{"id":4216,"date":"2020-04-08T02:19:14","date_gmt":"2020-04-08T02:19:14","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4216"},"modified":"2021-02-05T23:59:06","modified_gmt":"2021-02-05T23:59:06","slug":"multi-step-linear-equations","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/multi-step-linear-equations\/","title":{"raw":"Multi-step Linear Equations","rendered":"Multi-step Linear Equations"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use properties of equality to isolate variables and solve algebraic equations<\/li>\r\n \t<li>Use the distributive property<\/li>\r\n \t<li>Clear fractions and decimals from equations to make them easier to solve<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Use properties of equality to isolate variables and solve algebraic equations<\/h2>\r\nThere are some <b>equations<\/b> that you can solve in your head quickly. For example\u2014what is the value of <i>y<\/i> in the equation [latex]2y=6[\/latex]? Chances are you didn\u2019t need to get out a pencil and paper to calculate that [latex]y=3[\/latex]. You only needed to do one thing to get the answer: divide 6 by 2.\r\n\r\nOther equations are more complicated. Solving [latex]\\displaystyle 4\\left( \\frac{1}{3}t+\\frac{1}{2}\\right)=6[\/latex] without writing anything down is difficult. That\u2019s because this equation contains not just a <b>variable<\/b> but also fractions and <b>terms<\/b> inside parentheses. This is a <b>multi-step equation<\/b>, one that takes several steps to solve. You've probably studied these equations previously and seen that, although multi-step equations take more time and require more operations, they can still be simplified and solved by applying basic algebraic rules.\r\n\r\nRemember that you can think of an equation as a balance scale, with the goal being to rewrite the equation so that it is easier to solve but still balanced. The <b>addition property of equality<\/b> and the <b>multiplication property of equality<\/b> explain how you can keep the scale, or the equation, balanced. Whenever you perform an operation to one side of the equation, if you perform the same exact operation to the other side, you\u2019ll keep both sides of the equation equal.\r\n\r\nIf the equation is in the form [latex]ax+b=c[\/latex], where <i>x<\/i> 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=\"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 2 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 3 to get a coefficient of 1 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\nWatch the following video to see examples of solving two step linear equations.\r\nhttps:\/\/youtu.be\/fCyxSVQKeRw\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve [latex]3x+5x+4-x+7=88[\/latex].\r\n\r\n[reveal-answer q=\"455516\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"455516\"]\r\n\r\nThere are three like terms [latex]3x[\/latex], [latex]5x[\/latex],\u00a0and\u00a0[latex]\u2013x[\/latex]\u00a0involving a variable.\u00a0Combine these like terms.\u00a04 and 7 are also like terms and can be added.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\,\\,3x+5x+4-x+7=\\,\\,\\,88\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7x+4+7=\\,\\,\\,88\\end{array}[\/latex]<\/p>\r\nThe equation is now in the form\u00a0[latex]ax+b=c[\/latex], so we can solve as before.\r\n<p style=\"text-align: center\">[latex]7x+11\\,\\,\\,=\\,\\,\\,88[\/latex]<\/p>\r\nSubtract 11 from both sides.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}7x+11\\,\\,\\,=\\,\\,\\,88\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{-11\\,\\,\\,\\,\\,\\,\\,-11}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7x\\,\\,\\,=\\,\\,\\,77\\end{array}[\/latex]<\/p>\r\nDivide both sides by 7.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{7x}\\,\\,\\,=\\,\\,\\,\\underline{77}\\\\7\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7\\,\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,\\,=\\,\\,\\,11\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]x=11[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nThe following video shows an example of solving a linear equation that requires combining like terms.\r\n\r\nhttps:\/\/youtu.be\/ez_sP2OTGjU\r\n\r\nSome equations may have the variable on both sides of the equal sign, as in this equation: [latex]4x-6=2x+10[\/latex].\r\n\r\nTo solve this equation, we need to \u201cmove\u201d one of the variable terms.\u00a0This can make it difficult to decide which side to work with. It doesn\u2019t matter which term gets moved, [latex]4x[\/latex] or [latex]2x[\/latex], however, to avoid negative coefficients, you can move the smaller term.\r\n<div class=\"textbox exercises\">\r\n<h3>Examples<\/h3>\r\nSolve:\u00a0[latex]4x-6=2x+10[\/latex]\r\n\r\n[reveal-answer q=\"457216\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"457216\"]\r\n\r\nChoose the variable term to move\u2014to avoid negative terms choose [latex]2x[\/latex]\r\n<p style=\"text-align: center\">[latex]\\,\\,\\,4x-6=2x+10\\\\\\underline{-2x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-2x}\\\\\\,\\,\\,4x-6=10[\/latex]<\/p>\r\n<p style=\"text-align: left\">Now add\u00a06 to both\u00a0sides to isolate the term with the variable.<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4x-6=10\\\\\\underline{\\,\\,\\,\\,+6\\,\\,\\,+6}\\\\4x=16\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left\">Now divide each side by 4 to isolate the variable x.<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\frac{4x}{4}=\\frac{16}{4}\\\\\\\\x=4\\end{array}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn this video, you can see an example of solving equations that have variables on both sides of the equal sign.\r\nhttps:\/\/youtu.be\/f3ujWNPL0Bw\r\n<h2 id=\"title2\">The Distributive Property<\/h2>\r\nAs we solve linear equations, we often need to do some work to write\u00a0the linear equations in a form we are familiar with solving.\u00a0This section will focus on manipulating an equation we are asked to solve in such a way that we can use the skills we learned for solving multi-step equations to ultimately arrive at the solution.\r\n\r\nParentheses can\u00a0make solving a problem difficult, if not impossible. To get rid of these unwanted parentheses we have the distributive property. Using this property we multiply the number in front of the parentheses by each term inside of the parentheses.\r\n<div class=\"textbox shaded\">\r\n<h3>The Distributive Property of Multiplication<\/h3>\r\nFor all real numbers <i>a, b,<\/i> and <i>c<\/i>,\u00a0[latex]a(b+c)=ab+ac[\/latex].\r\n\r\nWhat this means is that when a number multiplies an expression inside parentheses, you can distribute the multiplication to each term of the expression individually. Then, you can follow the steps we have already practiced\u00a0to <b>isolate the variable<\/b>\u00a0and solve the equation.\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve for [latex]a[\/latex]. [latex]4\\left(2a+3\\right)=28[\/latex]\r\n\r\n[reveal-answer q=\"372387\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"372387\"]\r\n\r\nApply the distributive property to expand [latex]4\\left(2a+3\\right)[\/latex] to [latex]8a+12[\/latex]\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\left(2a+3\\right)=28\\\\ 8a+12=28\\end{array}[\/latex]<\/p>\r\nSubtract 12\u00a0from both sides to isolate\u00a0the variable term.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}8a+12\\,\\,\\,=\\,\\,\\,28\\\\ \\underline{-12\\,\\,\\,\\,\\,\\,-12}\\\\ 8a\\,\\,\\,=\\,\\,\\,16\\end{array}[\/latex]<\/p>\r\nDivide both terms by 8 to get a coefficient of 1.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\underline{8a}=\\underline{16}\\\\8\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,8\\\\a\\,=\\,\\,2\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]a=2[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nIn the video that follows, see another example of how to use the distributive property to solve a multi-step linear equation.\r\n\r\nhttps:\/\/youtu.be\/aQOkD8L57V0\r\n\r\nIn the next example, you will see that there are parentheses on both sides of the equal sign, so you will need to use the distributive property twice. Notice that you are going to need to distribute a negative number, so be careful with negative signs!\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve for [latex]t[\/latex].\u00a0\u00a0[latex]2\\left(4t-5\\right)=-3\\left(2t+1\\right)[\/latex]\r\n\r\n[reveal-answer q=\"302387\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"302387\"]\r\n\r\nApply the distributive property to expand [latex]2\\left(4t-5\\right)[\/latex] to [latex]8t-10[\/latex] and [latex]-3\\left(2t+1\\right)[\/latex] to[latex]-6t-3[\/latex]. Be careful in this step\u2014you are distributing a negative number, so keep track of the sign of each number after you multiply.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}2\\left(4t-5\\right)=-3\\left(2t+1\\right)\\,\\,\\,\\,\\,\\, \\\\ 8t-10=-6t-3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\nAdd [latex]-6t[\/latex] to both sides to begin combining like terms.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}8t-10=-6t-3\\\\ \\underline{+6t\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+6t}\\,\\,\\,\\,\\,\\,\\,\\\\ 14t-10=\\,\\,\\,\\,-3\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\nAdd 10 to both sides of the equation to isolate <em>t<\/em>.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}14t-10=-3\\\\ \\underline{+10\\,\\,\\,+10}\\\\ 14t=\\,\\,\\,7\\,\\end{array}[\/latex]<\/p>\r\nThe last step is to divide both sides by 14 to completely isolate <em>t<\/em>.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}14t=7\\,\\,\\,\\,\\\\\\frac{14t}{14}=\\frac{7}{14}\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]t=\\frac{1}{2}[\/latex]\r\n\r\nWe simplified the fraction [latex]\\frac{7}{14}[\/latex] into [latex]\\frac{1}{2}[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video, we solve another multi-step equation with two sets of parentheses.\r\n\r\nhttps:\/\/youtu.be\/StomYTb7Xb8\r\n\r\nSometimes, you will encounter a multi-step equation with fractions. If you prefer not working with fractions, you can use the multiplication property of equality to multiply both sides of the equation by a common denominator of all of the fractions in the equation. This will clear all the fractions out of the equation. See the example below.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve \u00a0[latex]\\frac{1}{2}x-3=2-\\frac{3}{4}x[\/latex] by clearing the fractions in the equation first.\r\n\r\n[reveal-answer q=\"129951\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"129951\"]\r\n\r\nMultiply both sides of the equation by 4, the common denominator of the fractional coefficients.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\frac{1}{2}x-3=2-\\frac{3}{4}x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\\\\\\\ 4\\left(\\frac{1}{2}x-3\\right)=4\\left(2-\\frac{3}{4}x\\right)\\end{array}[\/latex]<\/p>\r\nUse the distributive property to expand the expressions on both sides.\u00a0Multiply.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\left(\\frac{1}{2}x\\right)-4\\left(3\\right)=4\\left(2\\right)-4\\left(-\\frac{3}{4}x\\right)\\\\\\\\ \\frac{4}{2}x-12=8-\\frac{12}{4}x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\\\\\\\ 2x-12=8-3x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\end{array}[\/latex]<\/p>\r\nAdd 3<em>x<\/em> to both sides to move the variable terms to only one side. Add 12 to both sides to move the variable\u00a0terms to only one side.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}2x-12=8-3x\\, \\\\\\underline{+3x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+3x}\\\\ 5x-12=8\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\nAdd 12 to both sides to move the <b>constant<\/b> terms to the other side.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}5x-12=8\\,\\,\\\\ \\underline{\\,\\,\\,\\,\\,\\,+12\\,+12} \\\\5x=20\\end{array}[\/latex]<\/p>\r\nDivide to isolate the variable.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\underline{5x}=\\underline{5}\\\\ 5\\,\\,\\,\\,\\,\\,\\,\\,\\,5\\\\ x=4\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]x=4[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nIf you are more comfortable working directly with the fractions, you can. It's handy to have this technique available though, especially when the fractions are complicated or involve larger numbers.\r\n\r\nIn the following video, we show how to solve a multi-step equation with fractions.\r\n\r\nhttps:\/\/youtu.be\/AvJTPeACTY0\r\n\r\nRegardless of which method you use to solve equations containing variables, you will get the same answer. You can choose the method you find the easiest! Remember to check your answer by substituting your solution into the original equation.\r\n\r\nSometimes, you will encounter a multi-step equation with decimals. If you prefer not working with decimals, you can use the multiplication property of equality to multiply both sides of the equation by a a factor of 10 that will help clear the decimals. See the example below.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSolve [latex]3y+10.5=6.5+2.5y[\/latex] by clearing the decimals in the equation first.\r\n\r\n[reveal-answer q=\"159951\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"159951\"]\r\n\r\nSince the smallest decimal place represented in the equation is 0.10, we want to multiply by 10 to make 1.0\u00a0and clear\u00a0the decimals from the equation.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}3y+10.5=6.5+2.5y\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\\\\\\\ 10\\left(3y+10.5\\right)=10\\left(6.5+2.5y\\right)\\end{array}[\/latex]<\/p>\r\nUse the distributive property to expand the expressions on both sides.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}10\\left(3y\\right)+10\\left(10.5\\right)=10\\left(6.5\\right)+10\\left(2.5y\\right)\\end{array}[\/latex]<\/p>\r\nMultiply.\r\n<p style=\"text-align: center\">[latex]30y+105=65+25y[\/latex]<\/p>\r\nMove the smaller variable term, [latex]25y[\/latex], by subtracting it from both sides.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}30y+105=65+25y\\,\\,\\\\ \\underline{-25y\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-25y} \\\\5y+105=65\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\nSubtract 105 from both sides to isolate the term with the variable.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{r}5y+105=65\\,\\,\\,\\\\ \\underline{\\,\\,\\,\\,\\,\\,-105\\,-105} \\\\5y=-40\\end{array}[\/latex]<\/p>\r\nDivide both sides by 5 to isolate the <em>y<\/em>.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{l}\\underline{5y}=\\underline{-40}\\\\ 5\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,5\\\\ \\,\\,\\,x=-8\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]x=-8[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video, we show another example of clearing decimals first to solve a multi-step linear equation.\r\n\r\nhttps:\/\/youtu.be\/wtwepTZZnlY\r\n\r\nHere are some steps to follow when you solve multi-step equations.\r\n<div class=\"textbox shaded\">\r\n<h3>Solving Multi-Step Equations<\/h3>\r\n1. (Optional) Multiply to clear any fractions or decimals.\r\n\r\n2. Simplify each side by clearing parentheses and combining like terms.\r\n\r\n3. Add or subtract to isolate the variable term\u2014you may have to move a term with the variable.\r\n\r\n4. Multiply or divide to isolate the variable.\r\n\r\n5. Check the solution.\r\n\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use properties of equality to isolate variables and solve algebraic equations<\/li>\n<li>Use the distributive property<\/li>\n<li>Clear fractions and decimals from equations to make them easier to solve<\/li>\n<\/ul>\n<\/div>\n<h2>Use properties of equality to isolate variables and solve algebraic equations<\/h2>\n<p>There are some <b>equations<\/b> that you can solve in your head quickly. For example\u2014what is the value of <i>y<\/i> in the equation [latex]2y=6[\/latex]? Chances are you didn\u2019t need to get out a pencil and paper to calculate that [latex]y=3[\/latex]. You only needed to do one thing to get the answer: divide 6 by 2.<\/p>\n<p>Other equations are more complicated. Solving [latex]\\displaystyle 4\\left( \\frac{1}{3}t+\\frac{1}{2}\\right)=6[\/latex] without writing anything down is difficult. That\u2019s because this equation contains not just a <b>variable<\/b> but also fractions and <b>terms<\/b> inside parentheses. This is a <b>multi-step equation<\/b>, one that takes several steps to solve. You&#8217;ve probably studied these equations previously and seen that, although multi-step equations take more time and require more operations, they can still be simplified and solved by applying basic algebraic rules.<\/p>\n<p>Remember that you can think of an equation as a balance scale, with the goal being to rewrite the equation so that it is easier to solve but still balanced. The <b>addition property of equality<\/b> and the <b>multiplication property of equality<\/b> explain how you can keep the scale, or the equation, balanced. Whenever you perform an operation to one side of the equation, if you perform the same exact operation to the other side, you\u2019ll keep both sides of the equation equal.<\/p>\n<p>If the equation is in the form [latex]ax+b=c[\/latex], where <i>x<\/i> 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=\"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 2 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 3 to get a coefficient of 1 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>Watch the following video to see examples of solving two step linear equations.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-1\" 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<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve [latex]3x+5x+4-x+7=88[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q455516\">Show Solution<\/span><\/p>\n<div id=\"q455516\" class=\"hidden-answer\" style=\"display: none\">\n<p>There are three like terms [latex]3x[\/latex], [latex]5x[\/latex],\u00a0and\u00a0[latex]\u2013x[\/latex]\u00a0involving a variable.\u00a0Combine these like terms.\u00a04 and 7 are also like terms and can be added.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\,\\,3x+5x+4-x+7=\\,\\,\\,88\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7x+4+7=\\,\\,\\,88\\end{array}[\/latex]<\/p>\n<p>The equation is now in the form\u00a0[latex]ax+b=c[\/latex], so we can solve as before.<\/p>\n<p style=\"text-align: center\">[latex]7x+11\\,\\,\\,=\\,\\,\\,88[\/latex]<\/p>\n<p>Subtract 11 from both sides.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}7x+11\\,\\,\\,=\\,\\,\\,88\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{-11\\,\\,\\,\\,\\,\\,\\,-11}\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7x\\,\\,\\,=\\,\\,\\,77\\end{array}[\/latex]<\/p>\n<p>Divide both sides by 7.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\underline{7x}\\,\\,\\,=\\,\\,\\,\\underline{77}\\\\7\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,7\\,\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,x\\,\\,\\,=\\,\\,\\,11\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]x=11[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>The following video shows an example of solving a linear equation that requires combining like terms.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Solving an Equation that Requires Combining Like Terms\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ez_sP2OTGjU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Some equations may have the variable on both sides of the equal sign, as in this equation: [latex]4x-6=2x+10[\/latex].<\/p>\n<p>To solve this equation, we need to \u201cmove\u201d one of the variable terms.\u00a0This can make it difficult to decide which side to work with. It doesn\u2019t matter which term gets moved, [latex]4x[\/latex] or [latex]2x[\/latex], however, to avoid negative coefficients, you can move the smaller term.<\/p>\n<div class=\"textbox exercises\">\n<h3>Examples<\/h3>\n<p>Solve:\u00a0[latex]4x-6=2x+10[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q457216\">Show Solution<\/span><\/p>\n<div id=\"q457216\" class=\"hidden-answer\" style=\"display: none\">\n<p>Choose the variable term to move\u2014to avoid negative terms choose [latex]2x[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\,\\,\\,4x-6=2x+10\\\\\\underline{-2x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-2x}\\\\\\,\\,\\,4x-6=10[\/latex]<\/p>\n<p style=\"text-align: left\">Now add\u00a06 to both\u00a0sides to isolate the term with the variable.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4x-6=10\\\\\\underline{\\,\\,\\,\\,+6\\,\\,\\,+6}\\\\4x=16\\end{array}[\/latex]<\/p>\n<p style=\"text-align: left\">Now divide each side by 4 to isolate the variable x.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\frac{4x}{4}=\\frac{16}{4}\\\\\\\\x=4\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In this video, you can see an example of solving equations that have variables on both sides of the equal sign.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-3\" title=\"Solve an Equation with Variable on Both Sides\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/f3ujWNPL0Bw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2 id=\"title2\">The Distributive Property<\/h2>\n<p>As we solve linear equations, we often need to do some work to write\u00a0the linear equations in a form we are familiar with solving.\u00a0This section will focus on manipulating an equation we are asked to solve in such a way that we can use the skills we learned for solving multi-step equations to ultimately arrive at the solution.<\/p>\n<p>Parentheses can\u00a0make solving a problem difficult, if not impossible. To get rid of these unwanted parentheses we have the distributive property. Using this property we multiply the number in front of the parentheses by each term inside of the parentheses.<\/p>\n<div class=\"textbox shaded\">\n<h3>The Distributive Property of Multiplication<\/h3>\n<p>For all real numbers <i>a, b,<\/i> and <i>c<\/i>,\u00a0[latex]a(b+c)=ab+ac[\/latex].<\/p>\n<p>What this means is that when a number multiplies an expression inside parentheses, you can distribute the multiplication to each term of the expression individually. Then, you can follow the steps we have already practiced\u00a0to <b>isolate the variable<\/b>\u00a0and solve the equation.<\/p>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve for [latex]a[\/latex]. [latex]4\\left(2a+3\\right)=28[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q372387\">Show Solution<\/span><\/p>\n<div id=\"q372387\" class=\"hidden-answer\" style=\"display: none\">\n<p>Apply the distributive property to expand [latex]4\\left(2a+3\\right)[\/latex] to [latex]8a+12[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\left(2a+3\\right)=28\\\\ 8a+12=28\\end{array}[\/latex]<\/p>\n<p>Subtract 12\u00a0from both sides to isolate\u00a0the variable term.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}8a+12\\,\\,\\,=\\,\\,\\,28\\\\ \\underline{-12\\,\\,\\,\\,\\,\\,-12}\\\\ 8a\\,\\,\\,=\\,\\,\\,16\\end{array}[\/latex]<\/p>\n<p>Divide both terms by 8 to get a coefficient of 1.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\underline{8a}=\\underline{16}\\\\8\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,8\\\\a\\,=\\,\\,2\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]a=2[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>In the video that follows, see another example of how to use the distributive property to solve a multi-step linear equation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Solving an Equation with One Set of Parentheses\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/aQOkD8L57V0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In the next example, you will see that there are parentheses on both sides of the equal sign, so you will need to use the distributive property twice. Notice that you are going to need to distribute a negative number, so be careful with negative signs!<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve for [latex]t[\/latex].\u00a0\u00a0[latex]2\\left(4t-5\\right)=-3\\left(2t+1\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q302387\">Show Solution<\/span><\/p>\n<div id=\"q302387\" class=\"hidden-answer\" style=\"display: none\">\n<p>Apply the distributive property to expand [latex]2\\left(4t-5\\right)[\/latex] to [latex]8t-10[\/latex] and [latex]-3\\left(2t+1\\right)[\/latex] to[latex]-6t-3[\/latex]. Be careful in this step\u2014you are distributing a negative number, so keep track of the sign of each number after you multiply.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}2\\left(4t-5\\right)=-3\\left(2t+1\\right)\\,\\,\\,\\,\\,\\, \\\\ 8t-10=-6t-3\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p>Add [latex]-6t[\/latex] to both sides to begin combining like terms.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}8t-10=-6t-3\\\\ \\underline{+6t\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+6t}\\,\\,\\,\\,\\,\\,\\,\\\\ 14t-10=\\,\\,\\,\\,-3\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p>Add 10 to both sides of the equation to isolate <em>t<\/em>.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}14t-10=-3\\\\ \\underline{+10\\,\\,\\,+10}\\\\ 14t=\\,\\,\\,7\\,\\end{array}[\/latex]<\/p>\n<p>The last step is to divide both sides by 14 to completely isolate <em>t<\/em>.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}14t=7\\,\\,\\,\\,\\\\\\frac{14t}{14}=\\frac{7}{14}\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]t=\\frac{1}{2}[\/latex]<\/p>\n<p>We simplified the fraction [latex]\\frac{7}{14}[\/latex] into [latex]\\frac{1}{2}[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>In the following video, we solve another multi-step equation with two sets of parentheses.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-5\" title=\"Solving an Equation with Parentheses on Both Sides\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/StomYTb7Xb8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Sometimes, you will encounter a multi-step equation with fractions. If you prefer not working with fractions, you can use the multiplication property of equality to multiply both sides of the equation by a common denominator of all of the fractions in the equation. This will clear all the fractions out of the equation. See the example below.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve \u00a0[latex]\\frac{1}{2}x-3=2-\\frac{3}{4}x[\/latex] by clearing the fractions in the equation first.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q129951\">Show Solution<\/span><\/p>\n<div id=\"q129951\" class=\"hidden-answer\" style=\"display: none\">\n<p>Multiply both sides of the equation by 4, the common denominator of the fractional coefficients.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\frac{1}{2}x-3=2-\\frac{3}{4}x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\\\\\\\ 4\\left(\\frac{1}{2}x-3\\right)=4\\left(2-\\frac{3}{4}x\\right)\\end{array}[\/latex]<\/p>\n<p>Use the distributive property to expand the expressions on both sides.\u00a0Multiply.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}4\\left(\\frac{1}{2}x\\right)-4\\left(3\\right)=4\\left(2\\right)-4\\left(-\\frac{3}{4}x\\right)\\\\\\\\ \\frac{4}{2}x-12=8-\\frac{12}{4}x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\\\\\\\ 2x-12=8-3x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\end{array}[\/latex]<\/p>\n<p>Add 3<em>x<\/em> to both sides to move the variable terms to only one side. Add 12 to both sides to move the variable\u00a0terms to only one side.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}2x-12=8-3x\\, \\\\\\underline{+3x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,+3x}\\\\ 5x-12=8\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p>Add 12 to both sides to move the <b>constant<\/b> terms to the other side.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}5x-12=8\\,\\,\\\\ \\underline{\\,\\,\\,\\,\\,\\,+12\\,+12} \\\\5x=20\\end{array}[\/latex]<\/p>\n<p>Divide to isolate the variable.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\underline{5x}=\\underline{5}\\\\ 5\\,\\,\\,\\,\\,\\,\\,\\,\\,5\\\\ x=4\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]x=4[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>If you are more comfortable working directly with the fractions, you can. It&#8217;s handy to have this technique available though, especially when the fractions are complicated or involve larger numbers.<\/p>\n<p>In the following video, we show how to solve a multi-step equation with fractions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-6\" title=\"Solving an Equation with Fractions (Clear Fractions)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/AvJTPeACTY0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Regardless of which method you use to solve equations containing variables, you will get the same answer. You can choose the method you find the easiest! Remember to check your answer by substituting your solution into the original equation.<\/p>\n<p>Sometimes, you will encounter a multi-step equation with decimals. If you prefer not working with decimals, you can use the multiplication property of equality to multiply both sides of the equation by a a factor of 10 that will help clear the decimals. See the example below.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Solve [latex]3y+10.5=6.5+2.5y[\/latex] by clearing the decimals in the equation first.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q159951\">Show Solution<\/span><\/p>\n<div id=\"q159951\" class=\"hidden-answer\" style=\"display: none\">\n<p>Since the smallest decimal place represented in the equation is 0.10, we want to multiply by 10 to make 1.0\u00a0and clear\u00a0the decimals from the equation.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}3y+10.5=6.5+2.5y\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\\\\\\\ 10\\left(3y+10.5\\right)=10\\left(6.5+2.5y\\right)\\end{array}[\/latex]<\/p>\n<p>Use the distributive property to expand the expressions on both sides.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}10\\left(3y\\right)+10\\left(10.5\\right)=10\\left(6.5\\right)+10\\left(2.5y\\right)\\end{array}[\/latex]<\/p>\n<p>Multiply.<\/p>\n<p style=\"text-align: center\">[latex]30y+105=65+25y[\/latex]<\/p>\n<p>Move the smaller variable term, [latex]25y[\/latex], by subtracting it from both sides.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}30y+105=65+25y\\,\\,\\\\ \\underline{-25y\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,-25y} \\\\5y+105=65\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p>Subtract 105 from both sides to isolate the term with the variable.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}5y+105=65\\,\\,\\,\\\\ \\underline{\\,\\,\\,\\,\\,\\,-105\\,-105} \\\\5y=-40\\end{array}[\/latex]<\/p>\n<p>Divide both sides by 5 to isolate the <em>y<\/em>.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{l}\\underline{5y}=\\underline{-40}\\\\ 5\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,5\\\\ \\,\\,\\,x=-8\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]x=-8[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\n<p>In the following video, we show another example of clearing decimals first to solve a multi-step linear equation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-7\" title=\"Solving an Equation with Decimals (Clear Decimals)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/wtwepTZZnlY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Here are some steps to follow when you solve multi-step equations.<\/p>\n<div class=\"textbox shaded\">\n<h3>Solving Multi-Step Equations<\/h3>\n<p>1. (Optional) Multiply to clear any fractions or decimals.<\/p>\n<p>2. Simplify each side by clearing parentheses and combining like terms.<\/p>\n<p>3. Add or subtract to isolate the variable term\u2014you may have to move a term with the variable.<\/p>\n<p>4. Multiply or divide to isolate the variable.<\/p>\n<p>5. Check the solution.<\/p>\n<\/div>\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-4216\">\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>Revision and Adaptation. <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><\/li><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><li>Solving Two Step Equations (Basic). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/fCyxSVQKeRw\">https:\/\/youtu.be\/fCyxSVQKeRw<\/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>Solving an Equation that Requires Combining Like Terms. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/ez_sP2OTGjU\">https:\/\/youtu.be\/ez_sP2OTGjU<\/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>Solve an Equation with Variable on Both Sides. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/f3ujWNPL0Bw\">https:\/\/youtu.be\/f3ujWNPL0Bw<\/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>Solving an Equation with One Set of Parentheses. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/aQOkD8L57V0\">https:\/\/youtu.be\/aQOkD8L57V0<\/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>Solving an Equation with Parentheses on Both Sides. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/StomYTb7Xb8\">https:\/\/youtu.be\/StomYTb7Xb8<\/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>Solving an Equation with Fractions (Clear Fractions). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/AvJTPeACTY0\">https:\/\/youtu.be\/AvJTPeACTY0<\/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>Solving an Equation with Decimals (Clear Decimals). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/wtwepTZZnlY\">https:\/\/youtu.be\/wtwepTZZnlY<\/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>Solve One-Step Equations Using Addition and Subtraction (Whole Numbers). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/VsWrFKFerSY\">https:\/\/youtu.be\/VsWrFKFerSY<\/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>Solving One Step Equations Using Addition and Subtraction (Decimals). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/D8wKGlxf6bM\">https:\/\/youtu.be\/D8wKGlxf6bM<\/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>Solving One Step Equations Using Addition and Subtraction (Fractions). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/O7SPM7Cs8Ds\">https:\/\/youtu.be\/O7SPM7Cs8Ds<\/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>Unit 10: Solving Equations and Inequalities, First Edition Developmental Math: An Open Program . <strong>Provided by<\/strong>: Monterey Institute of Technology. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/\">http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/<\/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>Solving One Step Equations Using Multiplication (Fractions). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <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>Beginning and Intermediate Algebra. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/Beginning%20and%20Intermediate%20Algebra\">http:\/\/Beginning%20and%20Intermediate%20Algebra<\/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>\n\t\t\t\t\t\t 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