{"id":9019,"date":"2017-05-01T15:07:26","date_gmt":"2017-05-01T15:07:26","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9019"},"modified":"2020-10-22T09:07:12","modified_gmt":"2020-10-22T09:07:12","slug":"using-the-division-and-multiplication-properties-of-equality-for-single-step-equations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/using-the-division-and-multiplication-properties-of-equality-for-single-step-equations\/","title":{"raw":"7.1.b - Using the Division and Multiplication Properties of Equality to Solve Equations","rendered":"7.1.b &#8211; Using the Division and Multiplication Properties of Equality to Solve Equations"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Determine whether a number is a solution to an equation<\/li>\r\n \t<li>Check your solution to a linear equation to verify its accuracy<\/li>\r\n \t<li>Solve equations using the Division and Multiplication Properties of Equality<\/li>\r\n \t<li>Solve equations that need to be simplified<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2 id=\"title2\">Solve algebraic equations using the multiplication and division properties of equality<\/h2>\r\nJust as you can add or subtract the same exact quantity on both sides of an equation, you can also multiply or divide both sides of an equation by the same quantity to write an equivalent equation. To start, let\u2019s look at a numeric equation, [latex]5\\cdot3=15[\/latex], as an example. If you multiply both sides of this equation by \u00a0[latex]2[\/latex], you will still have a true equation.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}5\\cdot 3=15\\,\\,\\,\\,\\,\\,\\, \\\\ 5\\cdot3\\cdot2=15\\cdot2 \\\\ 30=30\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\nThis characteristic of equations is generalized in the <strong>M<\/strong><b>ultiplication Property of Equality<\/b>.\r\n\r\nLet's review the Division and Multiplication Properties of Equality as we prepare to use them to solve single-step equations.\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Division Property of Equality<\/h3>\r\nFor 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\nIf two expressions are equal to each other and you divide both sides by the same number that is not equal to zero, the resulting expressions will also be equivalent.\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Multiplication Property of Equality<\/h3>\r\nFor all real numbers [latex]a,b,c[\/latex], if [latex]a=b[\/latex], then [latex]ac=bc[\/latex].\r\n\r\nIf two expressions are equal to each other and you multiply both sides by the same number, the resulting expressions will also be equivalent.\r\n\r\n<\/div>\r\nStated simply, when you divide or multiply both sides of an equation by the same quantity, you still have equality.\u00a0 When the equation involves multiplication or division, you can \u201cundo\u201d these operations by using the inverse operation to isolate the variable.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve [latex]3x=24[\/latex]. When you are done, check your solution.\r\n\r\n[reveal-answer q=\"42404\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"42404\"]\r\n\r\nDivide both sides of the equation by [latex]3[\/latex] to isolate the variable (this is will give you a coefficient of \u00a0[latex]1[\/latex]).\u00a0Dividing by [latex]3[\/latex] is the same as multiplying by [latex] \\frac{1}{3}[\/latex].\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\underline{3x}=\\underline{24}\\\\3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\,\\\\x=8\\,\\,\\,\\end{array}[\/latex]<\/p>\r\nCheck by substituting your solution, [latex]8[\/latex], for the variable in the original equation.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}3x=24 \\\\ 3\\cdot8=24 \\\\ 24=24\\end{array}[\/latex]<\/p>\r\nThe solution is correct!\r\n<h4>Answer<\/h4>\r\n[latex]x=8[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn 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<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSolve: [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<table id=\"eip-id1168468288515\" class=\"unnumbered unstyled\" summary=\"The top shows a over negative 7 equals negative 42. The next line says \">\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\Large\\frac{a}{-7}\\normalsize =-42[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply both sides by [latex]-7[\/latex] .<\/td>\r\n<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]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]a=294[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check your answer.<\/td>\r\n<td>[latex]\\Large\\frac{a}{-7}\\normalsize=-42[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Let [latex]a=294[\/latex] .<\/td>\r\n<td>[latex]\\Large\\frac{\\color{red}{294}}{-7}\\normalsize\\stackrel{\\text{?}}{=}-42[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-42=-42\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow see if you can solve a\u00a0problem that requires multiplication to undo division. Recall the rules for multiplying two negative numbers \u2014 two negatives give a positive when they are multiplied.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try\u00a0it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141868&amp;theme=oea&amp;iframe_resize_id=mom21[\/embed]\r\n\r\n<\/div>\r\nAnother way to think about solving an equation when the operation is multiplication or division is that we want to multiply the coefficient by the multiplicative inverse (reciprocal) in order to change the coefficient to [latex]1[\/latex].\r\n\r\nIn the following example, we\u00a0change the coefficient to \u00a0[latex]1[\/latex] by multiplying by the multiplicative inverse of [latex]\\frac{1}{2}[\/latex].\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve [latex] \\frac{1}{2 }{ x }={ 8}[\/latex] for [latex]x[\/latex].\r\n[reveal-answer q=\"128018\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"128018\"]\r\n\r\nThe only difference between this and the previous example is that the coefficient on\u00a0[latex]x[\/latex] is a fraction. In the last example we used the reciprocal of \u00a0[latex]3[\/latex] to isolate the [latex]x[\/latex] (disguised as division). Now we can use the reciprocal of [latex]\\frac{1}{2}[\/latex], which is [latex]2[\/latex].\r\n<p style=\"text-align: left\">Multiply both sides by [latex]2[\/latex]:<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\left(2\\right)\\frac{1}{2 }{ x }=\\left(2\\right){ 8}\\\\(1)x= 16\\,\\,\\,\\,\\\\{ x }=16\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: center\">[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\nIn the video below, you will see examples of how to use the Multiplication and Division Properties of Equality to solve one-step equations with integers and fractions.\r\n\r\nhttps:\/\/www.youtube.com\/watch?v=BN7iVWWl2y0&amp;feature=youtu.be\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSolve: [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<table>\r\n<tbody>\r\n<tr>\r\n<td>[latex]4x=-28[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by 4 to undo the multiplication.<\/td>\r\n<td>[latex]\\Large\\frac{4x}{\\color{red}4}\\normalsize =\\Large\\frac{-28}{\\color{red}4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]x =-7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check your answer.<\/td>\r\n<td>[latex]4x=-28[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Let [latex]x=-7[\/latex]. Substitute [latex]-7[\/latex] for x.<\/td>\r\n<td>[latex]4(\\color{red}{-7})\\stackrel{\\text{?}}{=}-28[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>\u00a0[latex]-28=-28[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSince this is a true statement, [latex]x=-7[\/latex] is a solution to [latex]4x=-28[\/latex].\r\n\r\n<\/div>\r\nNow you can try to solve an equation that requires division and\u00a0includes negative numbers.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try\u00a0it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141857&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\r\n\r\n<\/div>\r\nAs 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. \u00a0As 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<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSolve: [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<table id=\"eip-id1168469604717\" class=\"unnumbered unstyled\" summary=\"The first line says negative r equals 2. The next line says \">\r\n<tbody>\r\n<tr>\r\n<td>[latex]-r=2[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite [latex]-r[\/latex] as [latex]-1r[\/latex] .<\/td>\r\n<td>[latex]-1r=2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by [latex]-1[\/latex] .<\/td>\r\n<td>[latex]\\Large\\frac{-1r}{\\color{red}{-1}}\\normalsize =\\Large\\frac{2}{\\color{red}{-1}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]r=-2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check.<\/td>\r\n<td>[latex]-r=2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]r=-2[\/latex]<\/td>\r\n<td>[latex]-(\\color{red}{-2})\\stackrel{\\text{?}}{=}2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]2=2\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow you can try to solve an equation with a negative variable.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try\u00a0it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141865&amp;theme=oea&amp;iframe_resize_id=mom22[\/embed]\r\n\r\n<\/div>\r\nThe 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<h3>Two-Step Linear Equations<\/h3>\r\nIf the equation is in the form [latex]ax+b=c[\/latex], where [latex]x[\/latex] is the variable, you can solve the equation as before. First \u201cundo\u201d the addition and subtraction, and then \u201cundo\u201d the multiplication and division.\r\n<div class=\"textbox exercises\">\r\n<h3>Examples<\/h3>\r\nSolve: [latex]4x+6=-14[\/latex]\r\n\r\nSolution:\r\n\r\nIn this equation, the variable is only on the left side. It makes sense to call the left side the variable side. Therefore, the right side will be the constant side.\r\n<table style=\"width: 70%\" summary=\"The top line says 4x plus 6 equals negative 14.\">\r\n<tbody>\r\n<tr style=\"height: 45.8594px\">\r\n<td style=\"height: 45.8594px;width: 1179.02px\" colspan=\"2\">Since the left side is the variable side, the 6 is out of place. We must \"undo\" adding [latex]6[\/latex] by subtracting [latex]6[\/latex], and to keep the equality we must subtract [latex]6[\/latex] from both sides. Use the Subtraction Property of Equality.<\/td>\r\n<td style=\"height: 45.8594px;width: 176px\">[latex]4x+6\\color{red}{-6}=-14\\color{red}{-6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\">Simplify.<\/td>\r\n<td style=\"height: 15px;width: 176px\">[latex]4x=-20[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\">Now all the [latex]x[\/latex] s are on the left and the constant on the right.<\/td>\r\n<td style=\"height: 15px;width: 176px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 60px\">\r\n<td style=\"height: 60px;width: 1179.02px\" colspan=\"2\">Use the Division Property of Equality.<\/td>\r\n<td style=\"height: 60px;width: 176px\">[latex]\\Large\\frac{4x}{\\color{red}{4}}\\normalsize =\\Large\\frac{-20}{\\color{red}{4}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\">Simplify.<\/td>\r\n<td style=\"height: 15px;width: 176px\">[latex]x=-5[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\">Check:<\/td>\r\n<td style=\"height: 15px;width: 176px\">[latex]4x+6=-14[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\">Let [latex]x=-5[\/latex] .<\/td>\r\n<td style=\"height: 15px;width: 176px\">[latex]4(\\color{red}{-5})+6=-14[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\"><\/td>\r\n<td style=\"height: 15px;width: 176px\">[latex]-20+6=-14[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\"><\/td>\r\n<td style=\"height: 15px;width: 176px\">[latex]-14=-14\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSolve: [latex]2y - 7=15[\/latex]\r\n[reveal-answer q=\"629971\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"629971\"]\r\n\r\nSolution:\r\nNotice that the variable is only on the left side of the equation, so this will be the variable side, and the right side will be the constant side. Since the left side is the variable side, the [latex]7[\/latex] is out of place. It is subtracted from the [latex]2y[\/latex], so to \"undo\" subtraction, add [latex]7[\/latex] to both sides.\r\n<table id=\"eip-id1168469592645\" class=\"unnumbered unstyled\" summary=\"The first line says 2y minus 7 equals 15. The left side is labeled \">\r\n<tbody>\r\n<tr>\r\n<td>[latex]2y-7[\/latex] is the side containing a <span style=\"color: #000000\"><span style=\"color: #ff0000\">variable<\/span>.<\/span><span style=\"color: #000000\">[latex]15[\/latex] is the side containing only a <span style=\"color: #ff0000\">constant<\/span>.<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Add [latex]7[\/latex] to both sides.<\/td>\r\n<td>[latex]2y-7\\color{red}{+7}=15\\color{red}{+7}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Simplify.<\/td>\r\n<td>[latex]2y=22[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"3\">The variables are now on one side and the constants on the other.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Divide both sides by [latex]2[\/latex].<\/td>\r\n<td>[latex]\\Large\\frac{2y}{\\color{red}{2}}\\normalsize =\\Large\\frac{22}{\\color{red}{2}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Simplify.<\/td>\r\n<td>[latex]y=11[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Check:<\/td>\r\n<td>[latex]2y-7=15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Let [latex]y=11[\/latex] .<\/td>\r\n<td>[latex]2\\cdot\\color{red}{11}-7\\stackrel{\\text{?}}{=}15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\"><\/td>\r\n<td>[latex]22-7\\stackrel{\\text{?}}{=}15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\"><\/td>\r\n<td>[latex]15=15\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve [latex]3y+2=11[\/latex]\r\n\r\n[reveal-answer q=\"843520\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"843520\"]\r\n\r\nSubtract [latex]2[\/latex] from both sides of the equation to get the term with the variable by itself.\r\n<p style=\"text-align: center\">[latex] \\displaystyle \\begin{array}{r}3y+2\\,\\,\\,=\\,\\,11\\\\\\underline{\\,\\,\\,\\,\\,\\,\\,-2\\,\\,\\,\\,\\,\\,\\,\\,-2}\\\\3y\\,\\,\\,\\,=\\,\\,\\,\\,\\,9\\end{array}[\/latex]<\/p>\r\nDivide both sides of the equation by [latex]3[\/latex] to get a coefficient of [latex]1[\/latex] for the variable.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\,\\,\\,\\,\\,\\,\\underline{3y}\\,\\,\\,\\,=\\,\\,\\,\\,\\,\\underline{9}\\\\3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,9\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,y\\,\\,\\,\\,=\\,\\,\\,\\,3\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]y=3[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nNow you can try\u00a0a similar problem.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try\u00a0It<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142131&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nIn the following video, we show examples of solving two step linear equations.\r\n\r\nhttps:\/\/youtu.be\/fCyxSVQKeRw\r\n\r\nRemember to check the solution of an algebraic equation by substituting the value of the variable into the original equation.\r\n\r\nIn the next section, we will learn how to solve equations that need to be simplified before they can be solved.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Determine whether a number is a solution to an equation<\/li>\n<li>Check your solution to a linear equation to verify its accuracy<\/li>\n<li>Solve equations using the Division and Multiplication Properties of Equality<\/li>\n<li>Solve equations that need to be simplified<\/li>\n<\/ul>\n<\/div>\n<h2 id=\"title2\">Solve algebraic equations using the multiplication and division properties of equality<\/h2>\n<p>Just as you can add or subtract the same exact quantity on both sides of an equation, you can also multiply or divide both sides of an equation by the same quantity to write an equivalent equation. To start, let\u2019s look at a numeric equation, [latex]5\\cdot3=15[\/latex], as an example. If you multiply both sides of this equation by \u00a0[latex]2[\/latex], you will still have a true equation.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}5\\cdot 3=15\\,\\,\\,\\,\\,\\,\\, \\\\ 5\\cdot3\\cdot2=15\\cdot2 \\\\ 30=30\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p>This characteristic of equations is generalized in the <strong>M<\/strong><b>ultiplication Property of Equality<\/b>.<\/p>\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<p>If two expressions are equal to each other and you divide both sides by the same number that is not equal to zero, the resulting expressions will also be equivalent.<\/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<p>If two expressions are equal to each other and you multiply both sides by the same number, the resulting expressions will also be equivalent.<\/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.\u00a0 When the equation involves multiplication or division, you can \u201cundo\u201d these operations by using the inverse operation to isolate the variable.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve [latex]3x=24[\/latex]. When you are done, check your solution.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q42404\">Show Solution<\/span><\/p>\n<div id=\"q42404\" class=\"hidden-answer\" style=\"display: none\">\n<p>Divide both sides of the equation by [latex]3[\/latex] to isolate the variable (this is will give you a coefficient of \u00a0[latex]1[\/latex]).\u00a0Dividing by [latex]3[\/latex] is the same as multiplying by [latex]\\frac{1}{3}[\/latex].<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\underline{3x}=\\underline{24}\\\\3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,3\\,\\\\x=8\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p>Check by substituting your solution, [latex]8[\/latex], for the variable in the original equation.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}3x=24 \\\\ 3\\cdot8=24 \\\\ 24=24\\end{array}[\/latex]<\/p>\n<p>The solution is correct!<\/p>\n<h4>Answer<\/h4>\n<p>[latex]x=8[\/latex]<\/p>\n<\/div>\n<\/div>\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]<\/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\u00a0problem that requires multiplication to undo division. Recall the rules for multiplying two negative numbers \u2014 two negatives give a positive when they are multiplied.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try\u00a0it<\/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>Another way to think about solving an equation when the operation is multiplication or division is that we want to multiply the coefficient by the multiplicative inverse (reciprocal) in order to change the coefficient to [latex]1[\/latex].<\/p>\n<p>In the following example, we\u00a0change the coefficient to \u00a0[latex]1[\/latex] by multiplying by the multiplicative inverse of [latex]\\frac{1}{2}[\/latex].<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve [latex]\\frac{1}{2 }{ x }={ 8}[\/latex] for [latex]x[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q128018\">Show Solution<\/span><\/p>\n<div id=\"q128018\" class=\"hidden-answer\" style=\"display: none\">\n<p>The only difference between this and the previous example is that the coefficient on\u00a0[latex]x[\/latex] is a fraction. In the last example we used the reciprocal of \u00a0[latex]3[\/latex] to isolate the [latex]x[\/latex] (disguised as division). Now we can use the reciprocal of [latex]\\frac{1}{2}[\/latex], which is [latex]2[\/latex].<\/p>\n<p style=\"text-align: left\">Multiply both sides by [latex]2[\/latex]:<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\left(2\\right)\\frac{1}{2 }{ x }=\\left(2\\right){ 8}\\\\(1)x= 16\\,\\,\\,\\,\\\\{ x }=16\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p style=\"text-align: center\"><\/div>\n<\/div>\n<\/div>\n<p>In the video below, you will see examples of how to use the Multiplication and Division Properties of Equality to solve one-step equations with integers and fractions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Solving One Step Equations Using Multiplication and Division (Basic)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/BN7iVWWl2y0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/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>\u00a0[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\u00a0includes negative numbers.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try\u00a0it<\/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>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. \u00a0As 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\u00a0it<\/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>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-2\" 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<h3>Two-Step Linear Equations<\/h3>\n<p>If the equation is in the form [latex]ax+b=c[\/latex], where [latex]x[\/latex] is the variable, you can solve the equation as before. First \u201cundo\u201d the addition and subtraction, and then \u201cundo\u201d the multiplication and division.<\/p>\n<div class=\"textbox exercises\">\n<h3>Examples<\/h3>\n<p>Solve: [latex]4x+6=-14[\/latex]<\/p>\n<p>Solution:<\/p>\n<p>In this equation, the variable is only on the left side. It makes sense to call the left side the variable side. Therefore, the right side will be the constant side.<\/p>\n<table style=\"width: 70%\" summary=\"The top line says 4x plus 6 equals negative 14.\">\n<tbody>\n<tr style=\"height: 45.8594px\">\n<td style=\"height: 45.8594px;width: 1179.02px\" colspan=\"2\">Since the left side is the variable side, the 6 is out of place. We must &#8220;undo&#8221; adding [latex]6[\/latex] by subtracting [latex]6[\/latex], and to keep the equality we must subtract [latex]6[\/latex] from both sides. Use the Subtraction Property of Equality.<\/td>\n<td style=\"height: 45.8594px;width: 176px\">[latex]4x+6\\color{red}{-6}=-14\\color{red}{-6}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\">Simplify.<\/td>\n<td style=\"height: 15px;width: 176px\">[latex]4x=-20[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\">Now all the [latex]x[\/latex] s are on the left and the constant on the right.<\/td>\n<td style=\"height: 15px;width: 176px\"><\/td>\n<\/tr>\n<tr style=\"height: 60px\">\n<td style=\"height: 60px;width: 1179.02px\" colspan=\"2\">Use the Division Property of Equality.<\/td>\n<td style=\"height: 60px;width: 176px\">[latex]\\Large\\frac{4x}{\\color{red}{4}}\\normalsize =\\Large\\frac{-20}{\\color{red}{4}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\">Simplify.<\/td>\n<td style=\"height: 15px;width: 176px\">[latex]x=-5[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\">Check:<\/td>\n<td style=\"height: 15px;width: 176px\">[latex]4x+6=-14[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\">Let [latex]x=-5[\/latex] .<\/td>\n<td style=\"height: 15px;width: 176px\">[latex]4(\\color{red}{-5})+6=-14[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\"><\/td>\n<td style=\"height: 15px;width: 176px\">[latex]-20+6=-14[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px;width: 1179.02px\" colspan=\"2\"><\/td>\n<td style=\"height: 15px;width: 176px\">[latex]-14=-14\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Solve: [latex]2y - 7=15[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q629971\">Show Solution<\/span><\/p>\n<div id=\"q629971\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nNotice that the variable is only on the left side of the equation, so this will be the variable side, and the right side will be the constant side. Since the left side is the variable side, the [latex]7[\/latex] is out of place. It is subtracted from the [latex]2y[\/latex], so to &#8220;undo&#8221; subtraction, add [latex]7[\/latex] to both sides.<\/p>\n<table id=\"eip-id1168469592645\" class=\"unnumbered unstyled\" summary=\"The first line says 2y minus 7 equals 15. The left side is labeled\">\n<tbody>\n<tr>\n<td>[latex]2y-7[\/latex] is the side containing a <span style=\"color: #000000\"><span style=\"color: #ff0000\">variable<\/span>.<\/span><span style=\"color: #000000\">[latex]15[\/latex] is the side containing only a <span style=\"color: #ff0000\">constant<\/span>.<\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Add [latex]7[\/latex] to both sides.<\/td>\n<td>[latex]2y-7\\color{red}{+7}=15\\color{red}{+7}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]2y=22[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"3\">The variables are now on one side and the constants on the other.<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Divide both sides by [latex]2[\/latex].<\/td>\n<td>[latex]\\Large\\frac{2y}{\\color{red}{2}}\\normalsize =\\Large\\frac{22}{\\color{red}{2}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]y=11[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Check:<\/td>\n<td>[latex]2y-7=15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Let [latex]y=11[\/latex] .<\/td>\n<td>[latex]2\\cdot\\color{red}{11}-7\\stackrel{\\text{?}}{=}15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><\/td>\n<td>[latex]22-7\\stackrel{\\text{?}}{=}15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><\/td>\n<td>[latex]15=15\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve [latex]3y+2=11[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q843520\">Show Solution<\/span><\/p>\n<div id=\"q843520\" class=\"hidden-answer\" style=\"display: none\">\n<p>Subtract [latex]2[\/latex] from both sides of the equation to get the term with the variable by itself.<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle \\begin{array}{r}3y+2\\,\\,\\,=\\,\\,11\\\\\\underline{\\,\\,\\,\\,\\,\\,\\,-2\\,\\,\\,\\,\\,\\,\\,\\,-2}\\\\3y\\,\\,\\,\\,=\\,\\,\\,\\,\\,9\\end{array}[\/latex]<\/p>\n<p>Divide both sides of the equation by [latex]3[\/latex] to get a coefficient of [latex]1[\/latex] for the variable.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\,\\,\\,\\,\\,\\,\\underline{3y}\\,\\,\\,\\,=\\,\\,\\,\\,\\,\\underline{9}\\\\3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,9\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,y\\,\\,\\,\\,=\\,\\,\\,\\,3\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]y=3[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>Now you can try\u00a0a similar problem.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try\u00a0It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm142131\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142131&#38;theme=oea&#38;iframe_resize_id=ohm142131&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In the following video, we show examples of solving two step linear equations.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Solving Two Step Equations (Basic)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/fCyxSVQKeRw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Remember to check the solution of an algebraic equation by substituting the value of the variable into the original equation.<\/p>\n<p>In the next section, we will learn how to solve equations that need to be simplified before they can be solved.<\/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-9019\">\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":17533,"menu_order":4,"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":"0bdb5d89bfce4d0ebafbee429e80baf4, 6a5c6d9323474472bd9b3d091bd1875e, 242b2223cfeb453ea99e57ba86b2eafb","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9019","chapter","type-chapter","status-publish","hentry"],"part":7476,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9019","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":57,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9019\/revisions"}],"predecessor-version":[{"id":20297,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9019\/revisions\/20297"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/7476"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9019\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/media?parent=9019"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=9019"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=9019"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/license?post=9019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}