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 313.406px; height: 15px;\"><\/td>\n<td style=\"width: 304.406px; height: 15px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503054706\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503168975\" data-type=\"exercise\">\n<div id=\"fs-id1166503320020\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503054706\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503168975\" data-type=\"exercise\">\n<div id=\"fs-id1166503320020\" data-type=\"problem\">\n<p id=\"fs-id1166503150177\">Solve: \\(6\\left[4-2\\left(7y-1\\right)\\right]=8\\left(13-8y\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503536404\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503327434\">\\(y=-\\frac{17}{5}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503131607\" data-type=\"problem\">\n<p id=\"fs-id1166503206850\">Solve: \\(12\\left[1-5\\left(4z-1\\right)\\right]=3\\left(24+11z\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503320069\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503141830\">\\(z=0\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166499831164\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503150956\" data-type=\"exercise\">\n<div id=\"fs-id1166503320069\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503402782\" data-type=\"problem\">\n<p id=\"fs-id1166503205085\">Solve: \\(0.36\\left(100n+5\\right)=0.6\\left(30n+15\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503115846\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168183733452\" class=\"unnumbered unstyled can-break\" style=\"height: 419px; width: 637px;\" 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 0.36 times 100n plus 5, with 100n plus 5 in parentheses, equals 0.6 times 30n plus 15, with 30n plus 15 in parentheses. One line down on the left, the instructions say: \u201cDistribute.\u201d To the right of this instruction is the same equation with 0.36 distributed through the parentheses on the left side of the equation, and with 0.6 distributed through the parentheses on the right: 36n plus 1.8 equals 18n plus 9. Another line down on the left, the instructions say: \u201cSubtract 18n to get the variables on the left.\u201d To the right of this sentence is the same equation with 18n subtracted from both sides: 36 n minus 18 n plus 1.8 equals 18 n minus 18 n plus 9, with \u201cminus 18 n\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 18 n plus 1.8 equals 9. The next line down on the left, the instructions say: \u201cSubtract 1.8 to get the constants to the right.\u201d To the right of this sentence is the equation with 1.8 subtracted from both sides: 18n plus 1.8 minus 1.8 equals 9 minus 1.8, with \u201cminus 1.8\u201d written in red on both sides. The next line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the equation 18 n equals 7.2. Another line down on the left, the instructions say: \u201cDivide,\u201d and to the right of this word is the same equation divided by 18 on both sides: 18n over 18 equals 7.2 over 18. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right of this word is the answer to the equation: n equals 0.4. One more line down, the two columns merge into one. The instructions say: \u201cCheck,\u201d and to the right of this word is the original equation again: 0.36 times 100 n plus 5, with 100 n plus 5 in parentheses, equals 0.6 times 30 n plus 15, with 30n plus 15 in parentheses. Another line down on the left, the instructions say: \u201cLet n equal 0.4,\u201d and to the right is the original equation with 0.4 substituted in for n: 0.36 times 100 times 0.4 plus 5, with 100 times 0.4 plus 5 in parentheses, might equal 0.6 times 30 times 0.4 plus 15, with 30 times 0.4 plus 15 in parentheses. Below this is the equation 0.36 times 40 plus 5, with 40 plus 5 in parentheses, might equal 0.6 times 12 plus 15, with 12 plus 15 in parentheses. Below this is the equation 0.36 times 45 might equal 0.6 times 27. Below this is the equation 16.2 equals 16.2, with a check mark next to it.\" width=\"667\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 297.406px;\"><\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733520\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Distribute.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733541\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Subtract \\(18n\\) to get the variables to the left.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733569\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Simplify.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733590\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Subtract \\(1.8\\) to get the constants to the right.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733616\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Simplify.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733637\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Divide.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183921491\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Simplify.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183921512\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Check:<\/td>\n<td style=\"width: 309.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Let \\(n=0.4\\).<\/td>\n<td style=\"width: 309.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\"><\/td>\n<td style=\"width: 309.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\"><\/td>\n<td style=\"width: 309.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\"><\/td>\n<td style=\"width: 309.406px;\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503434322\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503078843\" data-type=\"exercise\">\n<div id=\"fs-id1166503325060\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503434322\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503078843\" data-type=\"exercise\">\n<div id=\"fs-id1166503325060\" data-type=\"problem\">\n<p id=\"fs-id1166503132087\">Solve: \\(0.55\\left(100n+8\\right)=0.6\\left(85n+14\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503469688\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503065965\">\\(n=1\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503505755\" data-type=\"problem\">\n<p id=\"fs-id1166503242147\">Solve: \\(0.15\\left(40m-120\\right)=0.5\\left(60m+12\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1166503193029\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503249616\">\\(m=-1\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Classify Equations<\/h1>\n<p id=\"fs-id1166503469799\">Consider the equation we solved at the start of the last section, \\(7x+8=-13\\). The solution we found was \\(x=-3\\). This means the equation \\(7x+8=-13\\) is true when we replace the variable, <em data-effect=\"italics\">x<\/em>, with the value \\(-3\\). We showed this when we checked the solution \\(x=-3\\) and evaluated \\(7x+8=-13\\) for \\(x=-3\\).<\/p>\n<span id=\"fs-id1166503290133\" data-type=\"media\" data-alt=\"This figure shows why we can say the equation 7x plus 8 equals negative 13 is true when the variable x is replaced with the value negative 3. The first line shows the equation with negative 3 substituted in for x: 7 times negative 3 plus 8 might equal negative 13. Below this is the equation negative 21 plus 8 might equal negative 13. Below this is the equation negative 13 equals negative 13, with a check mark next to it.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_016_img_new.jpg\" alt=\"This figure shows why we can say the equation 7x plus 8 equals negative 13 is true when the variable x is replaced with the value negative 3. The first line shows the equation with negative 3 substituted in for x: 7 times negative 3 plus 8 might equal negative 13. Below this is the equation negative 21 plus 8 might equal negative 13. Below this is the equation negative 13 equals negative 13, with a check mark next to it.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1166503088405\">If we evaluate \\(7x+8\\) for a different value of <em data-effect=\"italics\">x<\/em>, the left side will not be \\(-13\\).<\/p>\n<p id=\"fs-id1166503508816\">The equation \\(7x+8=-13\\) is true when we replace the variable, <em data-effect=\"italics\">x<\/em>, with the value \\(-3\\), but not true when we replace <em data-effect=\"italics\">x<\/em> with any other value. Whether or not the equation \\(7x+8=-13\\) is true depends on the value of the variable. Equations like this are called conditional equations.<\/p>\n<p id=\"fs-id1166503321316\">All the equations we have solved so far are conditional equations.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Conditional equation<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nAn equation that is true for one or more values of the variable and false for all other values of the variable is a conditional equation.\n\n<\/div>\n<\/div>\n<p id=\"fs-id1166503258857\">Now let\u2019s consider the equation \\(2y+6=2\\left(y+3\\right)\\). Do you recognize that the left side and the right side are equivalent? Let\u2019s see what happens when we solve for <em data-effect=\"italics\">y<\/em>.<\/p>\n\n<table id=\"eip-id1168182228792\" class=\"unnumbered unstyled can-break\" 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 2y plus 6 equals 2 times y plus 3, with y plus 3 in parentheses. One line down on the left, the instructions say: \u201cDistribute,\u201d and to the right of this instruction is the original equation with the 2 distributed through the parentheses on the right side of the equation: 2y plus 6 equals 2y plus 6. Another line down on the left, the instructions say: \u201cSubtract 2y to get the y\u2019s to one side.\u201d To the right of this sentence is the same equation with 2y subtracted from both sides: 2y minus 2y plus 6 equals 2y minus 2y plus 6, with \u201cminus 2y\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify\u2014the y\u2019s are gone!\u201d To the right is the equation 6 equals 6.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168183733303\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_017a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168183733328\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_017b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(2y\\) to get the \\(y\\)\u2019s to one side.<\/td>\n<td><span id=\"eip-id1168183733355\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_017c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify\u2014the \\(y\\)\u2019s are gone!<\/td>\n<td><span id=\"eip-id1168183733377\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_017d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166503467539\">But \\(6=6\\) is true.<\/p>\n<p id=\"fs-id1166503320056\">This means that the equation \\(2y+6=2\\left(y+3\\right)\\) is true for any value of <em data-effect=\"italics\">y<\/em>. We say the solution to the equation is all of the real numbers. An equation that is true for any value of the variable like this is called an <span class=\"no-emphasis\" data-type=\"term\">identity<\/span>.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Identity<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1166503080582\">An equation that is true for any value of the variable is called an <strong data-effect=\"bold\">identity<\/strong>.<\/p>\n<p id=\"fs-id1166503240115\">The solution of an identity is every real number.<\/p>\n\n<\/div>\n<\/div>\n<p id=\"fs-id1166503589391\">What happens when we solve the equation \\(5z=5z-1\\)?<\/p>\n\n<table id=\"eip-id1168183754184\" class=\"unnumbered unstyled\" 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 z equals 5 z minus 1. One line down on the left, the instructions say: \u201cSubtract 5 z to leave the constant alone on the right.\u201d To the right of this sentence is the original equation with 5 z subtracted from both sides: 5 z minus 5 z equals 5 z minus 5z minus 1, with \u201cminus 5 z\u201d written in red on both sides. The final line down on the left, the instructions say: \u201cSimplify\u2014the z\u2019s are gone!\u201d To the right of this instruction is the equation 0 equals negative 1.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168183754201\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_018a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(5z\\) to get the constant alone on the right.<\/td>\n<td><span id=\"eip-id1168183754225\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_018b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify\u2014the \\(z\\)\u2019s are gone!<\/td>\n<td><span id=\"eip-id1168183754246\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_018c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166503324896\">But \\(0\\ne 1\\).<\/p>\n<p id=\"fs-id1166503285925\">Solving the equation \\(5z=5z-1\\) led to the false statement \\(0=-1\\). The equation \\(5z=5z-1\\) will not be true for any value of z. It has no solution. An equation that has no solution, or that is false for all values of the variable, is called a <span class=\"no-emphasis\" data-type=\"term\">contradiction<\/span>.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Contradiction<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1166503595731\">An equation that is false for all values of the variable is called a contradiction.<\/p>\n<p id=\"fs-id1166503230561\">A contradiction has no solution.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"fs-id1166503595651\" data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503230476\" data-type=\"problem\">\n<p id=\"fs-id1166503415495\">Classify the equation as a conditional equation, an identity, or a contradiction. Then state the solution.<\/p>\n<p id=\"fs-id1166503156406\">\\(6\\left(2n-1\\right)+3=2n-8+5\\left(2n+1\\right)\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1166503325899\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168182169219\" class=\"unnumbered unstyled can-break\" style=\"width: 552px;\" 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 6 times 2 n minus 1, with 2 n minus 1 in parentheses, plus 3 equals 2 n minus 8 plus 5 times 2n plus 1, with 2 n plus 1 in parentheses. One line down on the left, the instructions say: \u201cDistribute,\u201d and to the right of this instruction is the same equation with the 6 distributed through the parentheses on the left side of the equation and with the 5 distributed through the parentheses on the right: 12 n minus 6 plus 3 equals 2n minus 8 plus 10 n plus 5. Another line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the equation 12 n minus 3 equals 12n minus 3. Another line down on the left, the instructions say: \u201cSubtract 12 n to get the n\u2019s to one side.\u201d To the right of this sentence is the same equation with 12 n subtracted from both sides: 12 n minus 12 n minus 3 equals 12 n minus 12 n minus 3, with \u201cminus 12 n\u201d written in red on both sides. Another line down to the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the equation negative 3 equals negative 3. Below this is the text: \u201cThe equation is an identity. The solution is all real numbers.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 267.729px;\"><\/td>\n<td style=\"width: 255.063px;\"><span id=\"eip-id1168182169255\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_019a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 267.729px;\">Distribute.<\/td>\n<td style=\"width: 255.063px;\"><span id=\"eip-id1168182169272\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_019b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 267.729px;\">Combine like terms.<\/td>\n<td style=\"width: 255.063px;\"><span id=\"eip-id1168182169289\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_019c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 267.729px;\">Subtract \\(12n\\) to get the \\(n\\)\u2019s to one side.<\/td>\n<td style=\"width: 255.063px;\"><span id=\"eip-id1168182169317\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_019d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 267.729px;\">Simplify.<\/td>\n<td style=\"width: 255.063px;\"><span id=\"eip-id1168182169334\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_019e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 267.729px;\">This is a true statement.<\/td>\n<td style=\"width: 255.063px;\">The equation is an identity.\nThe solution is every real number.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503404306\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503471713\" data-type=\"exercise\">\n<div id=\"fs-id1166503471716\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503404306\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503471713\" data-type=\"exercise\">\n<div id=\"fs-id1166503471716\" data-type=\"problem\">\n<p id=\"fs-id1166503509673\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution:<\/p>\n<p id=\"fs-id1166503397055\">\\(4+9\\left(3x-7\\right)=-42x-13+23\\left(3x-2\\right)\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1166503225185\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503403915\">identity; all real numbers<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503595248\" data-type=\"problem\">\n<p id=\"fs-id1166503362028\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution:<\/p>\n<p id=\"fs-id1166503554901\">\\(8\\left(1-3x\\right)+15\\left(2x+7\\right)=2\\left(x+50\\right)+4\\left(x+3\\right)+1\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1166503414970\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503414972\">identity; all real numbers<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503239110\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503595246\" data-type=\"exercise\">\n<div id=\"fs-id1166503414970\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503505298\" data-type=\"problem\">\n<p id=\"fs-id1166503505300\">Classify as a conditional equation, an identity, or a contradiction. Then state the solution.<\/p>\n<p id=\"fs-id1166503550760\">\\(10+4\\left(p-5\\right)=0\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1166503474377\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168182261320\" class=\"unnumbered unstyled\" style=\"height: 187px;\" 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 10 plus 4 times p minus 5, with p minus 5 in parentheses, equals 0. One line down on the left, the instructions say: \u201cDistribute.\u201d To the right of this instruction is the same equation with the 4 distributed through the parentheses: 10 plus 4p minus 20 equals 0. Another line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the equation 4p minus 10 equals 0. Another line down on the left, the instructions say: \u201cAdd 10 to both sides.\u201d To the right of this sentence is the same equation with 10 added to both sides: 4p minus 10 plus 10 equals 0 plus 10, with \u201cplus 10\u201d written in red on both sides. One more line down on the left, the instructions say: \u201cSimplify,\u201d and to the right of this word is the equation 4p equals 10. One more line down, the instructions say: \u201cDivide,\u201d and to the right of this instruction is the same equation divided by 4 on both sides: 4p over 4 equals 10 over 4, with \u201cdivided by 4\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the answer to the equation: p equals 5\/2. Then the last line down on the left, the instructions say: \u201cThe equation is true when p equals 5\/2.\u201d To the right of this statement is the text: \u201cThis is a conditional equation. The solution is p equals 5\/2.\u201d\" width=\"610\" data-label=\"\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 352.406px; height: 18px;\"><\/td>\n<td style=\"width: 228.406px; height: 18px;\"><span id=\"eip-id1168184012674\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 352.406px; height: 17px;\">Distribute.<\/td>\n<td style=\"width: 228.406px; height: 17px;\"><span id=\"eip-id1168184012692\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 352.406px; height: 17px;\">Combine like terms.<\/td>\n<td style=\"width: 228.406px; height: 17px;\"><span id=\"eip-id1168184012709\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 352.406px; height: 18px;\">Add \\(10\\) to both sides.<\/td>\n<td style=\"width: 228.406px; height: 18px;\"><span id=\"eip-id1168184012730\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 352.406px; height: 18px;\">Simplify.<\/td>\n<td style=\"width: 228.406px; height: 18px;\"><span id=\"eip-id1168184012747\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 35px;\">\n<td style=\"width: 352.406px; height: 35px;\">Divide.<\/td>\n<td style=\"width: 228.406px; height: 35px;\"><span id=\"eip-id1168184012764\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"width: 352.406px; height: 34px;\">Simplify.<\/td>\n<td style=\"width: 228.406px; height: 34px;\"><span id=\"eip-id1168184012781\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 352.406px; height: 30px;\">The equation is true when \\(p=\\frac{5}{2}\\).<\/td>\n<td style=\"width: 228.406px; height: 30px;\">This is a conditional equation.\nThe solution is \\(p=\\frac{5}{2}\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503556339\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503556342\" data-type=\"exercise\">\n<div id=\"fs-id1166499833606\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503556339\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503556342\" data-type=\"exercise\">\n<div id=\"fs-id1166499833606\" data-type=\"problem\">\n<p id=\"fs-id1166499833609\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: \\(11\\left(q+3\\right)-5=19\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1166503219178\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503219180\">conditional equation; \\(q=\\frac{9}{11}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503413914\" data-type=\"problem\">\n<p id=\"fs-id1166503413916\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: \\(6+14\\left(k-8\\right)=95\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1166503412243\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503412245\">conditional equation; \\(k=\\frac{193}{14}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503362822\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503362826\" data-type=\"exercise\">\n<div id=\"fs-id1166503412243\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503195940\" data-type=\"problem\">\n<p id=\"fs-id1166503195942\">Classify the equation as a conditional equation, an identity, or a contradiction. Then state the solution.<\/p>\n<p id=\"fs-id1166503563008\">\\(5m+3\\left(9+3m\\right)=2\\left(7m-11\\right)\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1166503238457\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168181388994\" class=\"unnumbered unstyled\" 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 5m plus 3 times 9 plus 3m, with 9 plus 3m in parentheses, equals 2 times 7 m minus 11, with 7 m minus 11 in parentheses. One line down on the left, the instructions say: \u201cDistribute,\u201d and on the left is the original equation with the 3 distributed through the parentheses on the left side of the equation and with the 2 distributed through the parentheses on the right side: 5 m plus 27 plus 9 m equals 14 m minus 22. Another line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this instruction is the equation 14m plus 27 equals 14 m minus 22. Another line down on the left, the instructions say: \u201cSubtract 14 m from both sides.\u201d To the right of this sentence is the same equation with 14 m subtracted from both sides: 14m plus 27 minus 14m equals 14 m minus 22 minus 14 m, with \u201cminus 14m\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 27 equals negative 22. The last line down on the left, the instructions say: \u201cBut 27 does not equal negative 22.\u201d To the right of this statement is the text: \u201cThe equation is a contradiction. It has no solution.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168179342683\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_021a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168179342700\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_021b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168185211432\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_021c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract \\(14m\\) from both sides.<\/td>\n<td><span id=\"eip-id1168184873611\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_021d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168184873628\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_021e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>But \\(27\\ne -22\\).<\/td>\n<td>The equation is a contradiction.\nIt has no solution.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503104273\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503236834\" data-type=\"exercise\">\n<div id=\"fs-id1166503236836\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503104273\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503236834\" data-type=\"exercise\">\n<div id=\"fs-id1166503236836\" data-type=\"problem\">\n<p id=\"fs-id1166503236838\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution:<\/p>\n<p id=\"fs-id1166503475071\">\\(12c+5\\left(5+3c\\right)=3\\left(9c-4\\right)\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1166503212260\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503212262\">contradiction; no solution<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503505344\" data-type=\"problem\">\n<p id=\"fs-id1166503505346\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution:<\/p>\n<p id=\"fs-id1166503320305\">\\(4\\left(7d+18\\right)=13\\left(3d-2\\right)-11d\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1166503154344\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503470459\">contradiction; no solution<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503169721\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503169724\" data-type=\"exercise\">\n<div id=\"fs-id1166503154344\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Type of equation - Solution<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<table id=\"fs-id1166503594789\" style=\"height: 86px;\" summary=\"This is a table that has four rows and three columns. The title of the table is \u201cCharacteristics of Conditional Equations, Identities, and Contradictions.\u201d In the first row, which is a header row, the cells read from left to right: \u201cType of equation,\u201d \u201cWhat happens when you solve it?\u201d, and \u201cSolution.\u201d In the second row, the cells read from left to right: \u201cConditional Equation,\u201d \u201cTrue for one or more values of the variables and false for all other variables,\u201d and \u201cOne or more values.\u201d In the third row, the cells read from left to right: \u201cIdentity,\u201d \u201cTrue for any value of the variable,\u201d and \u201cAll real numbers.\u201d In the fourth row, the cells read from left to right: \u201cContradiction,\u201d \u201cFalse for all values of the variable,\u201d and \u201cFalse for all values of the variable.\u201d\">\n<thead>\n<tr style=\"height: 17px;\" valign=\"top\">\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">Type of equation<\/th>\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">What happens when you solve it?<\/th>\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">Solution<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 35px;\" valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">Conditional Equation<\/td>\n<td style=\"width: 349.617px; height: 35px;\" data-valign=\"middle\" data-align=\"left\">True for one or more values of the variables and false for all other values<\/td>\n<td style=\"width: 113.2px; height: 35px;\" data-valign=\"middle\" data-align=\"left\">One or more values<\/td>\n<\/tr>\n<tr style=\"height: 17px;\" valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">Identity<\/td>\n<td style=\"width: 349.617px; height: 17px;\" data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">True<\/strong> for any value of the variable<\/td>\n<td style=\"width: 113.2px; height: 17px;\" data-valign=\"middle\" data-align=\"left\">All real numbers<\/td>\n<\/tr>\n<tr style=\"height: 17px;\" valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">Contradiction<\/td>\n<td style=\"width: 349.617px; height: 17px;\" data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">False<\/strong> for all values of the variable<\/td>\n<td style=\"width: 113.2px; height: 17px;\" data-valign=\"middle\" data-align=\"left\">No solution<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1166503104618\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">General Strategy for Solving Linear Equations<\/strong>\n<ol id=\"fs-id1166503405366\" class=\"stepwise\" type=\"1\">\n \t<li>Simplify each side of the equation as much as possible.\nUse the Distributive Property to remove any parentheses.\nCombine like terms.<\/li>\n \t<li>Collect all the variable terms on one side of the equation.\nUse the Addition or Subtraction Property of Equality.<\/li>\n \t<li>Collect all the constant terms on the other side of the equation.\nUse the Addition or Subtraction Property of Equality.<\/li>\n \t<li>Make the coefficient of the variable term to equal to 1.\nUse the Multiplication or Division Property of Equality.\nState the solution to the equation.<\/li>\n \t<li>Check the solution.\nSubstitute the solution into the original equation.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1 data-type=\"title\">Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1166499832771\">\n \t<dt>conditional equation<\/dt>\n \t<dd id=\"fs-id1166499832776\">An equation that is true for one or more values of the variable and false for all other values of the variable is a conditional equation.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166499832782\">\n \t<dt>contradiction<\/dt>\n \t<dd id=\"fs-id1166499832787\">An equation that is false for all values of the variable is called a contradiction. A contradiction has no solution.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166499832793\">\n \t<dt>identity<\/dt>\n \t<dd id=\"fs-id1166499832798\">An equation that is true for any value of the variable is called an identity. The solution of an identity is all real numbers.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1166503129024\">Solve Equations Using the General Strategy for Solving Linear Equations<\/h2>\n<p id=\"fs-id1169753282040\">In the following exercises, solve each linear equation.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\">1. \\(21\\left(y-5\\right)=-42\\)<\/td>\n<td style=\"width: 49.9086%;\">2. \\(15\\left(y-9\\right)=-60\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">3. \\(-16\\left(3n+4\\right)=32\\)<\/td>\n<td style=\"width: 49.9086%;\">4. \\(-9\\left(2n+1\\right)=36\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">5. \\(5\\left(8+6p\\right)=0\\)<\/td>\n<td style=\"width: 49.9086%;\">6. \\(8\\left(22+11r\\right)=0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">7. \\(-\\left(t-19\\right)=28\\)<\/td>\n<td style=\"width: 49.9086%;\">8. \\(-\\left(w-12\\right)=30\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">9. \\(21+2\\left(m-4\\right)=25\\)<\/td>\n<td style=\"width: 49.9086%;\">10. \\(32+3\\left(z+4\\right)=41\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">11. \\(-6+6\\left(5-k\\right)=15\\)<\/td>\n<td style=\"width: 49.9086%;\">12. \\(51+5\\left(4-q\\right)=56\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">13. \\(8\\left(6t-5\\right)-35=-27\\)<\/td>\n<td style=\"width: 49.9086%;\">14. \\(2\\left(9s-6\\right)-62=16\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">15. \\(-2\\left(11-7x\\right)+54=4\\)<\/td>\n<td style=\"width: 49.9086%;\">16. \\(3\\left(10-2x\\right)+54=0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">17.\u00a0 \\(\\frac{3}{5}\\left(10x-5\\right)=27\\)<\/td>\n<td style=\"width: 49.9086%;\">18. \\(\\frac{2}{3}\\left(9c-3\\right)=22\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">19. \\(\\frac{1}{4}\\left(20d+12\\right)=d+7\\)<\/td>\n<td style=\"width: 49.9086%;\">20. \\(\\frac{1}{5}\\left(15c+10\\right)=c+7\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">21. \\(15-\\left(3r+8\\right)=28\\)<\/td>\n<td style=\"width: 49.9086%;\">22. \\(18-\\left(9r+7\\right)=-16\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">23. \\(-3-\\left(m-1\\right)=13\\)<\/td>\n<td style=\"width: 49.9086%;\">24. \\(5-\\left(n-1\\right)=19\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">25. \\(18-2\\left(y-3\\right)=32\\)<\/td>\n<td style=\"width: 49.9086%;\">26. \\(11-4\\left(y-8\\right)=43\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">27. \\(35-5\\left(2w+8\\right)=-10\\)<\/td>\n<td style=\"width: 49.9086%;\">28. \\(24-8\\left(3v+6\\right)=0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">29. \\(-2\\left(a-6\\right)=4\\left(a-3\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">30. \\(4\\left(a-12\\right)=3\\left(a+5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">31. \\(5\\left(8-r\\right)=-2\\left(2r-16\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">32. \\(2\\left(5-u\\right)=-3\\left(2u+6\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">33. \\(9\\left(2m-3\\right)-8=4m+7\\)<\/td>\n<td style=\"width: 49.9086%;\">34. \\(3\\left(4n-1\\right)-2=8n+3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">35. \\(-15+4\\left(2-5y\\right)=-7\\left(y-4\\right)+4\\)<\/td>\n<td style=\"width: 49.9086%;\">36. \\(12+2\\left(5-3y\\right)=-9\\left(y-1\\right)-2\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">37. \\(5\\left(x-4\\right)-4x=14\\)<\/td>\n<td style=\"width: 49.9086%;\">38. \\(8\\left(x-4\\right)-7x=14\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">39. \\(-12+8\\left(x-5\\right)=-4+3\\left(5x-2\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">40. \\(5+6\\left(3s-5\\right)=-3+2\\left(8s-1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">41. \\(7\\left(2n-5\\right)=8\\left(4n-1\\right)-9\\)<\/td>\n<td style=\"width: 49.9086%;\">42. \\(4\\left(u-1\\right)-8=6\\left(3u-2\\right)-7\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">43. \\(3\\left(a-2\\right)-\\left(a+6\\right)=4\\left(a-1\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">44. \\(4\\left(p-4\\right)-\\left(p+7\\right)=5\\left(p-3\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">45. \\(-\\left(7m+4\\right)-\\left(2m-5\\right)\\) \\(=14-\\left(5m-3\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">46. \\(-\\left(9y+5\\right)-\\left(3y-7\\right)\\) \\(=16-\\left(4y-2\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">47. \\(5\\left[9-2\\left(6d-1\\right)\\right]\\) \\(=11\\left(4-10d\\right)-139\\)<\/td>\n<td style=\"width: 49.9086%;\">48. \\(4\\left[5-8\\left(4c-3\\right)\\right]\\) \\(=12\\left(1-13c\\right)-8\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">49. \\(3\\left[-14+2\\left(15k-6\\right)\\right]\\) \\(=8\\left(3-5k\\right)-24\\)<\/td>\n<td style=\"width: 49.9086%;\">50. \\(3\\left[-9+8\\left(4h-3\\right)\\right]\\) \\(=2\\left(5-12h\\right)-19\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">51. \\(10\\left[5\\left(n+1\\right)+4\\left(n-1\\right)\\right]\\) \\(=11\\left[7\\left(5+n\\right)-\\left(25-3n\\right)\\right]\\)<\/td>\n<td style=\"width: 49.9086%;\">52. \\(5\\left[2\\left(m+4\\right)+8\\left(m-7\\right)\\right]\\) \\(=2\\left[3\\left(5+m\\right)-\\left(21-3m\\right)\\right]\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">53. \\(4\\left(2.5v-0.6\\right)=7.6\\)<\/td>\n<td style=\"width: 49.9086%;\">54. \\(5\\left(1.2u-4.8\\right)=-12\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">55. \\(0.2\\left(p-6\\right)=0.4\\left(p+14\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">56. \\(0.25\\left(q-6\\right)=0.1\\left(q+18\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">57. \\(0.5\\left(16m+34\\right)=-15\\)<\/td>\n<td style=\"width: 49.9086%;\">58. \\(0.2\\left(30n+50\\right)=28\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1166503546217\">Classify Equations<\/h2>\n<p id=\"fs-id1169747671603\">In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\">59. \\(15y+32=2\\left(10y-7\\right)-5y+46\\)<\/td>\n<td style=\"width: 49.9086%;\">60. \\(23z+19=3\\left(5z-9\\right)+8z+46\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">61. \\(9\\left(a-4\\right)+3\\left(2a+5\\right)=7\\left(3a-4\\right)-6a+7\\)<\/td>\n<td style=\"width: 49.9086%;\">62. \\(5\\left(b-9\\right)+4\\left(3b+9\\right)=6\\left(4b-5\\right)-7b+21\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">63. \\(24\\left(3d-4\\right)+100=52\\)<\/td>\n<td style=\"width: 49.9086%;\">64. \\(18\\left(5j-1\\right)+29=47\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">65. \\(30\\left(2n-1\\right)=5\\left(10n+8\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">66. \\(22\\left(3m-4\\right)=8\\left(2m+9\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">67. \\(18u-51=9\\left(4u+5\\right)-6\\left(3u-10\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">68. \\(7v+42=11\\left(3v+8\\right)-2\\left(13v-1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">69. \\(5\\left(p+4\\right)+8\\left(2p-1\\right)=9\\left(3p-5\\right)-6\\left(p-2\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">70. \\(3\\left(6q-9\\right)+7\\left(q+4\\right)=5\\left(6q+8\\right)-5\\left(q+1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">71. \\(9\\left(4k-7\\right)=11\\left(3k+1\\right)+4\\)<\/td>\n<td style=\"width: 49.9086%;\">72. \\(12\\left(6h-1\\right)=8\\left(8h+5\\right)-4\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">73. \\(60\\left(2x-1\\right)=15\\left(8x+5\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">74. \\(45\\left(3y-2\\right)=9\\left(15y-6\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">75. \\(36\\left(4m+5\\right)=12\\left(12m+15\\right)\\)<\/td>\n<td style=\"width: 49.9086%;\">76. \\(16 \\left(6n+15 \\right)= 48 \\left(2n+5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">77. \\(11\\left(8c+5\\right)-8c=2\\left(40c+25\\right)+5\\)<\/td>\n<td style=\"width: 49.9086%;\">78. \\(9\\left(14d+9\\right)+4d=13\\left(10d+6\\right)+3\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 data-type=\"title\">Everyday Math<\/h3>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">79. <strong data-effect=\"bold\">Coins.<\/strong> Rhonda has \\$1.90 in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, <em data-effect=\"italics\">n<\/em>, by solving the equation \\(0.05n+0.10\\left(2n-1\\right)=1.90\\).<\/td>\n<td style=\"width: 50%;\">80. <strong data-effect=\"bold\">Fencing.<\/strong> Micah has 44 feet of fencing to make a dog run in his yard. He wants the length to be 2.5 feet more than the width. Find the length, <em data-effect=\"italics\">L<\/em>, by solving the equation \\(2L+2\\left(L-2.5\\right)=44\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 data-type=\"title\">Writing Exercises<\/h3>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\">81. Explain why you should simplify both sides of an equation as much as possible before collecting the variable terms to one side and the constant terms to the other side.<\/td>\n<td style=\"width: 49.9086%;\">82. Using your own words, list the steps in the general strategy for solving linear equations.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">83. Solve the equation \\(\\frac{1}{4}\\left(8x+20\\right)=3x-4\\) explaining all the steps of your solution as in the examples in this section.<\/td>\n<td style=\"width: 49.9086%;\">84. What is the first step you take when solving the equation \\(3-7\\left(y-4\\right)=38\\) ? Why is this your first step?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\">1. \\(y=3\\)<\/td>\n<td style=\"width: 33.3333%;\">3. \\(n=-2\\)<\/td>\n<td style=\"width: 33.3333%;\">5. \\(p=-\\frac{4}{3}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">7. \\(t=-9\\)<\/td>\n<td style=\"width: 33.3333%;\">9. \\(m=6\\)<\/td>\n<td style=\"width: 33.3333%;\">11. \\(k=\\frac{3}{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">13. \\(t=1\\)<\/td>\n<td style=\"width: 33.3333%;\">15. \\(x=-2\\)<\/td>\n<td style=\"width: 33.3333%;\">17. \\(x=5\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">19. \\(d=1\\)<\/td>\n<td style=\"width: 33.3333%;\">21. \\(r=-7\\)<\/td>\n<td style=\"width: 33.3333%;\">23. \\(m=-15\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">25. \\(y=-4\\)<\/td>\n<td style=\"width: 33.3333%;\">27. \\(w=\\frac{1}{2}\\)<\/td>\n<td style=\"width: 33.3333%;\">29. \\(a=4\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">31. \\(r=8\\)<\/td>\n<td style=\"width: 33.3333%;\">33. \\(m=3\\)<\/td>\n<td style=\"width: 33.3333%;\">35. \\(y=-3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">37. \\(x=34\\)<\/td>\n<td style=\"width: 33.3333%;\">39. \\(x=-6\\)<\/td>\n<td style=\"width: 33.3333%;\">41. \\(n=-1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">43. \\(a=-4\\)<\/td>\n<td style=\"width: 33.3333%;\">45. \\(m=-4\\)<\/td>\n<td style=\"width: 33.3333%;\">47. \\(d=-3\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">49. \\(k=\\frac{3}{5}\\)<\/td>\n<td style=\"width: 33.3333%;\">51. \\(n=-5\\)<\/td>\n<td style=\"width: 33.3333%;\">53. \\(v=1\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">55. \\(p=-34\\)<\/td>\n<td style=\"width: 33.3333%;\">57. \\(m=-4\\)<\/td>\n<td style=\"width: 33.3333%;\">59. identity; all real numbers<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">61. identity; all real numbers<\/td>\n<td style=\"width: 33.3333%;\">63. conditional equation; \\(d=\\frac{2}{3}\\)<\/td>\n<td style=\"width: 33.3333%;\">65. conditional equation; \\(n=7\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">67. contradiction; no solution<\/td>\n<td style=\"width: 33.3333%;\">69. contradiction; no solution<\/td>\n<td style=\"width: 33.3333%;\">71. conditional equation; \\(k=26\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">73. contradiction; no solution<\/td>\n<td style=\"width: 33.3333%;\">75. identity; all real numbers<\/td>\n<td style=\"width: 33.3333%;\">77. identity; all real numbers<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">79. 8 nickels<\/td>\n<td style=\"width: 33.3333%;\">81. Answers will vary.<\/td>\n<td style=\"width: 33.3333%;\">83. Answers will vary.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cUse a General Strategy to Solve Linear Equations\u201d in <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 Copyright page for more information.","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Solve equations using a general strategy<\/li>\n<li>Classify equations<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Solve Equations Using the General Strategy<\/h1>\n<p id=\"fs-id1166503235300\">Until now we have dealt with solving one specific form of a linear equation. It is time now to lay out one overall strategy that can be used to solve any linear equation. Some equations we solve will not require all these steps to solve, but many will.<\/p>\n<p id=\"fs-id1166503225036\">Beginning by simplifying each side of the equation makes the remaining steps easier.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1. How to Solve Linear Equations Using the General Strategy<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22c3a7e492fc769e4ed67d63e4af85ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -5px;\" \/>.<\/div>\n<div id=\"fs-id1166503439330\" data-type=\"exercise\">\n<div id=\"fs-id1166503414798\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><\/div>\n<p><span id=\"fs-id1166503550871\" data-type=\"media\" data-alt=\"This figure is a table that has three columns and five 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. Simplify each side of the equation as much as possible.\u201d The text in the second cell reads: \u201cUse the Distributive Property. Notice that each side of the equation is simplified as much as possible.\u201d The third cell contains the equation negative 6 times x plus 3, where x plus 3 is in parentheses, equals 24. Below this is the same equation with the negative 6 distributed across the parentheses: negative 6x minus 18 equals 24.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_02_04_001a_img_new.jpg\" alt=\"This figure is a table that has three columns and five 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. Simplify each side of the equation as much as possible.\u201d The text in the second cell reads: \u201cUse the Distributive Property. Notice that each side of the equation is simplified as much as possible.\u201d The third cell contains the equation negative 6 times x plus 3, where x plus 3 is in parentheses, equals 24. Below this is the same equation with the negative 6 distributed across the parentheses: negative 6x minus 18 equals 24.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1166503588359\" data-type=\"media\" data-alt=\"In the second row of the table, the first cell says: \u201cStep 2. Collect all variable terms on one side of the equation.\u201d In the second cell, the instructions say: \u201cNothing to do\u2014all x\u2019s are on the left side. The third cell is blank.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_001b_img_new.jpg\" alt=\"In the second row of the table, the first cell says: \u201cStep 2. Collect all variable terms on one side of the equation.\u201d In the second cell, the instructions say: \u201cNothing to do\u2014all x\u2019s are on the left side. The third cell is blank.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1166503595352\" data-type=\"media\" data-alt=\"In the third row of the table, the first cell says: \u201cStep 3. Collect constant terms on the other side of the equation. In the second cell, the instructions say: \u201cTo get constants only on the right, add 18 to each side. Simplify.\u201d The third cell contains the same equation with 18 added to both sides: negative 6x minus 18 plus 18 equals 24 plus 18. Below this is the equation negative 6x equals 42.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_001c_img_new.jpg\" alt=\"In the third row of the table, the first cell says: \u201cStep 3. Collect constant terms on the other side of the equation. In the second cell, the instructions say: \u201cTo get constants only on the right, add 18 to each side. Simplify.\u201d The third cell contains the same equation with 18 added to both sides: negative 6x minus 18 plus 18 equals 24 plus 18. Below this is the equation negative 6x equals 42.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1166503436790\" data-type=\"media\" data-alt=\"In the fourth row of the table, the first cell says: \u201cStep 4. Make the coefficient of the variable term equal to 1.\u201d In the second cell, the instructions say: \u201cDivide each side by negative 6. Simplify. The third cell contains the same equation divided by negative 6 on both sides: negative 6x over negative 6 equals 42 over negative 6, with \u201cdivided by negative 6\u201d written in red on both sides. Below this is the answer to the equation: x equals negative 7.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_001d_img_new.jpg\" alt=\"In the fourth row of the table, the first cell says: \u201cStep 4. Make the coefficient of the variable term equal to 1.\u201d In the second cell, the instructions say: \u201cDivide each side by negative 6. Simplify. The third cell contains the same equation divided by negative 6 on both sides: negative 6x over negative 6 equals 42 over negative 6, with \u201cdivided by negative 6\u201d written in red on both sides. Below this is the answer to the equation: x equals negative 7.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1166503410270\" data-type=\"media\" data-alt=\"In the fifth row of the table, the first cell says: \u201cStep 5. Check the solution.\u201d In the second cell, the instructions say: \u201cLet x equal negative 7. Simplify. Multiply.\u201d In the third cell, there is the instruction: \u201cCheck,\u201d and to the right of this is the original equation again: negative 6 times x plus 3, with x plus 3 in parentheses, equal 24. Below this is the same equation with negative 7 substituted in for x: negative 6 times negative 7 plus 3, with negative 7 plus 3 in parentheses, might equal 24. Below this is the equation negative 6 times negative 4 might equal 24. Below this is the equation 24 equals 24, with a check mark next to it.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_001e_img_new.jpg\" alt=\"In the fifth row of the table, the first cell says: \u201cStep 5. Check the solution.\u201d In the second cell, the instructions say: \u201cLet x equal negative 7. Simplify. Multiply.\u201d In the third cell, there is the instruction: \u201cCheck,\u201d and to the right of this is the original equation again: negative 6 times x plus 3, with x plus 3 in parentheses, equal 24. Below this is the same equation with negative 7 substituted in for x: negative 6 times negative 7 plus 3, with negative 7 plus 3 in parentheses, might equal 24. Below this is the equation negative 6 times negative 4 might equal 24. Below this is the equation 24 equals 24, 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 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503445017\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503509611\" data-type=\"exercise\">\n<div id=\"fs-id1166503215410\" data-type=\"problem\">\n<p id=\"fs-id1166503362084\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e006e4f8396be2de905a7126b7b5b651_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503415875\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503193709\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503605525\" data-type=\"problem\">\n<p id=\"fs-id1166503252098\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec26a9edf119dc75acf6c6b0805e18f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503229225\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503246990\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0e3ca3f6eb8810e090b4ceee7f6e129b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503156030\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503186090\" data-type=\"exercise\">\n<div id=\"fs-id1166503229225\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">General strategy for solving linear equations.<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169750704770\" class=\"stepwise\" type=\"1\">\n<li><strong data-effect=\"bold\">Simplify each side of the equation as much as possible.<\/strong><br \/>\nUse the Distributive Property to remove any parentheses.<br \/>\nCombine like terms.<\/li>\n<li><strong data-effect=\"bold\">Collect all the variable terms on one side of the equation.<\/strong><br \/>\nUse the Addition or Subtraction Property of Equality.<\/li>\n<li><strong data-effect=\"bold\">Collect all the constant terms on the other side of the equation.<\/strong><br \/>\nUse the Addition or Subtraction Property of Equality.<\/li>\n<li><strong data-effect=\"bold\">Make the coefficient of the variable term to equal to 1.<\/strong><br \/>\nUse the Multiplication or Division Property of Equality.<br \/>\nState the solution to the equation.<\/li>\n<li><strong data-effect=\"bold\">Check the solution.<\/strong> Substitute the solution into the original equation to make sure the result is a true statement.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503317199\" class=\"howto\" data-type=\"note\">\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-id1166503130441\" data-type=\"problem\">\n<p id=\"fs-id1166503227410\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-67f5a5bfcf77794ceaa6240db6596eac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503286200\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168186270143\" class=\"unnumbered unstyled can-break\" 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 negative y plus 9, with y plus 9 in parentheses, equals 8. One line down on the left, the instructions say: \u201cSimplify each side of the equation as much as possible by distributing.\u201d To the right of this sentence is the equation with the negative 1 distributed across the parentheses: negative y minus 9 equals 8. Another line down on the left, the instructions say: \u201cThe only y term is on the left side, so all variable terms are on the left side of the equation.\u201d Another line down on the left, the instructions say: \u201cAdd 9 to both sides to get all constant terms on the right side of the equation.\u201d To the right of this sentence is the same equation with 9 added to both sides: negative y minus 9 plus 9 equals 8 plus 9, with the \u201cplus 9\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation negative y equals 17. The next line down on the left, the instructions say: \u201cRewrite negative y as negative 1y.\u201d To the right of this sentence is the equation negative 1y equals 17. Another line down on the left, the instructions say: \u201cMake the coefficient of the variable term equal to 1 by dividing both sides by negative 1.\u201d To the right of this sentence is the same equation divided by negative 1 on both sides: negative 1y over negative 1 equals 17 over negative 1, with \u201cdivided by negative 1\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: y equals negative 17. One more line down, the two columns merge into one. The instructions say: \u201cCheck,\u201d and to the right is the original equation again: negative y plus 9, with y plus 9 in parentheses, equals 8. Another line down on the left, the instructions say: \u201cLet y equal negative 17.\u201d To the right of this sentence is the original equation with negative 17 substituted in for y: negative negative 17 plus 9, with negative 17 (written in red) plus 9 in parentheses, might equal 8. Below this is the equation negative negative 8, with negative 8 in parentheses, might equal 8. Below this is the equation 8 equals 8, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\"><\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168182926599\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Simplify each side of the equation as much as possible by distributing.<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168182925961\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">The only <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/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;\" \/> term is on the left side, so all variable terms are on the left side of the equation.<\/td>\n<td style=\"width: 190.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> to both sides to get all constant terms on the right side of the equation.<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168182479309\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168183617621\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Rewrite <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee7ffd10780498e6daa0b55f23b33c97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: -4px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aad8cd4b079d2c751cccdc097ba881cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168186319838\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Make the coefficient of the variable term to equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> by dividing both sides by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168183711455\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\">Simplify.<\/td>\n<td style=\"width: 190.406px;\"><span id=\"eip-id1168186255231\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 462.406px;\" colspan=\"2\" rowspan=\"4\">Check:<br \/>\nLet <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb32303f3fb262f9613a2066efc40c33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"65\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td style=\"width: 190.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 190.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 190.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 190.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_002d_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 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503134908\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503071906\" data-type=\"exercise\">\n<div id=\"fs-id1166503598697\" data-type=\"problem\">\n<p id=\"fs-id1166503410124\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cd2573e062e8f587d34a2f69d8c5dfc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503105719\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503552701\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/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;\" \/><\/p>\n<\/details>\n<\/div>\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 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503250323\" data-type=\"problem\">\n<p id=\"fs-id1166503135907\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2e28e24d04b07bcbb67c1bdd0f5c663a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503151758\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503151452\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-984612a208153a75b8f97467e67043c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503129226\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503085255\" data-type=\"exercise\">\n<div id=\"fs-id1166503151758\" data-type=\"solution\">\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-id1166503112659\" data-type=\"problem\">\n<p id=\"fs-id1166503129418\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b00c202d65b9273987ab0dfa424f0d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;&#61;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503095216\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168183921388\" class=\"unnumbered unstyled can-break\" style=\"width: 652px;\" 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 times a minus 3, with a minus 3 in parentheses, plus 5 equals negative 10. One line down on the left, the instructions say: \u201cSimplify each side of the equation as much as possible.\u201d Below this is the instruction: \u201cDistribute.\u201d To the right of this sentence is the equation with the 5 distributed across the parentheses: 5a minus 15 plus 5 equals negative 10. Another line down to the left, the instructions say: \u201cCombine like terms,\u201d and to the right is the equation 5a minus 10 equals negative 10. Another line down on the left, the instructions say: \u201cThe only a term is on the left side, so all variable terms are on one side of the equation.\u201d Another line down on the left, the instructions say, \u201cAdd 10 to both sides to get all constant terms on the other side of the equation.\u201d To the right of this sentence is the same equation with 10 added to both sides: 5a minus 10 plus 10 equals negative 10 plus 10, with \u201cplus 10\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation 5a equals 0. Then the next line down on the left, the instructions say: \u201cMake the coefficient of the variable term equal to 1 by dividing both sides by 5.\u201d To the right of this instruction is the same equation divided by 5 on both sides: 5a over 5 equals 0 over 5, with \u201cdivided by 5\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: a equals 0. Another line down, the two columns merge into one, and the instructions say: \u201cCheck\u201d. To the right of this instruction is the original equation again: 5 times a minus 3, with a minus 3 in parentheses, plus 5 equals negative 10. Another line down on the left, the instructions say: \u201cLet a equal 0,\u201d and to the right is the original equation with 0 substituted in for a: 5 times 0 minus 3, with 0 minus 3 in parentheses, plus 5 might equal negative 10. Below this is the equation 5 times negative 3, with negative 3 in parentheses, plus 5 might equal negative 10. Below this is the equation negative 15 plus 5 might equal negative 10. Below this is the equation negative 10 equals negative 10, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 411.406px;\"><\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168183700800\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Simplify each side of the equation as much as possible.<\/td>\n<td style=\"width: 210.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Distribute.<\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168186310229\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Combine like terms.<\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168186310250\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">The only <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> term is on the left side, so all variable terms are on one side of the equation.<\/td>\n<td style=\"width: 210.406px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> to both sides to get all constant terms on the other side of the equation.<\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168180438670\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Simplify.<\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168180438691\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Make the coefficient of the variable term to equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> by dividing both sides by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 210.406px;\"><span id=\"eip-id1168183706781\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Simplify.<\/td>\n<td style=\"width: 210.406px;\"><span id=\"fs-id1169148972308\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Check:<\/td>\n<td style=\"width: 210.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-072bed0ebf929f9d7c14da365c8512a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 210.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\"><\/td>\n<td style=\"width: 210.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\"><\/td>\n<td style=\"width: 210.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 411.406px;\"><\/td>\n<td style=\"width: 210.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_004e_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 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503171465\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503111561\" data-type=\"exercise\">\n<div id=\"fs-id1166503415945\" data-type=\"problem\">\n<p id=\"fs-id1166503595258\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a73814d8ffc4eb517bf8b5a09defa14e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"148\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503589379\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503203687\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ee3bb14bbe97a1114d697f8b45a9f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\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 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503414548\" data-type=\"problem\">\n<p id=\"fs-id1166503107223\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1d52a466ca54488260c24f130392923f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#56;&#61;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503130262\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503210362\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8b4c6cd9d27ba344abe355a47d378bb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503131879\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503102000\" data-type=\"exercise\">\n<div id=\"fs-id1166503130262\" 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-id1166503096427\" data-type=\"problem\">\n<p id=\"fs-id1166503250994\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-82019f9802d83ebfead742fde86eee9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#109;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#56;&#45;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"150\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503182988\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168183634185\" class=\"unnumbered unstyled can-break\" style=\"height: 470px; width: 621px; width: 651px;\" 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 two thirds times 6 m minus 3, with 6 m minus 3 in parentheses, equals 8 minus m. One line down on the left, the instructions say: \u201cDistribute.\u201d To the right of this instruction is the equation with the two thirds distributed across the parentheses: 4 m minus 2 equals 8 minus m. Another line down to the left, the instructions say: \u201cAdd m to get the variables only on the left.\u201d To the right of this sentence is the equation with m added to both sides: 4 m plus m minus 2 equals 8 minus m plus m, with \u201cplus m\u201d written in red on both sides. One more line down to the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation 5 m minus 2 equals 8. Another line down to the left, the instructions say: \u201cAdd 2 to get constants only on the right.\u201d To the right of this sentence is the equation 5m minus 2 plus 2 equals 8 plus 2, with \u201cplus 2\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation 5m equals 10. Another line down on the left, the instructions say: \u201cDivide by 5,\u201d and to the right of this instruction is the equation divided by 5 on both sides: 5m over 5 equals 10 over 5, with \u201cdivided by 5\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: m equals 2. The next line down, the two columns merge into one. The instructions say: \u201cCheck,\u201d and to the right of this is the original equation: two thirds times 6 m minus 3, with 6m minus 3 in parentheses, equals 8 minus m. The next line down on the left, the instructions say: \u201cLet m equal 2,\u201d and to the right of this is the original equation with 2 substituted in for m: two thirds times 6 times 2 minus 3, with 6 times 2 minus 3 in parentheses, might equal 8 minus 2. The 2 on both sides is written in red. Below this is the equation two thirds times 12 minus 3, with 12 minus 3 in parentheses, might equal 6. Below this is the equation two thirds times 9 might equal 6. Below this is the equation 6 equals 6, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 379.406px;\"><\/td>\n<td style=\"height: 34px; width: 211.406px;\"><span id=\"eip-id1168186258867\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 379.406px;\">Distribute.<\/td>\n<td style=\"height: 15px; width: 211.406px;\"><span id=\"eip-id1168186258904\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px; width: 379.406px;\">Add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> to get the variables only to the left.<\/td>\n<td style=\"height: 16px; width: 211.406px;\"><span id=\"eip-id1168186258926\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 379.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 211.406px;\"><span id=\"eip-id1168186258951\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 379.406px;\">Add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> to get constants only on the right.<\/td>\n<td style=\"height: 14px; width: 211.406px;\"><span id=\"eip-id1168182090489\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 379.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 211.406px;\"><span id=\"eip-id1168182090515\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 35px;\">\n<td style=\"height: 35px; width: 379.406px;\">Divide by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"height: 35px; width: 211.406px;\"><span id=\"eip-id1168182090536\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 379.406px;\">Simplify.<\/td>\n<td style=\"height: 14px; width: 211.406px;\"><span id=\"eip-id1168181361933\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 379.406px;\">Check:<\/td>\n<td style=\"height: 34px; width: 211.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 379.406px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ee3bb14bbe97a1114d697f8b45a9f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"height: 34px; width: 211.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 379.406px;\"><\/td>\n<td style=\"height: 34px; width: 211.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 379.406px;\"><\/td>\n<td style=\"height: 34px; width: 211.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 379.406px;\"><\/td>\n<td style=\"height: 14px; width: 211.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_006e_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 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503065666\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503438703\" data-type=\"exercise\">\n<div id=\"fs-id1166503509060\" data-type=\"problem\">\n<p id=\"fs-id1166503290734\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63a583371704d17603b9eece946a1239_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#117;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#55;&#45;&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"139\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503474602\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503363073\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8b267f9cd38a51f762c91bde8120afca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\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 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503241695\" data-type=\"problem\">\n<p id=\"fs-id1166503220607\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e00847127c6a5e0c4694dfbf9b38985_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#120;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#56;&#43;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"157\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503251979\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503205461\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503239723\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503072103\" data-type=\"exercise\">\n<div id=\"fs-id1166503251979\" data-type=\"solution\">\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-id1166503598333\" data-type=\"problem\">\n<p id=\"fs-id1166503120009\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b9f8a8e5285d83146663c13b4507f65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"137\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503062316\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168181353799\" class=\"unnumbered unstyled can-break\" style=\"height: 543px; width: 613px;\" 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 8 minus 2 times 3y plus 5, with 3y plus 5 in parentheses, equals 0. One line down on the left, the instructions say: \u201cSimplify\u2014use the Distributive Property.\u201d To the right of this instruction is the same equation with the negative 2 distributed through the parentheses: 8 minus 6y minus 10 equals 0. Another line down to the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the equation negative 6y minus 2 equals 0. Another line down to the left, the instructions say: \u201cAdd 2 to both sides to collect constants on the right.\u201d To the right of this instruction is the equation with 2 added to both sides: negative 6y minus 2 plus 2 equals 0 plus 2. Another line down to the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation negative 6y equals 2. Another line down to the left, the instructions say: \u201cDivide both sides by negative 6.\u201d To the right is the equation divided by negative 6 on both sides: negative 6y over negative 6 equals 2 over negative 6. The next line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the answer to the equation: y equals negative 1\/3. Another line down, the two columns merge into one, and the instructions say: \u201cCheck: Let y equal negative 1\/3.\u201d Below this is the original equation again: 8 minus 2 times 3y plus 5, with 3y plus 5 in parentheses, equals 0. Below this is the original equation with negative 1\/3 substituted in for y: 8 minus 2 times 3 times negative 1\/3 plus 5, with 3 times negative 1\/3 plus 5 in brackets, equals 0. Below this is the equation 8 minus 2 times negative 1 plus 5, with negative 1 plus 5 in parentheses, might equal 0. Below this is the equation 8 minus 2 times 4 might equal 0. Below this is the equation 8 minus 8 might equal 0. Below this is the equation 0 equals 0, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 374.406px;\"><\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168181353818\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Simplify\u2014use the Distributive Property.<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168184849050\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Combine like terms.<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168184849067\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> to both sides to collect constants on the right.<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168181427139\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Simplify.<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168181427156\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Divide both sides by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168185239692\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Simplify.<\/td>\n<td style=\"width: 209.406px;\"><span id=\"eip-id1168185239709\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 374.406px;\">Check: Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9c6dfce7ea311b94f51717efc951c245_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td style=\"width: 209.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_008a_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 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503203417\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503241592\" data-type=\"exercise\">\n<div id=\"fs-id1166503123493\" data-type=\"problem\">\n<p id=\"fs-id1166503326742\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9cb921bacc174b647f1aabb3a2c54d16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#106;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"167\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503285200\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503207949\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4874eebd278f01816931e53b52b1804a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#106;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503083669\" data-type=\"problem\">\n<p id=\"fs-id1166503406468\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2bc5d875061c3d1e2e6701637e9a945f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"165\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503589411\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503111804\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9339b82b1ffffbe08086d2a1216e45e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503258808\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503129268\" data-type=\"exercise\">\n<div id=\"fs-id1166503589411\" data-type=\"solution\">\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-id1166503052806\" data-type=\"problem\">\n<p id=\"fs-id1166503414130\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a4dbac3c1c7ecd0a43d62dc9762d7944_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;&#61;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"226\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503131392\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168183715192\" class=\"unnumbered unstyled can-break\" style=\"height: 343px; width: 652px;\" 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 4 times x minus 1, with x minus 1 in parentheses, minus 2 equals 5 times 2 x plus 3, with 2 x plus 3 in parentheses, plus 6. One line down on the left, the instructions say: \u201cDistribute.\u201d To the right is the same equation with the 4 distributed through the parentheses on the left, and with the 5 distributed through the parentheses on the right: 4 x minus 4 minus 2 equals 10 x plus 15 plus 6. Another line down on the left, the instructions say: \u201cCombine like terms,\u201d and to the right is the equation 4x minus 6 equals 10 x plus 21. Another line down on the left, the instructions say: \u201cSubtract 4 x to get the variables only on the right since 10 is greater than 4.\u201d To the right of this instruction is the equation with 4 x subtracted from both sides: 4 x minus 4 x minus 6 equals 10 x minus 4x plus 21, with \u201cminus 4 x\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation negative 6 equals 6 x plus 21. The next line down on the left, the instructions say: \u201cSubtract 21 to get the constants on the left.\u201d To the right of this sentence is the equation with 21 subtracted from both sides: negative 6 minus 21 equals 6 x plus 21 minus 21, with \u201cminus 21\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation negative 27 equals 6 x. Another line down on the left, the instructions say: \u201c Divide by 6.\u201d To the right is the same equation divided by 6 on both sides: negative 27 over 6 equals 6x over 6, with \u201cdivided by 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: negative 9\/2 equals x. The next line down, the two columns merge into one. The instructions say: \u201cCheck,\u201d and to the right is the original equation again: 4 times x minus 1, with x minus 1 in parentheses, minus 2 equals 5 times 2 x plus 3, with 2 x plus 3 in parentheses, plus 6. Another line down on the left, the instructions say: \u201cLet x equal negative 9\/2,\u201d and to the right is the original equation with negative 9\/2 substituted in for x: 4 times negative 9\/2 (written in red) minus 1, with negative 9\/2 minus 1 in parentheses, minus 2 might equal 5 times 2 times negative 9\/2 (written in red) plus 2, with 2 times negative 9\/2 plus 3 in parentheses, plus 6. Below this is the equation 4 times negative 11\/2 minus 2 might equal 5 times negative 9 plus 3, with negative 9 plus 3 in parentheses, plus 6. Below this is the equation negative 22 minus 2 might equal 5 times negative 6 plus 6. Below this is the equation negative 24 might equal negative 30 plus 6. 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: 16px;\">\n<td style=\"height: 16px; width: 393.406px;\"><\/td>\n<td style=\"height: 16px; width: 228.406px;\"><span id=\"eip-id1168186221884\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 393.406px;\">Distribute.<\/td>\n<td style=\"height: 14px; width: 228.406px;\"><span id=\"eip-id1168186221905\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 393.406px;\">Combine like terms.<\/td>\n<td style=\"height: 15px; width: 228.406px;\"><span id=\"eip-id1168186221926\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"height: 30px; width: 393.406px;\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5fa4d35b5c4377934245a54e07e43e7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"19\" style=\"vertical-align: -1px;\" \/> to get the variables only on the right side since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td style=\"height: 30px; width: 228.406px;\"><span id=\"eip-id1168186221962\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 393.406px;\">Simplify.<\/td>\n<td style=\"height: 15px; width: 228.406px;\"><span id=\"eip-id1168186221983\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 393.406px;\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b44aa122f73c22d86f2d764af01f919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> to get the constants on left.<\/td>\n<td style=\"height: 15px; width: 228.406px;\"><span id=\"eip-id1168186222009\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 393.406px;\">Simplify.<\/td>\n<td style=\"height: 15px; width: 228.406px;\"><span id=\"eip-id1168186222030\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"height: 34px; width: 393.406px;\">Divide by 6.<\/td>\n<td style=\"height: 34px; width: 228.406px;\"><span id=\"eip-id1168186222051\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010n_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 33px;\">\n<td style=\"height: 33px; width: 393.406px;\">Simplify.<\/td>\n<td style=\"height: 33px; width: 228.406px;\"><span id=\"eip-id1168186222072\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010o_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"height: 17px; width: 393.406px;\">Check:<\/td>\n<td style=\"height: 17px; width: 228.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 43px;\">\n<td style=\"height: 43px; width: 393.406px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb620e697d3aa350ecab3cb794cb3f1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td style=\"height: 43px; width: 228.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"height: 36px; width: 393.406px;\"><\/td>\n<td style=\"height: 36px; width: 228.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px; width: 393.406px;\"><\/td>\n<td style=\"height: 24px; width: 228.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px; width: 393.406px;\"><\/td>\n<td style=\"height: 22px; width: 228.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 393.406px;\"><\/td>\n<td style=\"height: 14px; width: 228.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_010f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503596018\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503508080\" data-type=\"exercise\">\n<div id=\"fs-id1166503203543\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503596018\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503508080\" data-type=\"exercise\">\n<div id=\"fs-id1166503203543\" data-type=\"problem\">\n<p id=\"fs-id1166503539599\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-393ba0f2bd3ed3449fbc5f008dfd8116_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;&#61;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#112;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"232\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503472126\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503474200\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e42b5341681aa874f384909b3cb6b14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\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 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503053175\" data-type=\"problem\">\n<p id=\"fs-id1166503437786\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da7f3442d4e666cfcc2b07af22757d8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#53;&#61;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#113;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"222\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503472134\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503362137\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2c7be79160d0111891f868d7257bba89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503471538\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503251554\" data-type=\"exercise\">\n<div id=\"fs-id1166503472134\" data-type=\"solution\">\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-id1166503080422\" data-type=\"problem\">\n<p id=\"fs-id1166503106025\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17da43c7e64c31b1dc3e32d5bf001e61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#91;&#51;&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#115;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#61;&#49;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#48;&#45;&#53;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"247\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503168241\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168182924453\" class=\"unnumbered unstyled can-break\" style=\"width: 648px; height: 563px;\" 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 10 times 3 minus 8 times 2 s minus 5, with 2 s minus 5 in parentheses, and with 3 minus 8 times 2 s minus 5 in brackets, equals 15 times 40 minus 5 s, with 40 minus 5s in parentheses. One line down on the left, the instructions say: \u201cSimplify from the innermost parentheses first.\u201d To the right of this instruction is the equation with the 8 distributed through the innermost parentheses on the left: 10 times 3 minus 16 s plus 40, with 3 minus 16 s plus 40 in brackets, equals 15 times 40 minus 5 s, with 40 minus 5s in parentheses. Another line down on the left, the instructions say: \u201cCombine like terms in the brackets.\u201d To the right of this sentence is the equation 10 times 43 minus 16 s, with 43 minus 16 s in brackets, equals 15 times 40 minus 5 s, with 40 minus 5 s in parentheses. Another line down on the left, the instructions say: \u201cDistribute.\u201d To the right of this instruction is the equation with the 10 distributed through the brackets on the left, and the 15 distributed through the parentheses on the right: 430 minus 160s equals 600 minus 75 s. Another line down on the left, the instructions say: \u201cAdd 160 s to get the s\u2019s to the right.\u201d To the right of this instruction is the equation with 160 s added to both sides: 430 minus 160 s plus 160 s equals 600 minus 75 s plus 160 s, with \u201cplus 160 s\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right is the equation 430 equals 600 plus 85s. The next line down on the left, the instructions say: \u201cSubtract 600 to get the constants on the left.\u201d To the right of this sentence is the same equation with 600 subtracted from both sides: 430 minus 600 equals 600 plus 85 s minus 600. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right of this instruction is the equation negative 170 equals 85 s. Next line down on the left, the instructions say: \u201cDivide,\u201d and to the right of this instruction is the same equation divided by 85 on both sides: negative 170 over 85 equals 85 s over 85, with \u201cdivided by 85\u201d written in red on both sides. One more line down, the instructions say: \u201cSimplify,\u201d and to the right of this word is the answer to the equation: negative 2 equals s. Below this, the two columns merge into one. The instructions say: \u201cCheck,\u201d and to the right of this is the original equation again: 10 times 3 minus 8 times 2s minus 5, with 2 s minus 5 in parentheses, and with 3 minus 8 times 2s minus 5 in brackets, equals 15 times 40 minus 5 s, with 40 minus 5 s in parentheses. Another line down on the left, the instructions say: \u201cSubstitute negative 2 for s,\u201d and to the right is the original equation with negative 2 substituted in for s: 10 times 3 minus 8 times 2 times negative 2 (written in red) minus 5, with 2 times negative 2 minus 5 in parentheses, and with 3 minus 8 times 2 times negative 2 minus 5 in brackets, might equal 15 times 40 minus 5 times negative 2 (written in red), with 40 minus 5 times negative 2 in parentheses. Below this is the equation 10 times 3 minus 8 times negative 4 minus 5, with negative 4 minus 5 in parentheses, and with 3 minus 8 times negative 4 minus 5 in brackets, might equal 15 times 40 plus 10, with 40 plus 10 in parentheses. Below this is the equation 10 times 3 minus 8 times negative 9, with 3 minus 8 times negative 9 in brackets, might equal 15 times 50. Below this is the equation 10 times 3 plus 72, with 3 plus 72 in brackets, might equal 750. Below this is the equation 10 times 75 might equal 750. Below this is the equation 750 equals 750, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"width: 313.406px; height: 17px;\"><\/td>\n<td style=\"width: 304.406px; height: 17px;\"><span id=\"eip-id1168182924494\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 313.406px; height: 16px;\">Simplify from the innermost parentheses first.<\/td>\n<td style=\"width: 304.406px; height: 16px;\"><span id=\"eip-id1168182924552\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 313.406px; height: 17px;\">Combine like terms in the brackets.<\/td>\n<td style=\"width: 304.406px; height: 17px;\"><span id=\"eip-id1168182924574\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 313.406px; height: 15px;\">Distribute.<\/td>\n<td style=\"width: 304.406px; height: 15px;\"><span id=\"eip-id1168182924595\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 313.406px; height: 16px;\">Add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9218f8b1d5662b2542837bf393be575b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#48;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"34\" style=\"vertical-align: -1px;\" \/> to get the s\u2019s to the right.<\/td>\n<td style=\"width: 304.406px; height: 16px;\"><span id=\"eip-id1168182924623\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 313.406px; height: 15px;\">Simplify.<\/td>\n<td style=\"width: 304.406px; height: 15px;\"><span id=\"eip-id1168182924644\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 313.406px; height: 17px;\">Subtract 600 to get the constants to the left.<\/td>\n<td style=\"width: 304.406px; height: 17px;\"><span id=\"eip-id1168182924665\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012n_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 313.406px; height: 15px;\">Simplify.<\/td>\n<td style=\"width: 304.406px; height: 15px;\"><span id=\"eip-id1168182924686\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012o_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"width: 313.406px; height: 34px;\">Divide.<\/td>\n<td style=\"width: 304.406px; height: 34px;\"><span id=\"eip-id1168182924707\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012p_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 313.406px; height: 14px;\">Simplify.<\/td>\n<td style=\"width: 304.406px; height: 14px;\"><span id=\"eip-id1168183693287\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012q_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 313.406px; height: 17px;\">Check:<\/td>\n<td style=\"width: 304.406px; height: 17px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 25px;\">\n<td style=\"width: 313.406px; height: 25px;\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d47c56e677c8fd54cbb15107490c01fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"54\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 304.406px; height: 25px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 313.406px; height: 23px;\"><\/td>\n<td style=\"width: 304.406px; height: 23px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 313.406px; height: 24px;\"><\/td>\n<td style=\"width: 304.406px; height: 24px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 313.406px; height: 24px;\"><\/td>\n<td style=\"width: 304.406px; height: 24px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 313.406px; height: 24px;\"><\/td>\n<td style=\"width: 304.406px; height: 24px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 313.406px; height: 15px;\"><\/td>\n<td style=\"width: 304.406px; height: 15px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_012g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503054706\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503168975\" data-type=\"exercise\">\n<div id=\"fs-id1166503320020\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503054706\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503168975\" data-type=\"exercise\">\n<div id=\"fs-id1166503320020\" data-type=\"problem\">\n<p id=\"fs-id1166503150177\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1672f14cc5f2e201d309ef003cc66c9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#91;&#52;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#121;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#61;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#51;&#45;&#56;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"232\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503536404\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503327434\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-16c59de61a143ecf13d5436658776dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"63\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\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 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503131607\" data-type=\"problem\">\n<p id=\"fs-id1166503206850\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a8ef9f112dca68f37de134b453a290c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#91;&#49;&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#122;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#61;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#52;&#43;&#49;&#49;&#122;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"249\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503320069\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503141830\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e381c273c9f7ca5b93029ee2e8bab16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166499831164\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503150956\" data-type=\"exercise\">\n<div id=\"fs-id1166503320069\" 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-id1166503402782\" data-type=\"problem\">\n<p id=\"fs-id1166503205085\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7a8ee8c8309a6e584431a4608f07b0c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#51;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#48;&#110;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#48;&#110;&#43;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"246\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503115846\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168183733452\" class=\"unnumbered unstyled can-break\" style=\"height: 419px; width: 637px; width: 667px;\" 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 0.36 times 100n plus 5, with 100n plus 5 in parentheses, equals 0.6 times 30n plus 15, with 30n plus 15 in parentheses. One line down on the left, the instructions say: \u201cDistribute.\u201d To the right of this instruction is the same equation with 0.36 distributed through the parentheses on the left side of the equation, and with 0.6 distributed through the parentheses on the right: 36n plus 1.8 equals 18n plus 9. Another line down on the left, the instructions say: \u201cSubtract 18n to get the variables on the left.\u201d To the right of this sentence is the same equation with 18n subtracted from both sides: 36 n minus 18 n plus 1.8 equals 18 n minus 18 n plus 9, with \u201cminus 18 n\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 18 n plus 1.8 equals 9. The next line down on the left, the instructions say: \u201cSubtract 1.8 to get the constants to the right.\u201d To the right of this sentence is the equation with 1.8 subtracted from both sides: 18n plus 1.8 minus 1.8 equals 9 minus 1.8, with \u201cminus 1.8\u201d written in red on both sides. The next line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the equation 18 n equals 7.2. Another line down on the left, the instructions say: \u201cDivide,\u201d and to the right of this word is the same equation divided by 18 on both sides: 18n over 18 equals 7.2 over 18. Another line down on the left, the instructions say: \u201cSimplify,\u201d and to the right of this word is the answer to the equation: n equals 0.4. One more line down, the two columns merge into one. The instructions say: \u201cCheck,\u201d and to the right of this word is the original equation again: 0.36 times 100 n plus 5, with 100 n plus 5 in parentheses, equals 0.6 times 30 n plus 15, with 30n plus 15 in parentheses. Another line down on the left, the instructions say: \u201cLet n equal 0.4,\u201d and to the right is the original equation with 0.4 substituted in for n: 0.36 times 100 times 0.4 plus 5, with 100 times 0.4 plus 5 in parentheses, might equal 0.6 times 30 times 0.4 plus 15, with 30 times 0.4 plus 15 in parentheses. Below this is the equation 0.36 times 40 plus 5, with 40 plus 5 in parentheses, might equal 0.6 times 12 plus 15, with 12 plus 15 in parentheses. Below this is the equation 0.36 times 45 might equal 0.6 times 27. Below this is the equation 16.2 equals 16.2, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 297.406px;\"><\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733520\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Distribute.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733541\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bcb7fae7779fbe3f620c386c6ac596a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"28\" style=\"vertical-align: -1px;\" \/> to get the variables to the left.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733569\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Simplify.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733590\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1fb38ae2f4ce1afad84a82c7256c2cf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> to get the constants to the right.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733616\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Simplify.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183733637\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Divide.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183921491\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Simplify.<\/td>\n<td style=\"width: 309.406px;\"><span id=\"eip-id1168183921512\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Check:<\/td>\n<td style=\"width: 309.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ccd5b764b4b6fcdc397b926be3524b5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#48;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td style=\"width: 309.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\"><\/td>\n<td style=\"width: 309.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\"><\/td>\n<td style=\"width: 309.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 297.406px;\"><\/td>\n<td style=\"width: 309.406px;\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_014e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503434322\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503078843\" data-type=\"exercise\">\n<div id=\"fs-id1166503325060\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503434322\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503078843\" data-type=\"exercise\">\n<div id=\"fs-id1166503325060\" data-type=\"problem\">\n<p id=\"fs-id1166503132087\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66173cad7c9c268d72e17dcd75e9e1a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#53;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#48;&#110;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#53;&#110;&#43;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"246\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503469688\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503065965\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a51661019cc26a5931f8cb0d5fd63f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\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 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503505755\" data-type=\"problem\">\n<p id=\"fs-id1166503242147\">Solve: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8731a5d569fdd04fe3a3c5353db2781e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#49;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#48;&#109;&#45;&#49;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#48;&#109;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"265\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1166503193029\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503249616\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec3d084a8add5b00b06df1310c62281e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Classify Equations<\/h1>\n<p id=\"fs-id1166503469799\">Consider the equation we solved at the start of the last section, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07d65de3bc010229f22614695d27af09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#56;&#61;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"105\" style=\"vertical-align: -2px;\" \/>. The solution we found was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/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;\" \/>. This means the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07d65de3bc010229f22614695d27af09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#56;&#61;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"105\" style=\"vertical-align: -2px;\" \/> is true when we replace the variable, <em data-effect=\"italics\">x<\/em>, with the value <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>. We showed this when we checked the solution <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/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;\" \/> and evaluated <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07d65de3bc010229f22614695d27af09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#56;&#61;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"105\" style=\"vertical-align: -2px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/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;\" \/>.<\/p>\n<p><span id=\"fs-id1166503290133\" data-type=\"media\" data-alt=\"This figure shows why we can say the equation 7x plus 8 equals negative 13 is true when the variable x is replaced with the value negative 3. The first line shows the equation with negative 3 substituted in for x: 7 times negative 3 plus 8 might equal negative 13. Below this is the equation negative 21 plus 8 might equal negative 13. Below this is the equation negative 13 equals negative 13, with a check mark next to it.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_016_img_new.jpg\" alt=\"This figure shows why we can say the equation 7x plus 8 equals negative 13 is true when the variable x is replaced with the value negative 3. The first line shows the equation with negative 3 substituted in for x: 7 times negative 3 plus 8 might equal negative 13. Below this is the equation negative 21 plus 8 might equal negative 13. Below this is the equation negative 13 equals negative 13, with a check mark next to it.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1166503088405\">If we evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-af56084d9f63b63671eb9a268fbedba8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: -2px;\" \/> for a different value of <em data-effect=\"italics\">x<\/em>, the left side will not be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee7bea24371f97fb5673002404153494_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"fs-id1166503508816\">The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07d65de3bc010229f22614695d27af09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#56;&#61;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"105\" style=\"vertical-align: -2px;\" \/> is true when we replace the variable, <em data-effect=\"italics\">x<\/em>, with the value <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>, but not true when we replace <em data-effect=\"italics\">x<\/em> with any other value. Whether or not the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07d65de3bc010229f22614695d27af09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#56;&#61;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"105\" style=\"vertical-align: -2px;\" \/> is true depends on the value of the variable. Equations like this are called conditional equations.<\/p>\n<p id=\"fs-id1166503321316\">All the equations we have solved so far are conditional equations.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Conditional equation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>An equation that is true for one or more values of the variable and false for all other values of the variable is a conditional equation.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1166503258857\">Now let\u2019s consider the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fbac6133c8eb59b36d319161c49a2495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#121;&#43;&#54;&#61;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"137\" style=\"vertical-align: -4px;\" \/>. Do you recognize that the left side and the right side are equivalent? Let\u2019s see what happens when we solve for <em data-effect=\"italics\">y<\/em>.<\/p>\n<table id=\"eip-id1168182228792\" class=\"unnumbered unstyled can-break\" 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 2y plus 6 equals 2 times y plus 3, with y plus 3 in parentheses. One line down on the left, the instructions say: \u201cDistribute,\u201d and to the right of this instruction is the original equation with the 2 distributed through the parentheses on the right side of the equation: 2y plus 6 equals 2y plus 6. Another line down on the left, the instructions say: \u201cSubtract 2y to get the y\u2019s to one side.\u201d To the right of this sentence is the same equation with 2y subtracted from both sides: 2y minus 2y plus 6 equals 2y minus 2y plus 6, with \u201cminus 2y\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify\u2014the y\u2019s are gone!\u201d To the right is the equation 6 equals 6.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168183733303\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_017a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168183733328\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_017b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85ca23a1e42ccdfafecd1cf9622b44c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"18\" style=\"vertical-align: -4px;\" \/> to get the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/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 to one side.<\/td>\n<td><span id=\"eip-id1168183733355\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_017c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify\u2014the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/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 gone!<\/td>\n<td><span id=\"eip-id1168183733377\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_017d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166503467539\">But <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-99975051d2bc46beccdb3b23456d01cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/> is true.<\/p>\n<p id=\"fs-id1166503320056\">This means that the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fbac6133c8eb59b36d319161c49a2495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#121;&#43;&#54;&#61;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"137\" style=\"vertical-align: -4px;\" \/> is true for any value of <em data-effect=\"italics\">y<\/em>. We say the solution to the equation is all of the real numbers. An equation that is true for any value of the variable like this is called an <span class=\"no-emphasis\" data-type=\"term\">identity<\/span>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Identity<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1166503080582\">An equation that is true for any value of the variable is called an <strong data-effect=\"bold\">identity<\/strong>.<\/p>\n<p id=\"fs-id1166503240115\">The solution of an identity is every real number.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1166503589391\">What happens when we solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-583905c6432effd33f261f0f6aad267e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#122;&#61;&#53;&#122;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"89\" style=\"vertical-align: -1px;\" \/>?<\/p>\n<table id=\"eip-id1168183754184\" class=\"unnumbered unstyled\" 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 z equals 5 z minus 1. One line down on the left, the instructions say: \u201cSubtract 5 z to leave the constant alone on the right.\u201d To the right of this sentence is the original equation with 5 z subtracted from both sides: 5 z minus 5 z equals 5 z minus 5z minus 1, with \u201cminus 5 z\u201d written in red on both sides. The final line down on the left, the instructions say: \u201cSimplify\u2014the z\u2019s are gone!\u201d To the right of this instruction is the equation 0 equals negative 1.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168183754201\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_018a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-94ff3d5e3431f7a54006c0820dc398ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> to get the constant alone on the right.<\/td>\n<td><span id=\"eip-id1168183754225\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_018b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify\u2014the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4586e340cb83d5b642972e97a288fec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>\u2019s are gone!<\/td>\n<td><span id=\"eip-id1168183754246\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_018c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1166503324896\">But <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b2e1a552e64cc3c55f0f6ffb31982ecd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#110;&#101;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p id=\"fs-id1166503285925\">Solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-583905c6432effd33f261f0f6aad267e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#122;&#61;&#53;&#122;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"89\" style=\"vertical-align: -1px;\" \/> led to the false statement <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ad58feae8d6508e2662b2811013c5c7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: -1px;\" \/>. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-583905c6432effd33f261f0f6aad267e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#122;&#61;&#53;&#122;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"89\" style=\"vertical-align: -1px;\" \/> will not be true for any value of z. It has no solution. An equation that has no solution, or that is false for all values of the variable, is called a <span class=\"no-emphasis\" data-type=\"term\">contradiction<\/span>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Contradiction<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1166503595731\">An equation that is false for all values of the variable is called a contradiction.<\/p>\n<p id=\"fs-id1166503230561\">A contradiction has no solution.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503595651\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503230476\" data-type=\"problem\">\n<p id=\"fs-id1166503415495\">Classify the equation as a conditional equation, an identity, or a contradiction. Then state the solution.<\/p>\n<p id=\"fs-id1166503156406\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d4e543c64d31d19c173b8fc0bfd86b8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#61;&#50;&#110;&#45;&#56;&#43;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"276\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166503325899\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168182169219\" class=\"unnumbered unstyled can-break\" style=\"width: 552px;\" 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 6 times 2 n minus 1, with 2 n minus 1 in parentheses, plus 3 equals 2 n minus 8 plus 5 times 2n plus 1, with 2 n plus 1 in parentheses. One line down on the left, the instructions say: \u201cDistribute,\u201d and to the right of this instruction is the same equation with the 6 distributed through the parentheses on the left side of the equation and with the 5 distributed through the parentheses on the right: 12 n minus 6 plus 3 equals 2n minus 8 plus 10 n plus 5. Another line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the equation 12 n minus 3 equals 12n minus 3. Another line down on the left, the instructions say: \u201cSubtract 12 n to get the n\u2019s to one side.\u201d To the right of this sentence is the same equation with 12 n subtracted from both sides: 12 n minus 12 n minus 3 equals 12 n minus 12 n minus 3, with \u201cminus 12 n\u201d written in red on both sides. Another line down to the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the equation negative 3 equals negative 3. Below this is the text: \u201cThe equation is an identity. The solution is all real numbers.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 267.729px;\"><\/td>\n<td style=\"width: 255.063px;\"><span id=\"eip-id1168182169255\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_019a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 267.729px;\">Distribute.<\/td>\n<td style=\"width: 255.063px;\"><span id=\"eip-id1168182169272\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_019b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 267.729px;\">Combine like terms.<\/td>\n<td style=\"width: 255.063px;\"><span id=\"eip-id1168182169289\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_019c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 267.729px;\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2d0ae1007475ba0769cbc696734c8a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"28\" style=\"vertical-align: -1px;\" \/> to get the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>\u2019s to one side.<\/td>\n<td style=\"width: 255.063px;\"><span id=\"eip-id1168182169317\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_019d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 267.729px;\">Simplify.<\/td>\n<td style=\"width: 255.063px;\"><span id=\"eip-id1168182169334\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_019e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 267.729px;\">This is a true statement.<\/td>\n<td style=\"width: 255.063px;\">The equation is an identity.<br \/>\nThe solution is every real number.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503404306\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503471713\" data-type=\"exercise\">\n<div id=\"fs-id1166503471716\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503404306\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503471713\" data-type=\"exercise\">\n<div id=\"fs-id1166503471716\" data-type=\"problem\">\n<p id=\"fs-id1166503509673\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution:<\/p>\n<p id=\"fs-id1166503397055\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-96b26d60fb1173f6849c1cfddcfa7f48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#43;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;&#50;&#120;&#45;&#49;&#51;&#43;&#50;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"315\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166503225185\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503403915\">identity; all real numbers<\/p>\n<\/details>\n<\/div>\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 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503595248\" data-type=\"problem\">\n<p id=\"fs-id1166503362028\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution:<\/p>\n<p id=\"fs-id1166503554901\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a30e9ebb8983753aa2a6bfa22de2d65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#45;&#51;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#49;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"397\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166503414970\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503414972\">identity; all real numbers<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503239110\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503595246\" data-type=\"exercise\">\n<div id=\"fs-id1166503414970\" 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-id1166503505298\" data-type=\"problem\">\n<p id=\"fs-id1166503505300\">Classify as a conditional equation, an identity, or a contradiction. Then state the solution.<\/p>\n<p id=\"fs-id1166503550760\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e577f7ac33e3a38c12b0e075255a7d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"136\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166503474377\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168182261320\" class=\"unnumbered unstyled\" style=\"height: 187px; width: 610px;\" 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 10 plus 4 times p minus 5, with p minus 5 in parentheses, equals 0. One line down on the left, the instructions say: \u201cDistribute.\u201d To the right of this instruction is the same equation with the 4 distributed through the parentheses: 10 plus 4p minus 20 equals 0. Another line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this sentence is the equation 4p minus 10 equals 0. Another line down on the left, the instructions say: \u201cAdd 10 to both sides.\u201d To the right of this sentence is the same equation with 10 added to both sides: 4p minus 10 plus 10 equals 0 plus 10, with \u201cplus 10\u201d written in red on both sides. One more line down on the left, the instructions say: \u201cSimplify,\u201d and to the right of this word is the equation 4p equals 10. One more line down, the instructions say: \u201cDivide,\u201d and to the right of this instruction is the same equation divided by 4 on both sides: 4p over 4 equals 10 over 4, with \u201cdivided by 4\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the answer to the equation: p equals 5\/2. Then the last line down on the left, the instructions say: \u201cThe equation is true when p equals 5\/2.\u201d To the right of this statement is the text: \u201cThis is a conditional equation. The solution is p equals 5\/2.\u201d\" data-label=\"\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 352.406px; height: 18px;\"><\/td>\n<td style=\"width: 228.406px; height: 18px;\"><span id=\"eip-id1168184012674\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 352.406px; height: 17px;\">Distribute.<\/td>\n<td style=\"width: 228.406px; height: 17px;\"><span id=\"eip-id1168184012692\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 352.406px; height: 17px;\">Combine like terms.<\/td>\n<td style=\"width: 228.406px; height: 17px;\"><span id=\"eip-id1168184012709\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 352.406px; height: 18px;\">Add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> to both sides.<\/td>\n<td style=\"width: 228.406px; height: 18px;\"><span id=\"eip-id1168184012730\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 352.406px; height: 18px;\">Simplify.<\/td>\n<td style=\"width: 228.406px; height: 18px;\"><span id=\"eip-id1168184012747\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 35px;\">\n<td style=\"width: 352.406px; height: 35px;\">Divide.<\/td>\n<td style=\"width: 228.406px; height: 35px;\"><span id=\"eip-id1168184012764\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 34px;\">\n<td style=\"width: 352.406px; height: 34px;\">Simplify.<\/td>\n<td style=\"width: 228.406px; height: 34px;\"><span id=\"eip-id1168184012781\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_020g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 352.406px; height: 30px;\">The equation is true when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fd3624caf30dbb55fc9282165b9b628d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td style=\"width: 228.406px; height: 30px;\">This is a conditional equation.<br \/>\nThe solution is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fd3624caf30dbb55fc9282165b9b628d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503556339\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503556342\" data-type=\"exercise\">\n<div id=\"fs-id1166499833606\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503556339\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503556342\" data-type=\"exercise\">\n<div id=\"fs-id1166499833606\" data-type=\"problem\">\n<p id=\"fs-id1166499833609\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3a6bf79a0590bffeb4928075516f026_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#53;&#61;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"145\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166503219178\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503219180\">conditional equation; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a90180309afc393c79860ee48f7a6b9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"48\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\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 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503413914\" data-type=\"problem\">\n<p id=\"fs-id1166503413916\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aa3620ae839aaec99cb44b0932135ece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#43;&#49;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#107;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#57;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"146\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166503412243\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503412245\">conditional equation; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ed26b7e4ec352a125bc63a40a308dc03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#57;&#51;&#125;&#123;&#49;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"56\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503362822\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503362826\" data-type=\"exercise\">\n<div id=\"fs-id1166503412243\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503195940\" data-type=\"problem\">\n<p id=\"fs-id1166503195942\">Classify the equation as a conditional equation, an identity, or a contradiction. Then state the solution.<\/p>\n<p id=\"fs-id1166503563008\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97311711816a58877eb2ca50f7bf090c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#109;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#43;&#51;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#109;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"239\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166503238457\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168181388994\" class=\"unnumbered unstyled\" 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 5m plus 3 times 9 plus 3m, with 9 plus 3m in parentheses, equals 2 times 7 m minus 11, with 7 m minus 11 in parentheses. One line down on the left, the instructions say: \u201cDistribute,\u201d and on the left is the original equation with the 3 distributed through the parentheses on the left side of the equation and with the 2 distributed through the parentheses on the right side: 5 m plus 27 plus 9 m equals 14 m minus 22. Another line down on the left, the instructions say: \u201cCombine like terms.\u201d To the right of this instruction is the equation 14m plus 27 equals 14 m minus 22. Another line down on the left, the instructions say: \u201cSubtract 14 m from both sides.\u201d To the right of this sentence is the same equation with 14 m subtracted from both sides: 14m plus 27 minus 14m equals 14 m minus 22 minus 14 m, with \u201cminus 14m\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 27 equals negative 22. The last line down on the left, the instructions say: \u201cBut 27 does not equal negative 22.\u201d To the right of this statement is the text: \u201cThe equation is a contradiction. It has no solution.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168179342683\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_021a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1168179342700\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_021b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168185211432\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_021c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-928588ac288615757d2725f04a840305_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/> from both sides.<\/td>\n<td><span id=\"eip-id1168184873611\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_021d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1168184873628\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_02_04_021e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>But <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a204d6873dc1849c33a4d2fab0c4ebdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#92;&#110;&#101;&#32;&#45;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"72\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td>The equation is a contradiction.<br \/>\nIt has no solution.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503104273\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503236834\" data-type=\"exercise\">\n<div id=\"fs-id1166503236836\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503104273\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503236834\" data-type=\"exercise\">\n<div id=\"fs-id1166503236836\" data-type=\"problem\">\n<p id=\"fs-id1166503236838\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution:<\/p>\n<p id=\"fs-id1166503475071\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-07966e06f76c19b66f4135ab8e2380e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#99;&#43;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#43;&#51;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#99;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"214\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166503212260\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503212262\">contradiction; no solution<\/p>\n<\/details>\n<\/div>\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 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1166503505344\" data-type=\"problem\">\n<p id=\"fs-id1166503505346\">Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution:<\/p>\n<p id=\"fs-id1166503320305\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ecfdd92fe5aaa70f13075ae3907e26cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#100;&#43;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#100;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#49;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"239\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1166503154344\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1166503470459\">contradiction; no solution<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1166503169721\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1166503169724\" data-type=\"exercise\">\n<div id=\"fs-id1166503154344\" data-type=\"solution\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Type of equation &#8211; Solution<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<table id=\"fs-id1166503594789\" style=\"height: 86px;\" summary=\"This is a table that has four rows and three columns. The title of the table is \u201cCharacteristics of Conditional Equations, Identities, and Contradictions.\u201d In the first row, which is a header row, the cells read from left to right: \u201cType of equation,\u201d \u201cWhat happens when you solve it?\u201d, and \u201cSolution.\u201d In the second row, the cells read from left to right: \u201cConditional Equation,\u201d \u201cTrue for one or more values of the variables and false for all other variables,\u201d and \u201cOne or more values.\u201d In the third row, the cells read from left to right: \u201cIdentity,\u201d \u201cTrue for any value of the variable,\u201d and \u201cAll real numbers.\u201d In the fourth row, the cells read from left to right: \u201cContradiction,\u201d \u201cFalse for all values of the variable,\u201d and \u201cFalse for all values of the variable.\u201d\">\n<thead>\n<tr style=\"height: 17px;\" valign=\"top\">\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">Type of equation<\/th>\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">What happens when you solve it?<\/th>\n<th scope=\"col\" data-valign=\"middle\" data-align=\"left\">Solution<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 35px;\" valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">Conditional Equation<\/td>\n<td style=\"width: 349.617px; height: 35px;\" data-valign=\"middle\" data-align=\"left\">True for one or more values of the variables and false for all other values<\/td>\n<td style=\"width: 113.2px; height: 35px;\" data-valign=\"middle\" data-align=\"left\">One or more values<\/td>\n<\/tr>\n<tr style=\"height: 17px;\" valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">Identity<\/td>\n<td style=\"width: 349.617px; height: 17px;\" data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">True<\/strong> for any value of the variable<\/td>\n<td style=\"width: 113.2px; height: 17px;\" data-valign=\"middle\" data-align=\"left\">All real numbers<\/td>\n<\/tr>\n<tr style=\"height: 17px;\" valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\">Contradiction<\/td>\n<td style=\"width: 349.617px; height: 17px;\" data-valign=\"middle\" data-align=\"left\"><strong data-effect=\"bold\">False<\/strong> for all values of the variable<\/td>\n<td style=\"width: 113.2px; height: 17px;\" data-valign=\"middle\" data-align=\"left\">No solution<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1166503104618\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">General Strategy for Solving Linear Equations<\/strong>\n<ol id=\"fs-id1166503405366\" class=\"stepwise\" type=\"1\">\n<li>Simplify each side of the equation as much as possible.<br \/>\nUse the Distributive Property to remove any parentheses.<br \/>\nCombine like terms.<\/li>\n<li>Collect all the variable terms on one side of the equation.<br \/>\nUse the Addition or Subtraction Property of Equality.<\/li>\n<li>Collect all the constant terms on the other side of the equation.<br \/>\nUse the Addition or Subtraction Property of Equality.<\/li>\n<li>Make the coefficient of the variable term to equal to 1.<br \/>\nUse the Multiplication or Division Property of Equality.<br \/>\nState the solution to the equation.<\/li>\n<li>Check the solution.<br \/>\nSubstitute the solution into the original equation.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1 data-type=\"title\">Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1166499832771\">\n<dt>conditional equation<\/dt>\n<dd id=\"fs-id1166499832776\">An equation that is true for one or more values of the variable and false for all other values of the variable is a conditional equation.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166499832782\">\n<dt>contradiction<\/dt>\n<dd id=\"fs-id1166499832787\">An equation that is false for all values of the variable is called a contradiction. A contradiction has no solution.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166499832793\">\n<dt>identity<\/dt>\n<dd id=\"fs-id1166499832798\">An equation that is true for any value of the variable is called an identity. The solution of an identity is all real numbers.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1166503129024\">Solve Equations Using the General Strategy for Solving Linear Equations<\/h2>\n<p id=\"fs-id1169753282040\">In the following exercises, solve each linear equation.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a7c4d47db4d38d2d419f1ca741e64be9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"129\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c22aedb016138c667792538df410de77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"129\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0f3c72f350ab467ffe0f0fb6f898055a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#110;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"138\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f38f72c3c493ccb52c3f3ddc6fb91e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bf90e881ae1065b3e2f9d568ecc3d8ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#43;&#54;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c06832f071e58b10e2a677577d352e38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#50;&#43;&#49;&#49;&#114;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d364b11f49ec22b308d903cb34578b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#45;&#49;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4934ae089e6147e54d06b74bc3c004f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#119;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-73c77d646c8f4d39b7b2a668b7b13fc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e2464eb9da8286e6c46ec59838726295_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"145\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d4a1e176ee3df57cdc716d537d95536d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#43;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#107;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"150\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1ba862be8d34b7ca9935146678fdd169_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#49;&#43;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#45;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"146\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1892c2f0e0b5445846b78e1f53ccae13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#116;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#51;&#53;&#61;&#45;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"166\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3b2b63b857247a87bfc83efe364e24d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#115;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#54;&#50;&#61;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"154\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-61555c4b64641935ae4e5f36d35794c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#45;&#55;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;&#52;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"169\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c861dcd54ab34068791c7c3b773fa6fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#45;&#50;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;&#52;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"156\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">17.\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c6778206856deacd41e6ca52d0e2465_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"126\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0c8875338505aeab253db3a2d6ba9f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#99;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"113\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18cd53e7012a97df14a39456731429e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#48;&#100;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#100;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"155\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2c8e2b875c08b0f604900832b9aa4677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#99;&#43;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#99;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"152\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5ada2d7192c97ac8265fb5a144a837c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#114;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"142\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b5a21fab8b494f1c077c206db56d8d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#114;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"156\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca67fc73f5dbc6425cd9a2ae924de32c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"145\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-034a48ffc8e257095bdc8c45981f043a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"127\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2607567980d551526dea46498cd59fd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-04f8b0993f8530ceacaa5643b10757d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"145\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7b7398fca8a033df710a8d900d31c37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#119;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"173\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf499ac7a0ea658cef0e91723507d330_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#118;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"146\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6162803fe386f59b579deeb92e3035b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"167\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-93659aae42115d42b55b756bf277ac0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"163\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ce1a5b880f485d13fc674600952b1feb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#45;&#114;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#114;&#45;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"184\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-714fdc517845441084b69bdf16bad8b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#117;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#117;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"178\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1123bf80d5a2074196f796b034eb9cfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#109;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#56;&#61;&#52;&#109;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"190\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e30d6516f5be48a6691035690823b22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;&#61;&#56;&#110;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"180\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b7ce9fe4340808af06519d8546bf2887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#45;&#53;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"260\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e6066d99323a0c3c78568a598c1c53a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#51;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"245\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d3e0ee130adddd011d6e6742062dec91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#52;&#120;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20712f96137100709ed6bed0753dd68c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;&#120;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ff63c98a7f9aa005146dea765cae380e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#43;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"261\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3bc95ed554c5cfafa75df5168fca296f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#115;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#115;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"244\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc31fa95ac1c4b6d8ab8c3372ad23569_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"206\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b476db62ca2dfc86a6607bc5fa5a0bfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#56;&#61;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#117;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"226\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cd8fae98485fbb1f4f0f77270f2de131_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"229\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3b15aaa1a162c3279a4d1abb9f7ac84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"228\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-99de8ca0b1a3d51a811ab1731002cf1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#109;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#109;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"174\" style=\"vertical-align: -5px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c89da6134631b35cd1c5002f7ce489ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#49;&#52;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#109;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"126\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7a528e7100002a14ffaeb33e34aa1bb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"162\" style=\"vertical-align: -5px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-25912e36a1022411e1e1d16bf27e5511_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#49;&#54;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#121;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"120\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7a485a000b683ec41becb4471d58479d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#91;&#57;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#100;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -5px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d2607471dcbd35ef7068b3e5c85f44b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#49;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#45;&#49;&#48;&#100;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#51;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"159\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d31b0be6e5230f88e857248e4a3fd862_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#91;&#53;&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#99;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-038baa279eddecc81cdf050b1b1b51bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#45;&#49;&#51;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"140\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-96e8ff1b9ee38cf5d5dcccbb7fa6911d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#49;&#52;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#107;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"157\" style=\"vertical-align: -5px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b7b66ee76dcb6d6374cf83efdfb4446b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#45;&#53;&#107;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"133\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd07d0cc8d1c746b864c9bc256158349_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#57;&#43;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#104;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -5px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-93490a36adcc13cbf49dd3764a08a8e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#49;&#50;&#104;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"142\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b19b83d20ec2f3b76a9b1166884a2e20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#91;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"183\" style=\"vertical-align: -5px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c29f200d533fe721e432ffcb6dff9005_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#49;&#49;&#92;&#108;&#101;&#102;&#116;&#91;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#43;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#53;&#45;&#51;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"208\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f44ec79ad6af354e021a613de8f3ac9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#91;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"185\" style=\"vertical-align: -5px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ccaf5bd423fe1b36358d0ea6cb9f4f9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#50;&#92;&#108;&#101;&#102;&#116;&#91;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#43;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#49;&#45;&#51;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"209\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d550d1a74a0b3b748f2fb5e6afc3a9c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#53;&#118;&#45;&#48;&#46;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#55;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"148\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-873e715d6b3adf08d9f6bf7efedc4c98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#46;&#50;&#117;&#45;&#52;&#46;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"157\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6f81e9130b2e79f41b1982da044e87ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"190\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d4ce5c6ac4e168a0b9edc0fcba60e74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#50;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"198\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26950d791092d7164fa8d0478cba2b9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#54;&#109;&#43;&#51;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"167\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5f3813b513aa78145dc3a8d68a96872e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#48;&#110;&#43;&#53;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1166503546217\">Classify Equations<\/h2>\n<p id=\"fs-id1169747671603\">In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f55eb067af949a802acd60f35360bfea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#121;&#43;&#51;&#50;&#61;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#53;&#121;&#43;&#52;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"252\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e7ce986b0d63bf172b5b50580fec8407_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;&#122;&#43;&#49;&#57;&#61;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#122;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#56;&#122;&#43;&#52;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"243\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf678776587c47725bade42b5d22b1ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#97;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#97;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#54;&#97;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"330\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-77720feed279579d31574cc53afd3f19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#98;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#98;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;&#98;&#43;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"331\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-91cb635beafbcda898641fa6e58f42a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#100;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#49;&#48;&#48;&#61;&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"172\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-65dde71c01b897de0cb87bbf9e9024a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#106;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#57;&#61;&#52;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"162\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-78f624cfb8729e1f6dbaf77dac4c1a44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#110;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"192\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aa725fce9133997e83090992f143bf77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#109;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#109;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"193\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7a9d738756cacde18dde84b1210834b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#117;&#45;&#53;&#49;&#61;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#117;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#117;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"270\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8aa6ebb7c53c764d603259e8d98c3b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#118;&#43;&#52;&#50;&#61;&#49;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#118;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#51;&#118;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"268\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1f4f0fb788009703b650e243846d6593_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#112;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#112;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"344\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e89ac31cd21ffc1e705c1b49af797849_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#113;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#113;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"343\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-64aada04201864a0d3e5ffba0f3ca979_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#107;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#107;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"213\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">72. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-acd46839248d5082cd2301e244960f63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#104;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#104;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"213\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f55040c6298e6dd12168ea6905d59009_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">74. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-96347630ab10fd00fd1bb0eb4cd1361d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#121;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#121;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"189\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b9a90f85ce6887e40914c0c9d52c6c22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#109;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#109;&#43;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"220\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">76. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-115f8da248a410c2114608569650305c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#110;&#43;&#49;&#53;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#32;&#52;&#56;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"200\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a7032457b280e8ce83839fd35af1bd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#99;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#56;&#99;&#61;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#48;&#99;&#43;&#50;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"262\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 49.9086%;\">78. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-37bfd769504360307fc45e958a82be15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#100;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;&#100;&#61;&#49;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#100;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"269\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 data-type=\"title\">Everyday Math<\/h3>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">79. <strong data-effect=\"bold\">Coins.<\/strong> Rhonda has &#36;1.90 in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, <em data-effect=\"italics\">n<\/em>, by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6e4db7258a9970cec755689f70ab59f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#53;&#110;&#43;&#48;&#46;&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#46;&#57;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"218\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td style=\"width: 50%;\">80. <strong data-effect=\"bold\">Fencing.<\/strong> Micah has 44 feet of fencing to make a dog run in his yard. He wants the length to be 2.5 feet more than the width. Find the length, <em data-effect=\"italics\">L<\/em>, by solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23df047a914d0f2748306c9f3aca4982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#76;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#76;&#45;&#50;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"166\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 data-type=\"title\">Writing Exercises<\/h3>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%;\">81. Explain why you should simplify both sides of an equation as much as possible before collecting the variable terms to one side and the constant terms to the other side.<\/td>\n<td style=\"width: 49.9086%;\">82. Using your own words, list the steps in the general strategy for solving linear equations.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.0914%;\">83. Solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c49fd33350b7a77a5dc7ff9142337942_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#120;&#43;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"157\" style=\"vertical-align: -6px;\" \/> explaining all the steps of your solution as in the examples in this section.<\/td>\n<td style=\"width: 49.9086%;\">84. What is the first step you take when solving the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8a1c610de180a5d19eeb6cb30a12935d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#45;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"138\" style=\"vertical-align: -4px;\" \/> ? Why is this your first step?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e36d35d8563f5053efd9935e88634f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f8cc5b6f8164d5b6c93684c182426431_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9fe74ae8e4a9b2d944b519ce8f1b9768_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0f9852dce0ad3f5ebb8beed88c840c64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"53\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e7fc72e96811a37d7cae11c613f3a11e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfe6b8302a0e2c1ad85c476cb050e428_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-abf8f2abfdf1913d009a51ad64786690_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"38\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3a646b25cb6c00cee4e7d119996f3078_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"41\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-06850848b9cb549439f0fdbd71d6fa08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70bc60ba30d69379856f5d206776546c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"70\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/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;\" \/><\/td>\n<td style=\"width: 33.3333%;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d99af0e768e77a0e7bfe6c7fa2e2a868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e1735c51b99ed2469a7f2a6f728de75f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca3085d981ac492e6a62aabf76e4de69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-260107cba86a7b21e919180b1130050e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-91f9ec631e44f3d108457c2f8adad27c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4dd06fd55a4adfd9e44a93b87941bfd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-77758982e3a224cd6ee6269fafa47055_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b3a9aaead32d845a3937892a6bb5f472_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/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;\" \/><\/td>\n<td style=\"width: 33.3333%;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-754283866fe7f24eadf016df34fe5cf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-204dd4bdcdec3879abb8d0135a9491c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf9a8216e1eaa7b74afb3f4e44b84fce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d06eda523b0f75b74b4c7d7f11ee69e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e41dc7a241b8abeadd8c2bc6b66d3e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-56f0d4b4d1329f11745467e18c80edac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#45;&#51;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-754283866fe7f24eadf016df34fe5cf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">59. identity; all real numbers<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">61. identity; all real numbers<\/td>\n<td style=\"width: 33.3333%;\">63. conditional equation; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cba653835f494f8ae527942ac353a9a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">65. conditional equation; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2698a1aeddec133436df9fa55dd4c666_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">67. contradiction; no solution<\/td>\n<td style=\"width: 33.3333%;\">69. contradiction; no solution<\/td>\n<td style=\"width: 33.3333%;\">71. conditional equation; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c2d492f433f0e4ed0826cd429a1fe667_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#61;&#50;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"51\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">73. contradiction; no solution<\/td>\n<td style=\"width: 33.3333%;\">75. identity; all real numbers<\/td>\n<td style=\"width: 33.3333%;\">77. identity; all real numbers<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">79. 8 nickels<\/td>\n<td style=\"width: 33.3333%;\">81. Answers will vary.<\/td>\n<td style=\"width: 33.3333%;\">83. Answers will vary.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cUse a General Strategy to Solve Linear Equations\u201d in <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 Copyright page for more information.<\/p>\n","protected":false},"author":90,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1247","chapter","type-chapter","status-publish","hentry"],"part":767,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1247","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1247\/revisions"}],"predecessor-version":[{"id":1248,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1247\/revisions\/1248"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/767"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/1247\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=1247"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1247"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=1247"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=1247"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}