{"id":4420,"date":"2020-04-13T12:59:47","date_gmt":"2020-04-13T12:59:47","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4420"},"modified":"2021-02-06T00:04:56","modified_gmt":"2021-02-06T00:04:56","slug":"using-the-division-and-multiplication-properties-of-equality-for-single-step-equations","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/using-the-division-and-multiplication-properties-of-equality-for-single-step-equations\/","title":{"raw":"Using the Division and Multiplication Properties of Equality for Single-Step Equations","rendered":"Using the Division and Multiplication Properties of Equality for Single-Step Equations"},"content":{"raw":"<div class=\"textbox learning-objectives\"><h3>Learning Outcomes<\/h3><ul><li>Review and use the division and multiplication properties of equality to solve linear equations<\/li><li>Use a reciprocal to solve a linear equation that contains fractions<\/li><\/ul><\/div>Let's review the Division and Multiplication Properties of Equality as we prepare to use them to solve single-step equations.\r\n\r\n<div class=\"textbox shaded\"><h3 class=\"title\">Division Property of Equality<\/h3>For all real numbers [latex]a,b,c[\/latex], and [latex]c\\ne 0[\/latex], if [latex]a=b[\/latex], then [latex]\\Large\\frac{a}{c}\\normalsize =\\Large\\frac{b}{c}[\/latex].\r\n\r\n<\/div><div class=\"textbox shaded\"><h3 class=\"title\">Multiplication Property of Equality<\/h3>For all real numbers [latex]a,b,c[\/latex], if [latex]a=b[\/latex], then [latex]ac=bc[\/latex].\r\n\r\n<\/div>Stated simply, when you divide or multiply both sides of an equation by the same quantity, you still have equality.\r\n\r\nLet\u2019s review how these properties of equality can be applied in order to solve equations. Remember, the goal is to \"undo\" the operation on the variable. In the example below the variable is multiplied by [latex]4[\/latex], so we will divide both sides by [latex]4[\/latex] to \"undo\" the multiplication.\r\n\r\n<div class=\"textbox exercises\"><h3>example<\/h3>Solve: [latex]4x=-28[\/latex]\r\n\r\nSolution:\r\n\r\nTo solve this equation, we use the Division Property of Equality to divide both sides by [latex]4[\/latex].\r\n\r\n<table><tbody><tr><td>[latex]4x=-28[\/latex]<\/td><\/tr><tr><td>Divide both sides by 4 to undo the multiplication.<\/td><td>[latex]\\Large\\frac{4x}{\\color{red}4}\\normalsize =\\Large\\frac{-28}{\\color{red}4}[\/latex]<\/td><\/tr><tr><td>Simplify.<\/td><td>[latex]x =-7[\/latex]<\/td><\/tr><tr><td>Check your answer.<\/td><td>[latex]4x=-28[\/latex]<\/td><\/tr><tr><td>Let [latex]x=-7[\/latex]. Substitute [latex]-7[\/latex] for x.<\/td><td>[latex]4(\\color{red}{-7})\\stackrel{\\text{?}}{=}-28[\/latex]<\/td><\/tr><tr><td><\/td><td>&nbsp;[latex]-28=-28[\/latex]<\/td><\/tr><\/tbody><\/table>Since this is a true statement, [latex]x=-7[\/latex] is a solution to [latex]4x=-28[\/latex].\r\n\r\n<\/div>Now you can try to solve an equation that requires division and&nbsp;includes negative numbers.\r\n\r\n<div class=\"textbox key-takeaways\"><h3>try&nbsp;it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141857&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\r\n\r\n\r\n\r\n<\/div>In the previous example, to \"undo\" multiplication, we divided. How do you think we \"undo\" division? Next, we will show an example that requires us to use multiplication to undo division.\r\n\r\n<div class=\"textbox exercises\"><h3>example<\/h3>Solve: [latex]\\Large\\frac{a}{-7}\\normalsize =-42[\/latex]\r\n\r\n[reveal-answer q=\"399032\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"399032\"]\r\n\r\nSolution:\r\nHere [latex]a[\/latex] is divided by [latex]-7[\/latex]. We can multiply both sides by [latex]-7[\/latex] to isolate [latex]a[\/latex].\r\n\r\n<table id=\"eip-id1168468288515\" class=\"unnumbered unstyled\" summary=\"The top shows a over negative 7 equals negative 42. The next line says \"><tbody><tr><td>[latex]\\Large\\frac{a}{-7}\\normalsize =-42[\/latex]<\/td><\/tr><tr><td>Multiply both sides by [latex]-7[\/latex] .<\/td><td>[latex]\\color{red}{-7}(\\Large\\frac{a}{-7}\\normalsize)=\\color{red}{-7}(-42)[\/latex]\r\n\r\n[latex]\r\n\r\n\\Large\\frac{-7a}{-7}\\normalsize=294[\/latex]\r\n\r\n<\/td><\/tr><tr><td>Simplify.<\/td><td>[latex]a=294[\/latex]<\/td><\/tr><tr><td>Check your answer.<\/td><td>[latex]\\Large\\frac{a}{-7}\\normalsize=-42[\/latex]<\/td><\/tr><tr><td>Let [latex]a=294[\/latex] .<\/td><td>[latex]\\Large\\frac{\\color{red}{294}}{-7}\\normalsize\\stackrel{\\text{?}}{=}-42[\/latex]<\/td><\/tr><tr><td><\/td><td>[latex]-42=-42\\quad\\checkmark[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\r\n\r\n<\/div>Now see if you can solve a&nbsp;problem that requires multiplication to undo division. Recall the rules for multiplying two negative numbers - two negatives give a positive when they are multiplied.\r\n\r\n<div class=\"textbox key-takeaways\"><h3>try&nbsp;it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141868&amp;theme=oea&amp;iframe_resize_id=mom21[\/embed]\r\n\r\n\r\n\r\n<\/div>As you begin to solve equations that require several steps you may find that you end up with an equation that looks like the one in the next example, with a negative variable. &nbsp;As a standard practice, it is good to ensure that variables are positive when you are solving equations. The next example will show you how.\r\n\r\n<div class=\"textbox exercises\"><h3>example<\/h3>Solve: [latex]-r=2[\/latex]\r\n\r\n[reveal-answer q=\"388033\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"388033\"]\r\n\r\nSolution:\r\nRemember [latex]-r[\/latex] is equivalent to [latex]-1r[\/latex].\r\n\r\n<table id=\"eip-id1168469604717\" class=\"unnumbered unstyled\" summary=\"The first line says negative r equals 2. The next line says \"><tbody><tr><td>[latex]-r=2[\/latex]<\/td><td><\/td><\/tr><tr><td>Rewrite [latex]-r[\/latex] as [latex]-1r[\/latex] .<\/td><td>[latex]-1r=2[\/latex]<\/td><\/tr><tr><td>Divide both sides by [latex]-1[\/latex] .<\/td><td>[latex]\\Large\\frac{-1r}{\\color{red}{-1}}\\normalsize =\\Large\\frac{2}{\\color{red}{-1}}[\/latex]<\/td><\/tr><tr><td>Simplify.<\/td><td>[latex]r=-2[\/latex]<\/td><\/tr><tr><td>Check.<\/td><td>[latex]-r=2[\/latex]<\/td><\/tr><tr><td>Substitute [latex]r=-2[\/latex]<\/td><td>[latex]-(\\color{red}{-2})\\stackrel{\\text{?}}{=}2[\/latex]<\/td><\/tr><tr><td>Simplify.<\/td><td>[latex]2=2\\quad\\checkmark[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\r\n\r\n<\/div>Now you can try to solve an equation with a negative variable.\r\n\r\n<div class=\"textbox key-takeaways\"><h3>try&nbsp;it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141865&amp;theme=oea&amp;iframe_resize_id=mom22[\/embed]\r\n\r\n\r\n\r\n<\/div>In our next example, we are given an equation that contains a variable multiplied by a fraction. We will use a reciprocal to isolate the variable.\r\n\r\n<div class=\"textbox exercises\"><h3>example<\/h3>Solve: [latex]\\Large\\frac{2}{3}\\normalsize x=18[\/latex]\r\n\r\n[reveal-answer q=\"444022\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"444022\"]\r\n\r\nSolution:\r\nSince the product of a number and its reciprocal is [latex]1[\/latex], our strategy will be to isolate [latex]x[\/latex] by multiplying by the reciprocal of [latex]\\Large\\frac{2}{3}[\/latex].\r\n\r\n<table id=\"eip-id1168468646645\" class=\"unnumbered unstyled\" summary=\"The first line shows two-thirds x equals 18. The next line says \"><tbody><tr style=\"height: 37px\"><td style=\"height: 37px\">[latex]\\Large\\frac{2}{3}\\normalsize x=18[\/latex]<\/td><\/tr><tr style=\"height: 38px\"><td style=\"height: 38px\">Multiply by the reciprocal of [latex]\\Large\\frac{2}{3}[\/latex] .<\/td><td style=\"height: 38px\">[latex]\\Large\\frac{\\color{red}{3}}{\\color{red}{2}}\\normalsize\\cdot\\Large\\frac{2}{3}\\normalsize x[\/latex]<\/td><\/tr><tr style=\"height: 37px\"><td style=\"height: 37px\">Reciprocals multiply to one.<\/td><td style=\"height: 37px\">[latex]1x=\\Large\\frac{3}{2}\\normalsize\\cdot\\Large\\frac{18}{1}[\/latex]<\/td><\/tr><tr style=\"height: 18px\"><td style=\"height: 18px\">Multiply.<\/td><td style=\"height: 18px\">[latex]x=27[\/latex]<\/td><\/tr><tr style=\"height: 14px\"><td style=\"height: 14px\">Check your answer.<\/td><td style=\"height: 44.8594px\">[latex]\\Large\\frac{2}{3}\\normalsize x=18[\/latex]<\/td><\/tr><tr style=\"height: 44.8594px\"><td style=\"height: 14px\">Let [latex]x=27[\/latex].<\/td><td style=\"height: 45px\">[latex]\\Large\\frac{2}{3}\\normalsize\\cdot\\color{red}{27}\\stackrel{\\text{?}}{=}18[\/latex]<\/td><\/tr><tr style=\"height: 24px\"><td><\/td><td style=\"height: 24px\">[latex]18=18\\quad\\checkmark[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\r\n\r\n<\/div>Notice that we could have divided both sides of the equation [latex]\\Large\\frac{2}{3}\\normalsize x=18[\/latex] by [latex]\\Large\\frac{2}{3}[\/latex] to isolate [latex]x[\/latex]. While this would work, multiplying by the reciprocal requires fewer steps.\r\n\r\n<div class=\"textbox key-takeaways\"><h3>try&nbsp;it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141871&amp;theme=oea&amp;iframe_resize_id=mom22[\/embed]\r\n\r\n\r\n\r\n<\/div>The next video includes examples of using the division and multiplication properties to solve equations with the variable on the right side of the equal sign.\r\n\r\nhttps:\/\/youtu.be\/TB1rkPbF8rA\r\n\r\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Review and use the division and multiplication properties of equality to solve linear equations<\/li>\n<li>Use a reciprocal to solve a linear equation that contains fractions<\/li>\n<\/ul>\n<\/div>\n<p>Let&#8217;s review the Division and Multiplication Properties of Equality as we prepare to use them to solve single-step equations.<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Division Property of Equality<\/h3>\n<p>For all real numbers [latex]a,b,c[\/latex], and [latex]c\\ne 0[\/latex], if [latex]a=b[\/latex], then [latex]\\Large\\frac{a}{c}\\normalsize =\\Large\\frac{b}{c}[\/latex].<\/p>\n<\/div>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Multiplication Property of Equality<\/h3>\n<p>For all real numbers [latex]a,b,c[\/latex], if [latex]a=b[\/latex], then [latex]ac=bc[\/latex].<\/p>\n<\/div>\n<p>Stated simply, when you divide or multiply both sides of an equation by the same quantity, you still have equality.<\/p>\n<p>Let\u2019s review how these properties of equality can be applied in order to solve equations. Remember, the goal is to &#8220;undo&#8221; the operation on the variable. In the example below the variable is multiplied by [latex]4[\/latex], so we will divide both sides by [latex]4[\/latex] to &#8220;undo&#8221; the multiplication.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Solve: [latex]4x=-28[\/latex]<\/p>\n<p>Solution:<\/p>\n<p>To solve this equation, we use the Division Property of Equality to divide both sides by [latex]4[\/latex].<\/p>\n<table>\n<tbody>\n<tr>\n<td>[latex]4x=-28[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 4 to undo the multiplication.<\/td>\n<td>[latex]\\Large\\frac{4x}{\\color{red}4}\\normalsize =\\Large\\frac{-28}{\\color{red}4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]x =-7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check your answer.<\/td>\n<td>[latex]4x=-28[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Let [latex]x=-7[\/latex]. Substitute [latex]-7[\/latex] for x.<\/td>\n<td>[latex]4(\\color{red}{-7})\\stackrel{\\text{?}}{=}-28[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>&nbsp;[latex]-28=-28[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since this is a true statement, [latex]x=-7[\/latex] is a solution to [latex]4x=-28[\/latex].<\/p>\n<\/div>\n<p>Now you can try to solve an equation that requires division and&nbsp;includes negative numbers.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try&nbsp;it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141857\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141857&#38;theme=oea&#38;iframe_resize_id=ohm141857&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the previous example, to &#8220;undo&#8221; multiplication, we divided. How do you think we &#8220;undo&#8221; division? Next, we will show an example that requires us to use multiplication to undo division.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Solve: [latex]\\Large\\frac{a}{-7}\\normalsize =-42[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q399032\">Show Solution<\/span><\/p>\n<div id=\"q399032\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nHere [latex]a[\/latex] is divided by [latex]-7[\/latex]. We can multiply both sides by [latex]-7[\/latex] to isolate [latex]a[\/latex].<\/p>\n<table id=\"eip-id1168468288515\" class=\"unnumbered unstyled\" summary=\"The top shows a over negative 7 equals negative 42. The next line says\">\n<tbody>\n<tr>\n<td>[latex]\\Large\\frac{a}{-7}\\normalsize =-42[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by [latex]-7[\/latex] .<\/td>\n<td>[latex]\\color{red}{-7}(\\Large\\frac{a}{-7}\\normalsize)=\\color{red}{-7}(-42)[\/latex]<\/p>\n<p>[latex]\\Large\\frac{-7a}{-7}\\normalsize=294[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]a=294[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check your answer.<\/td>\n<td>[latex]\\Large\\frac{a}{-7}\\normalsize=-42[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Let [latex]a=294[\/latex] .<\/td>\n<td>[latex]\\Large\\frac{\\color{red}{294}}{-7}\\normalsize\\stackrel{\\text{?}}{=}-42[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-42=-42\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now see if you can solve a&nbsp;problem that requires multiplication to undo division. Recall the rules for multiplying two negative numbers &#8211; two negatives give a positive when they are multiplied.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try&nbsp;it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141868\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141868&#38;theme=oea&#38;iframe_resize_id=ohm141868&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>As you begin to solve equations that require several steps you may find that you end up with an equation that looks like the one in the next example, with a negative variable. &nbsp;As a standard practice, it is good to ensure that variables are positive when you are solving equations. The next example will show you how.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Solve: [latex]-r=2[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q388033\">Show Solution<\/span><\/p>\n<div id=\"q388033\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nRemember [latex]-r[\/latex] is equivalent to [latex]-1r[\/latex].<\/p>\n<table id=\"eip-id1168469604717\" class=\"unnumbered unstyled\" summary=\"The first line says negative r equals 2. The next line says\">\n<tbody>\n<tr>\n<td>[latex]-r=2[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Rewrite [latex]-r[\/latex] as [latex]-1r[\/latex] .<\/td>\n<td>[latex]-1r=2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by [latex]-1[\/latex] .<\/td>\n<td>[latex]\\Large\\frac{-1r}{\\color{red}{-1}}\\normalsize =\\Large\\frac{2}{\\color{red}{-1}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]r=-2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check.<\/td>\n<td>[latex]-r=2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]r=-2[\/latex]<\/td>\n<td>[latex]-(\\color{red}{-2})\\stackrel{\\text{?}}{=}2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]2=2\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you can try to solve an equation with a negative variable.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try&nbsp;it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141865\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141865&#38;theme=oea&#38;iframe_resize_id=ohm141865&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In our next example, we are given an equation that contains a variable multiplied by a fraction. We will use a reciprocal to isolate the variable.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Solve: [latex]\\Large\\frac{2}{3}\\normalsize x=18[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q444022\">Show Solution<\/span><\/p>\n<div id=\"q444022\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nSince the product of a number and its reciprocal is [latex]1[\/latex], our strategy will be to isolate [latex]x[\/latex] by multiplying by the reciprocal of [latex]\\Large\\frac{2}{3}[\/latex].<\/p>\n<table id=\"eip-id1168468646645\" class=\"unnumbered unstyled\" summary=\"The first line shows two-thirds x equals 18. The next line says\">\n<tbody>\n<tr style=\"height: 37px\">\n<td style=\"height: 37px\">[latex]\\Large\\frac{2}{3}\\normalsize x=18[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 38px\">\n<td style=\"height: 38px\">Multiply by the reciprocal of [latex]\\Large\\frac{2}{3}[\/latex] .<\/td>\n<td style=\"height: 38px\">[latex]\\Large\\frac{\\color{red}{3}}{\\color{red}{2}}\\normalsize\\cdot\\Large\\frac{2}{3}\\normalsize x[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 37px\">\n<td style=\"height: 37px\">Reciprocals multiply to one.<\/td>\n<td style=\"height: 37px\">[latex]1x=\\Large\\frac{3}{2}\\normalsize\\cdot\\Large\\frac{18}{1}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"height: 18px\">Multiply.<\/td>\n<td style=\"height: 18px\">[latex]x=27[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px\">Check your answer.<\/td>\n<td style=\"height: 44.8594px\">[latex]\\Large\\frac{2}{3}\\normalsize x=18[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 44.8594px\">\n<td style=\"height: 14px\">Let [latex]x=27[\/latex].<\/td>\n<td style=\"height: 45px\">[latex]\\Large\\frac{2}{3}\\normalsize\\cdot\\color{red}{27}\\stackrel{\\text{?}}{=}18[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 24px\">\n<td><\/td>\n<td style=\"height: 24px\">[latex]18=18\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Notice that we could have divided both sides of the equation [latex]\\Large\\frac{2}{3}\\normalsize x=18[\/latex] by [latex]\\Large\\frac{2}{3}[\/latex] to isolate [latex]x[\/latex]. While this would work, multiplying by the reciprocal requires fewer steps.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try&nbsp;it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141871\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141871&#38;theme=oea&#38;iframe_resize_id=ohm141871&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The next video includes examples of using the division and multiplication properties to solve equations with the variable on the right side of the equal sign.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Solving One Step Equation by Mult\/Div.  Integers (Var on Right)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/TB1rkPbF8rA?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4420\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 141857, 141871, 141865, 141871. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License, CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Solving One Step Equations Using Multiplication (Fractions). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/AhBdGeUGgsI\">https:\/\/youtu.be\/AhBdGeUGgsI<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex: Solving One Step Equation by Mult\/Div. Integers (Var on Right). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/TB1rkPbF8rA\">https:\/\/youtu.be\/TB1rkPbF8rA<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":25777,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Solving One Step Equations Using Multiplication (Fractions)\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/AhBdGeUGgsI\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Solving One Step Equation by Mult\/Div. Integers (Var on Right)\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/TB1rkPbF8rA\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 141857, 141871, 141865, 141871\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License, CC-BY + GPL\"},{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4420","chapter","type-chapter","status-web-only","hentry"],"part":4412,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4420\/revisions"}],"predecessor-version":[{"id":4421,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4420\/revisions\/4421"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/4412"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4420\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4420"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4420"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4420"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}