{"id":3850,"date":"2020-02-09T20:01:10","date_gmt":"2020-02-09T20:01:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3850"},"modified":"2020-02-09T22:17:59","modified_gmt":"2020-02-09T22:17:59","slug":"solving-equations-that-contain-fractions-using-the-multiplication-property-of-equality","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/solving-equations-that-contain-fractions-using-the-multiplication-property-of-equality\/","title":{"raw":"Solving Equations That Contain Fractions Using the Multiplication Property of Equality","rendered":"Solving Equations That Contain Fractions Using the Multiplication Property of Equality"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use the multiplication and division properties to solve equations with fractions and division<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Solve Equations with Fractions Using the Multiplication and Division Properties of Equality<\/h2>\r\nWe will solve equations that require multiplication or division to isolate the variable. First, let's consider the division property of equality again.\r\n<div class=\"textbox shaded\">\r\n<h3>The Division Property of Equality<\/h3>\r\nFor any numbers [latex]a,b[\/latex], and [latex]c[\/latex],\r\n<p style=\"text-align: center\">[latex]\\text{if }a=b,\\text{ then }\\Large\\frac{a}{c}=\\Large\\frac{b}{c}[\/latex].<\/p>\r\nIf you divide both sides of an equation by the same quantity, you still have equality.\r\n\r\n<\/div>\r\nLet's put this idea in practice with an example. We are looking for the number you multiply by [latex]10[\/latex] to get [latex]44[\/latex], and we can use division to find out.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve: [latex]10q=44[\/latex]\r\n\r\nSolution:\r\n<table id=\"eip-id1168467284261\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td colspan=\"2\"><\/td>\r\n<td>[latex]10q=44[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Divide both sides by [latex]10[\/latex] to undo the multiplication.<\/td>\r\n<td>[latex]\\Large\\frac{10q}{10}=\\Large\\frac{44}{10}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Simplify.<\/td>\r\n<td>[latex]q=\\Large\\frac{22}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Check:<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]q=\\Large\\frac{22}{5}[\/latex] into the original equation.<\/td>\r\n<td>[latex]10\\left(\\Large\\frac{22}{5}\\right)\\stackrel{?}{=}44[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\stackrel{2}{\\overline{)10}}\\left(\\Large\\frac{22}{\\overline{)5}}\\right)\\stackrel{?}{=}44[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]44=44\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe solution to the equation was the fraction [latex]\\Large\\frac{22}{5}[\/latex]. We leave it as an improper fraction.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]146141[\/ohm_question]\r\n\r\n<\/div>\r\nNow, consider the equation [latex]\\Large\\frac{x}{4}\\normalsize=3[\/latex]. We want to know what number divided by [latex]4[\/latex] gives [latex]3[\/latex]. So to \"undo\" the division, we will need to multiply by [latex]4[\/latex]. The <em>Multiplication Property of Equality<\/em> will allow us to do this. This property says that if we start with two equal quantities and multiply both by the same number, the results are equal.\r\n<div class=\"textbox shaded\">\r\n<h3>The Multiplication Property of Equality<\/h3>\r\nFor any numbers [latex]a,b[\/latex], and [latex]c[\/latex],\r\n<p style=\"text-align: center\">[latex]\\text{if }a=b,\\text{ then }ac=bc[\/latex].<\/p>\r\nIf you multiply both sides of an equation by the same quantity, you still have equality.\r\n\r\n<\/div>\r\nLet\u2019s use the Multiplication Property of Equality to solve the equation [latex]\\Large\\frac{x}{7}\\normalsize=-9[\/latex].\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve: [latex]\\Large\\frac{x}{7}\\normalsize=-9[\/latex].\r\n\r\n[reveal-answer q=\"80567\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"80567\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1165722216597\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says x over 7 equals negative 9. The next line says, \">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"height: 14px\" colspan=\"2\"><\/td>\r\n<td style=\"height: 14px\">[latex]\\Large\\frac{x}{7}\\normalsize=-9[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px\">\r\n<td style=\"height: 30px\" colspan=\"2\">Use the Multiplication Property of Equality to multiply both sides by [latex]7[\/latex] . This will isolate the variable.<\/td>\r\n<td style=\"height: 30px\">[latex]\\color{red}{7}\\cdot\\Large\\frac{x}{7}\\normalsize=\\color{red}{7}(-9)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"height: 14px\" colspan=\"2\">Multiply.<\/td>\r\n<td style=\"height: 14px\">[latex]\\Large\\frac{7x}{7}\\normalsize=-63[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"height: 14px\" colspan=\"2\">Simplify.<\/td>\r\n<td style=\"height: 14px\">[latex]x=-63[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 74px\">\r\n<td style=\"height: 74px\">Check.\r\n\r\nSubstitute [latex]\\color{red}{-63}[\/latex] for x in the original equation.<\/td>\r\n<td style=\"height: 74px\">[latex]\\Large\\frac{\\color{red}{-63}}{7}\\normalsize\\stackrel{?}{=}-9[\/latex]<\/td>\r\n<td style=\"height: 74px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14.896px\">\r\n<td style=\"height: 14.896px\">The equation is true.<\/td>\r\n<td style=\"height: 14.896px\">[latex]-9=-9\\quad\\checkmark[\/latex]<\/td>\r\n<td style=\"height: 14.896px\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]146147[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve: [latex]\\Large\\frac{p}{-8}\\normalsize=-40[\/latex]\r\n[reveal-answer q=\"988357\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"988357\"]\r\n\r\nSolution:\r\nHere, [latex]p[\/latex] is divided by [latex]-8[\/latex]. We must multiply by [latex]-8[\/latex] to isolate [latex]p[\/latex].\r\n<table id=\"eip-id1165719561991\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says p over negative 8 equals negative 40. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td colspan=\"2\"><\/td>\r\n<td>[latex]\\Large\\frac{p}{-8}\\normalsize=-40[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Multiply both sides by [latex]-8[\/latex]<\/td>\r\n<td>[latex]\\color{red}{-8}\\Large(\\frac{p}{-8})\\normalsize=\\color{red}{-8}(-40)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Multiply.<\/td>\r\n<td>[latex]\\Large\\frac{-8p}{-8}\\normalsize=320[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Simplify.<\/td>\r\n<td>[latex]p=320[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]p=320[\/latex] .<\/td>\r\n<td>[latex]\\Large\\frac{\\color{red}{320}}{-8}\\normalsize\\stackrel{?}{=}-40[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The equation is true.<\/td>\r\n<td>[latex]-40=-40\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]146336[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show two more examples of when to use the multiplication and division properties to solve a one-step equation.\r\n\r\nhttps:\/\/youtu.be\/BN7iVWWl2y0\r\n<h2>Solve Equations with a Coefficient of [latex]-1[\/latex]<\/h2>\r\nLook at the equation [latex]-y=15[\/latex]. Does it look as if [latex]y[\/latex] is already isolated? But there is a negative sign in front of [latex]y[\/latex], so it is not isolated.\r\n\r\nThere are three different ways to isolate the variable in this type of equation. We will show all three ways in the next example.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve: [latex]-y=15[\/latex]\r\n[reveal-answer q=\"196640\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"196640\"]\r\n\r\nSolution:\r\nOne way to solve the equation is to rewrite [latex]-y[\/latex] as [latex]-1y[\/latex], and then use the Division Property of Equality to isolate [latex]y[\/latex].\r\n<table id=\"eip-id1168469574000\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says negative y equals 15. The following line says, \">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\"><\/td>\r\n<td style=\"height: 15px\">[latex]-y=15[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15.65625px\">\r\n<td style=\"height: 15.65625px\">Rewrite [latex]-y[\/latex] as [latex]-1y[\/latex] .<\/td>\r\n<td style=\"height: 15.65625px\">[latex]-1y = 15[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 40px\">\r\n<td style=\"height: 40px\">Divide both sides by [latex]\u22121[\/latex].<\/td>\r\n<td style=\"height: 40px\">[latex]\\Large\\frac{-1y}{\\color{red}{-1}}=\\Large\\frac{15}{\\color{red}{-1}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 24px\">\r\n<td style=\"height: 24px\">Simplify each side.<\/td>\r\n<td style=\"height: 24px\">[latex]y = -15[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAnother way to solve this equation is to multiply both sides of the equation by [latex]-1[\/latex].\r\n<table id=\"eip-id1168468554901\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says negative y equals 15. The following line says, \">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\"><\/td>\r\n<td style=\"height: 15px\">[latex]y=15[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15.84375px\">\r\n<td style=\"height: 15.84375px\">Multiply both sides by [latex]\u22121[\/latex].<\/td>\r\n<td style=\"height: 15.84375px\">[latex]\\color{red}{-1}(-y)=\\color{red}{-1}(15)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 26px\">\r\n<td style=\"height: 26px\">Simplify each side.<\/td>\r\n<td style=\"height: 26px\">[latex]y=-15[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe third way to solve the equation is to read [latex]-y[\/latex] as \"the opposite of [latex]y\\text{.\"}[\/latex] What number has [latex]15[\/latex] as its opposite? The opposite of [latex]15[\/latex] is [latex]-15[\/latex]. So [latex]y=-15[\/latex].\r\n\r\nFor all three methods, we isolated [latex]y[\/latex] is isolated and solved the equation.\r\nCheck:\r\n<table id=\"eip-id1168469681151\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says y equals negative 15. The next line says, \">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\"><\/td>\r\n<td style=\"height: 15px\">[latex]y=15[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Substitute [latex]y=-15[\/latex] .<\/td>\r\n<td style=\"height: 15px\">[latex]-(\\color{red}{-15})\\stackrel{?}{=}(15)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15.03125px\">\r\n<td style=\"height: 15.03125px\">Simplify. The equation is true.<\/td>\r\n<td style=\"height: 15.03125px\">[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=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]146153[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we show more examples of how to solve an equation with a negative variable.\r\n\r\nhttps:\/\/youtu.be\/FJmNpHeOcpo\r\n<h2>Solve Equations with a Fraction Coefficient<\/h2>\r\nWhen we have an equation with a fraction coefficient we can use the Multiplication Property of Equality to make the coefficient equal to [latex]1[\/latex].\r\n\r\nFor example, in the equation:\r\n<p style=\"text-align: center\">[latex]\\Large\\frac{3}{4}\\normalsize x=24[\/latex]<\/p>\r\nThe coefficient of [latex]x[\/latex] is [latex]\\Large\\frac{3}{4}[\/latex]. To solve for [latex]x[\/latex], we need its coefficient to be [latex]1[\/latex]. Since the product of a number and its reciprocal is [latex]1[\/latex], our strategy here will be to isolate [latex]x[\/latex] by multiplying by the reciprocal of [latex]\\Large\\frac{3}{4}[\/latex]. We will do this in the next example.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve: [latex]\\Large\\frac{3}{4}\\normalsize x=24[\/latex]\r\n[reveal-answer q=\"763998\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"763998\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1165721301772\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"Multiply both sides by the reciprocal of the coefficient,\">\r\n<tbody>\r\n<tr>\r\n<td colspan=\"2\"><\/td>\r\n<td>[latex]\\Large\\frac{3}{4}\\normalsize x = 24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Multiply both sides by the reciprocal of the coefficient.<\/td>\r\n<td>[latex]\\color{red}{\\Large\\frac{4}{3}}\\cdot\\Large\\frac{3}{4}\\normalsize x = \\color{red}{\\Large\\frac{4}{3}}\\cdot\\normalsize 24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Simplify.<\/td>\r\n<td>[latex]1x=\\Large\\frac{4}{3}\\cdot\\Large\\frac{24}{1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Multiply.<\/td>\r\n<td>[latex]x=32[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:<\/td>\r\n<td>[latex]\\Large\\frac{3}{4}\\normalsize x=24[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]x=32[\/latex] .<\/td>\r\n<td>[latex]\\Large\\frac{3}{4}\\normalsize\\cdot 32\\stackrel{?}{=}24[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite [latex]32[\/latex] as a fraction.<\/td>\r\n<td>[latex]\\Large\\frac{3}{4}\\cdot\\Large\\frac{32}{1}\\stackrel{?}{=}24[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply. The equation is true.<\/td>\r\n<td>[latex]24=24\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that in the equation [latex]\\Large\\frac{3}{4}\\normalsize x=24[\/latex], we could have divided both sides by [latex]\\Large\\frac{3}{4}[\/latex] to get [latex]x[\/latex] by itself. Dividing is the same as multiplying by the reciprocal, so we would get the same result. But most people agree that multiplying by the reciprocal is easier.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]146156[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve: [latex]-\\Large\\frac{3}{8}\\normalsize w=72[\/latex]\r\n[reveal-answer q=\"343946\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"343946\"]\r\n\r\nSolution:\r\nThe coefficient is a negative fraction. Remember that a number and its reciprocal have the same sign, so the reciprocal of the coefficient must also be negative.\r\n<table id=\"eip-id1165721064926\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says negative 3 eighths times w equals 72. The next line says to multiply by the reciprocal of negative 3 eighths and shows a red negative 8 thirds times negative 3 eighths times w equals a red negative 8 thirds times 72. The next step says, \">\r\n<tbody>\r\n<tr style=\"height: 15.21875px\">\r\n<td style=\"height: 15.21875px\" colspan=\"2\"><\/td>\r\n<td style=\"height: 15.21875px\">[latex]\\Large\\frac{3}{8}\\normalsize w=72[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 44px\">\r\n<td style=\"height: 44px\" colspan=\"2\">Multiply both sides by the reciprocal of [latex]-\\Large\\frac{3}{8}[\/latex] .<\/td>\r\n<td style=\"height: 44px\">[latex]\\color{red}{-\\Large\\frac{8}{3}}\\Large(-\\frac{3}{8}\\normalsize w\\Large)=(\\color{red}{-\\Large\\frac{8}{3}})\\normalsize 72[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 45px\">\r\n<td style=\"height: 45px\" colspan=\"2\">Simplify; reciprocals multiply to one.<\/td>\r\n<td style=\"height: 45px\">[latex]1w=-\\Large\\frac{8}{3}\\cdot\\Large\\frac{72}{1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 28px\">\r\n<td style=\"height: 28px\" colspan=\"2\">Multiply.<\/td>\r\n<td style=\"height: 28px\">[latex]w=-192[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 42px\">\r\n<td style=\"height: 42px\">Check:<\/td>\r\n<td style=\"height: 42px\">[latex]-\\Large\\frac{3}{8}\\normalsize w=72[\/latex]<\/td>\r\n<td style=\"height: 42px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 42px\">\r\n<td style=\"height: 42px\">Let [latex]w=-192[\/latex] .<\/td>\r\n<td style=\"height: 42px\">[latex]-\\Large\\frac{3}{8}\\normalsize(-192)\\stackrel{?}{=}72[\/latex]<\/td>\r\n<td style=\"height: 42px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 24px\">\r\n<td style=\"height: 24px\">Multiply. It checks.<\/td>\r\n<td style=\"height: 24px\">[latex]72=72\\quad\\checkmark[\/latex]<\/td>\r\n<td style=\"height: 24px\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]146158[\/ohm_question]\r\n\r\n<\/div>\r\n<p>In the next video example you will see another example of how to use the reciprocal of a fractional coefficient to solve an equation.<\/p>\r\nhttps:\/\/youtu.be\/Ea5eW8rZxEI","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use the multiplication and division properties to solve equations with fractions and division<\/li>\n<\/ul>\n<\/div>\n<h2>Solve Equations with Fractions Using the Multiplication and Division Properties of Equality<\/h2>\n<p>We will solve equations that require multiplication or division to isolate the variable. First, let&#8217;s consider the division property of equality again.<\/p>\n<div class=\"textbox shaded\">\n<h3>The Division Property of Equality<\/h3>\n<p>For any numbers [latex]a,b[\/latex], and [latex]c[\/latex],<\/p>\n<p style=\"text-align: center\">[latex]\\text{if }a=b,\\text{ then }\\Large\\frac{a}{c}=\\Large\\frac{b}{c}[\/latex].<\/p>\n<p>If you divide both sides of an equation by the same quantity, you still have equality.<\/p>\n<\/div>\n<p>Let&#8217;s put this idea in practice with an example. We are looking for the number you multiply by [latex]10[\/latex] to get [latex]44[\/latex], and we can use division to find out.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve: [latex]10q=44[\/latex]<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168467284261\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td>[latex]10q=44[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Divide both sides by [latex]10[\/latex] to undo the multiplication.<\/td>\n<td>[latex]\\Large\\frac{10q}{10}=\\Large\\frac{44}{10}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]q=\\Large\\frac{22}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Check:<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]q=\\Large\\frac{22}{5}[\/latex] into the original equation.<\/td>\n<td>[latex]10\\left(\\Large\\frac{22}{5}\\right)\\stackrel{?}{=}44[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\stackrel{2}{\\overline{)10}}\\left(\\Large\\frac{22}{\\overline{)5}}\\right)\\stackrel{?}{=}44[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]44=44\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The solution to the equation was the fraction [latex]\\Large\\frac{22}{5}[\/latex]. We leave it as an improper fraction.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146141\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146141&theme=oea&iframe_resize_id=ohm146141&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Now, consider the equation [latex]\\Large\\frac{x}{4}\\normalsize=3[\/latex]. We want to know what number divided by [latex]4[\/latex] gives [latex]3[\/latex]. So to &#8220;undo&#8221; the division, we will need to multiply by [latex]4[\/latex]. The <em>Multiplication Property of Equality<\/em> will allow us to do this. This property says that if we start with two equal quantities and multiply both by the same number, the results are equal.<\/p>\n<div class=\"textbox shaded\">\n<h3>The Multiplication Property of Equality<\/h3>\n<p>For any numbers [latex]a,b[\/latex], and [latex]c[\/latex],<\/p>\n<p style=\"text-align: center\">[latex]\\text{if }a=b,\\text{ then }ac=bc[\/latex].<\/p>\n<p>If you multiply both sides of an equation by the same quantity, you still have equality.<\/p>\n<\/div>\n<p>Let\u2019s use the Multiplication Property of Equality to solve the equation [latex]\\Large\\frac{x}{7}\\normalsize=-9[\/latex].<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve: [latex]\\Large\\frac{x}{7}\\normalsize=-9[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q80567\">Show Solution<\/span><\/p>\n<div id=\"q80567\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1165722216597\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says x over 7 equals negative 9. The next line says,\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px\" colspan=\"2\"><\/td>\n<td style=\"height: 14px\">[latex]\\Large\\frac{x}{7}\\normalsize=-9[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px\" colspan=\"2\">Use the Multiplication Property of Equality to multiply both sides by [latex]7[\/latex] . This will isolate the variable.<\/td>\n<td style=\"height: 30px\">[latex]\\color{red}{7}\\cdot\\Large\\frac{x}{7}\\normalsize=\\color{red}{7}(-9)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px\" colspan=\"2\">Multiply.<\/td>\n<td style=\"height: 14px\">[latex]\\Large\\frac{7x}{7}\\normalsize=-63[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px\" colspan=\"2\">Simplify.<\/td>\n<td style=\"height: 14px\">[latex]x=-63[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 74px\">\n<td style=\"height: 74px\">Check.<\/p>\n<p>Substitute [latex]\\color{red}{-63}[\/latex] for x in the original equation.<\/td>\n<td style=\"height: 74px\">[latex]\\Large\\frac{\\color{red}{-63}}{7}\\normalsize\\stackrel{?}{=}-9[\/latex]<\/td>\n<td style=\"height: 74px\"><\/td>\n<\/tr>\n<tr style=\"height: 14.896px\">\n<td style=\"height: 14.896px\">The equation is true.<\/td>\n<td style=\"height: 14.896px\">[latex]-9=-9\\quad\\checkmark[\/latex]<\/td>\n<td style=\"height: 14.896px\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146147\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146147&theme=oea&iframe_resize_id=ohm146147&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve: [latex]\\Large\\frac{p}{-8}\\normalsize=-40[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q988357\">Show Solution<\/span><\/p>\n<div id=\"q988357\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nHere, [latex]p[\/latex] is divided by [latex]-8[\/latex]. We must multiply by [latex]-8[\/latex] to isolate [latex]p[\/latex].<\/p>\n<table id=\"eip-id1165719561991\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says p over negative 8 equals negative 40. The next line says,\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td>[latex]\\Large\\frac{p}{-8}\\normalsize=-40[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Multiply both sides by [latex]-8[\/latex]<\/td>\n<td>[latex]\\color{red}{-8}\\Large(\\frac{p}{-8})\\normalsize=\\color{red}{-8}(-40)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Multiply.<\/td>\n<td>[latex]\\Large\\frac{-8p}{-8}\\normalsize=320[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]p=320[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]p=320[\/latex] .<\/td>\n<td>[latex]\\Large\\frac{\\color{red}{320}}{-8}\\normalsize\\stackrel{?}{=}-40[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The equation is true.<\/td>\n<td>[latex]-40=-40\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146336\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146336&theme=oea&iframe_resize_id=ohm146336&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show two more examples of when to use the multiplication and division properties to solve a one-step equation.<\/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<h2>Solve Equations with a Coefficient of [latex]-1[\/latex]<\/h2>\n<p>Look at the equation [latex]-y=15[\/latex]. Does it look as if [latex]y[\/latex] is already isolated? But there is a negative sign in front of [latex]y[\/latex], so it is not isolated.<\/p>\n<p>There are three different ways to isolate the variable in this type of equation. We will show all three ways in the next example.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve: [latex]-y=15[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q196640\">Show Solution<\/span><\/p>\n<div id=\"q196640\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nOne way to solve the equation is to rewrite [latex]-y[\/latex] as [latex]-1y[\/latex], and then use the Division Property of Equality to isolate [latex]y[\/latex].<\/p>\n<table id=\"eip-id1168469574000\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says negative y equals 15. The following line says,\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><\/td>\n<td style=\"height: 15px\">[latex]-y=15[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15.65625px\">\n<td style=\"height: 15.65625px\">Rewrite [latex]-y[\/latex] as [latex]-1y[\/latex] .<\/td>\n<td style=\"height: 15.65625px\">[latex]-1y = 15[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 40px\">\n<td style=\"height: 40px\">Divide both sides by [latex]\u22121[\/latex].<\/td>\n<td style=\"height: 40px\">[latex]\\Large\\frac{-1y}{\\color{red}{-1}}=\\Large\\frac{15}{\\color{red}{-1}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 24px\">\n<td style=\"height: 24px\">Simplify each side.<\/td>\n<td style=\"height: 24px\">[latex]y = -15[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Another way to solve this equation is to multiply both sides of the equation by [latex]-1[\/latex].<\/p>\n<table id=\"eip-id1168468554901\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says negative y equals 15. The following line says,\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><\/td>\n<td style=\"height: 15px\">[latex]y=15[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15.84375px\">\n<td style=\"height: 15.84375px\">Multiply both sides by [latex]\u22121[\/latex].<\/td>\n<td style=\"height: 15.84375px\">[latex]\\color{red}{-1}(-y)=\\color{red}{-1}(15)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 26px\">\n<td style=\"height: 26px\">Simplify each side.<\/td>\n<td style=\"height: 26px\">[latex]y=-15[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The third way to solve the equation is to read [latex]-y[\/latex] as &#8220;the opposite of [latex]y\\text{.\"}[\/latex] What number has [latex]15[\/latex] as its opposite? The opposite of [latex]15[\/latex] is [latex]-15[\/latex]. So [latex]y=-15[\/latex].<\/p>\n<p>For all three methods, we isolated [latex]y[\/latex] is isolated and solved the equation.<br \/>\nCheck:<\/p>\n<table id=\"eip-id1168469681151\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says y equals negative 15. The next line says,\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><\/td>\n<td style=\"height: 15px\">[latex]y=15[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Substitute [latex]y=-15[\/latex] .<\/td>\n<td style=\"height: 15px\">[latex]-(\\color{red}{-15})\\stackrel{?}{=}(15)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15.03125px\">\n<td style=\"height: 15.03125px\">Simplify. The equation is true.<\/td>\n<td style=\"height: 15.03125px\">[latex]15=15\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146153\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146153&theme=oea&iframe_resize_id=ohm146153&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we show more examples of how to solve an equation with a negative variable.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex:  Solving One Step Equation in the Form:  -x = a\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/FJmNpHeOcpo?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Solve Equations with a Fraction Coefficient<\/h2>\n<p>When we have an equation with a fraction coefficient we can use the Multiplication Property of Equality to make the coefficient equal to [latex]1[\/latex].<\/p>\n<p>For example, in the equation:<\/p>\n<p style=\"text-align: center\">[latex]\\Large\\frac{3}{4}\\normalsize x=24[\/latex]<\/p>\n<p>The coefficient of [latex]x[\/latex] is [latex]\\Large\\frac{3}{4}[\/latex]. To solve for [latex]x[\/latex], we need its coefficient to be [latex]1[\/latex]. Since the product of a number and its reciprocal is [latex]1[\/latex], our strategy here will be to isolate [latex]x[\/latex] by multiplying by the reciprocal of [latex]\\Large\\frac{3}{4}[\/latex]. We will do this in the next example.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve: [latex]\\Large\\frac{3}{4}\\normalsize x=24[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q763998\">Show Solution<\/span><\/p>\n<div id=\"q763998\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1165721301772\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"Multiply both sides by the reciprocal of the coefficient,\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td>[latex]\\Large\\frac{3}{4}\\normalsize x = 24[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Multiply both sides by the reciprocal of the coefficient.<\/td>\n<td>[latex]\\color{red}{\\Large\\frac{4}{3}}\\cdot\\Large\\frac{3}{4}\\normalsize x = \\color{red}{\\Large\\frac{4}{3}}\\cdot\\normalsize 24[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]1x=\\Large\\frac{4}{3}\\cdot\\Large\\frac{24}{1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Multiply.<\/td>\n<td>[latex]x=32[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:<\/td>\n<td>[latex]\\Large\\frac{3}{4}\\normalsize x=24[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]x=32[\/latex] .<\/td>\n<td>[latex]\\Large\\frac{3}{4}\\normalsize\\cdot 32\\stackrel{?}{=}24[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Rewrite [latex]32[\/latex] as a fraction.<\/td>\n<td>[latex]\\Large\\frac{3}{4}\\cdot\\Large\\frac{32}{1}\\stackrel{?}{=}24[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply. The equation is true.<\/td>\n<td>[latex]24=24\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that in the equation [latex]\\Large\\frac{3}{4}\\normalsize x=24[\/latex], we could have divided both sides by [latex]\\Large\\frac{3}{4}[\/latex] to get [latex]x[\/latex] by itself. Dividing is the same as multiplying by the reciprocal, so we would get the same result. But most people agree that multiplying by the reciprocal is easier.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146156\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146156&theme=oea&iframe_resize_id=ohm146156&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve: [latex]-\\Large\\frac{3}{8}\\normalsize w=72[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q343946\">Show Solution<\/span><\/p>\n<div id=\"q343946\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe coefficient is a negative fraction. Remember that a number and its reciprocal have the same sign, so the reciprocal of the coefficient must also be negative.<\/p>\n<table id=\"eip-id1165721064926\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says negative 3 eighths times w equals 72. The next line says to multiply by the reciprocal of negative 3 eighths and shows a red negative 8 thirds times negative 3 eighths times w equals a red negative 8 thirds times 72. The next step says,\">\n<tbody>\n<tr style=\"height: 15.21875px\">\n<td style=\"height: 15.21875px\" colspan=\"2\"><\/td>\n<td style=\"height: 15.21875px\">[latex]\\Large\\frac{3}{8}\\normalsize w=72[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 44px\">\n<td style=\"height: 44px\" colspan=\"2\">Multiply both sides by the reciprocal of [latex]-\\Large\\frac{3}{8}[\/latex] .<\/td>\n<td style=\"height: 44px\">[latex]\\color{red}{-\\Large\\frac{8}{3}}\\Large(-\\frac{3}{8}\\normalsize w\\Large)=(\\color{red}{-\\Large\\frac{8}{3}})\\normalsize 72[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 45px\">\n<td style=\"height: 45px\" colspan=\"2\">Simplify; reciprocals multiply to one.<\/td>\n<td style=\"height: 45px\">[latex]1w=-\\Large\\frac{8}{3}\\cdot\\Large\\frac{72}{1}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 28px\">\n<td style=\"height: 28px\" colspan=\"2\">Multiply.<\/td>\n<td style=\"height: 28px\">[latex]w=-192[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 42px\">\n<td style=\"height: 42px\">Check:<\/td>\n<td style=\"height: 42px\">[latex]-\\Large\\frac{3}{8}\\normalsize w=72[\/latex]<\/td>\n<td style=\"height: 42px\"><\/td>\n<\/tr>\n<tr style=\"height: 42px\">\n<td style=\"height: 42px\">Let [latex]w=-192[\/latex] .<\/td>\n<td style=\"height: 42px\">[latex]-\\Large\\frac{3}{8}\\normalsize(-192)\\stackrel{?}{=}72[\/latex]<\/td>\n<td style=\"height: 42px\"><\/td>\n<\/tr>\n<tr style=\"height: 24px\">\n<td style=\"height: 24px\">Multiply. It checks.<\/td>\n<td style=\"height: 24px\">[latex]72=72\\quad\\checkmark[\/latex]<\/td>\n<td style=\"height: 24px\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146158\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146158&theme=oea&iframe_resize_id=ohm146158&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video example you will see another example of how to use the reciprocal of a fractional coefficient to solve an equation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex: Solve a One Step Equation by Multiplying by Reciprocal (a\/b)x=-c\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Ea5eW8rZxEI?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-3850\">\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>Solving One Step Equations Using Multiplication and Division (Basic). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/BN7iVWWl2y0\">https:\/\/youtu.be\/BN7iVWWl2y0<\/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, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Solving One Step Equation in the Form: -x = a. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/FJmNpHeOcpo\">https:\/\/youtu.be\/FJmNpHeOcpo<\/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: Solve a One Step Equation by Multiplying by Reciprocal (a\/b)x=-c. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Ea5eW8rZxEI\">https:\/\/youtu.be\/Ea5eW8rZxEI<\/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>Question ID: 146141, 146147, 146336, 146153, 146156, 146158. <strong>Authored by<\/strong>: Alyson Day. <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, 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":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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