{"id":1279,"date":"2023-04-04T19:34:06","date_gmt":"2023-04-04T19:34:06","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=1279"},"modified":"2024-10-18T20:51:10","modified_gmt":"2024-10-18T20:51:10","slug":"algebraic-equations-learn-it-4","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/algebraic-equations-learn-it-4\/","title":{"raw":"Algebraic Equations: Learn It 4","rendered":"Algebraic Equations: Learn It 4"},"content":{"raw":"<h2>Solving Multi-Step Equations With Parentheses<\/h2>\r\n<p>If an equation you encounter contains parentheses, you\u2019ll need to clear them from the equations before attempting to combine like terms. To clear parentheses from an equation, use the distributive property to multiply the number in front of the parentheses by each term inside of the parentheses. If the number in front of the parentheses is negative, multiply the negative against each term inside the parentheses.<\/p>\r\n<section class=\"textbox recall\">\r\n<p><strong>The Distributive Property of Multiplication<\/strong><\/p>\r\n<p>For all real numbers [latex]a, b[\/latex] and [latex]c[\/latex],\u00a0[latex]a(b+c)=ab+ac[\/latex].<\/p>\r\n<\/section>\r\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 to isolate the variable and solve the equation.<\/p>\r\n<section class=\"textbox example\">Solve the following for [latex]a[\/latex]:\r\n\r\n\r\n<p><center>[latex]4\\left(2a+3\\right)=28[\/latex]<\/center>\r\n[reveal-answer q=\"372387\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"372387\"]Apply the distributive property to expand [latex]4\\left(2a+3\\right)[\/latex] to [latex]8a+12[\/latex].<\/p>\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\n<p>Subtract [latex]12[\/latex]\u00a0from both sides to isolate\u00a0the variable term.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}8a+12\\,\\,\\,=\\,\\,\\,28\\\\ \\underline{-12\\,\\,\\,\\,\\,\\,-12}\\\\ 8a\\,\\,\\,=\\,\\,\\,16\\end{array}[\/latex]<\/p>\r\n<p>Divide both terms by [latex]8[\/latex] to get a coefficient of [latex]1[\/latex].<\/p>\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<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<p>In the next example, there are parentheses on both sides of the equal sign. To clear them, you\u2019ll need to use the distributive property on both sides of the equation.<\/p>\r\n<section class=\"textbox example\">Solve the following for  [latex]t[\/latex]:\u00a0\r\n\r\n\r\n<p><center>[latex]2\\left(4t-5\\right)=-3\\left(2t+1\\right)[\/latex]<\/center>[reveal-answer q=\"302387\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"302387\"]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>\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\n<p>Add [latex]6t[\/latex] to both sides to begin combining like terms.<\/p>\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\n<p>Add [latex]10[\/latex] to both sides of the equation to isolate [latex]t[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}14t-10=-3\\\\ \\underline{+10\\,\\,\\,+10}\\\\ 14t=\\,\\,\\,7\\,\\end{array}[\/latex]<\/p>\r\n<p>The last step is to divide both sides by [latex]14[\/latex] to completely isolate [latex]t[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\Large\\frac{14t}{14}\\normalsize=\\Large\\frac{7}{14}\\end{array}[\/latex]<\/p>\r\n<p>We simplify the fraction [latex]\\Large\\frac{7}{14}[\/latex] into the final answer of [latex]t=\\Large\\frac{1}{2}[\/latex][\/hidden-answer]<\/p>\r\n<\/section>\r\n<h2>Clearing Fractions and Decimals from Equations<\/h2>\r\n<p>Sometimes, you will encounter a multi-step equation containing fractions. Before attempting to solve the equation, first 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. It is acceptable to simply do the operations on the fractions without clearing them first, but the technique used here will apply to more complicated situations you\u2019ll encounter later, so it is worthwhile to practice it. 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>\r\n<section class=\"textbox example\">Solve \u00a0[latex]\\Large\\frac{1}{2}\\normalsize x-3=2-\\Large\\frac{3}{4}\\normalsize x[\/latex] by clearing the fractions in the equation first.[reveal-answer q=\"129951\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"129951\"]Multiply both sides of the equation by [latex]4[\/latex], the common denominator of the fractional coefficients.\r\n\r\n\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\Large\\frac{1}{2}\\normalsize{x-3=2-}\\Large\\frac{3}{4}\\normalsize{x}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\\\\\\\ 4\\left(\\Large\\frac{1}{2}\\normalsize{x-3}\\right)=4\\left(2-\\Large\\frac{3}{4}\\normalsize{x}\\right)\\end{array}[\/latex]<\/p>\r\n<p>Use the distributive property to expand the expressions on both sides.\u00a0Multiply.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}4\\left(\\Large\\frac{1}{2}\\normalsize{x}\\right)-4\\left(3\\right)=4\\left(2\\right)-4\\left(-\\Large\\frac{3}{4}\\normalsize{x}\\right)\\\\\\\\ \\Large\\frac{4}{2}\\normalsize{x}-12=8-\\Large\\frac{12}{4}\\normalsize{x}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\\\\\\\ 2x-12=8-3x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\end{array}[\/latex]<\/p>\r\n<p>Add [latex]3x[\/latex] to both sides to move the variable terms to only one side.<\/p>\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\n<p>Add [latex]12[\/latex] to both sides to move the <b>constant<\/b> terms to the other side.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}5x-12=8\\,\\,\\\\ \\underline{\\,\\,\\,\\,\\,\\,+12\\,+12} \\\\5x=20\\end{array}[\/latex]<\/p>\r\n<p>Divide to isolate the variable.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\underline{5x}=\\underline{20}\\\\ 5\\,\\,\\,\\,\\,\\,\\,\\,\\,5\\,\\,\\\\ x=4\\end{array}[\/latex]<\/p>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<p>Sometimes, you will encounter a multi-step equation with decimals. To clear the decimals from the equation, use the multiplication property of equality to multiply both sides of the equation by a factor of [latex]10[\/latex], that will help clear the decimals.<\/p>\r\n<section class=\"textbox example\">Solve [latex]3y+10.5=6.5+2.5y[\/latex] by clearing the decimals in the equation first.[reveal-answer q=\"159951\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"159951\"]Since the smallest decimal place value represented in the equation is [latex]0.10[\/latex], we want to multiply by [latex]10[\/latex] to clear\u00a0the decimals from the equation.\r\n\r\n\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\n<p>Use the distributive property to expand the expressions on both sides.<\/p>\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\n<p>Multiply.<\/p>\r\n<p style=\"text-align: center;\">[latex]30y+105=65+25y[\/latex]<\/p>\r\n<p>Move the smaller variable term, [latex]25y[\/latex], by subtracting it from both sides.<\/p>\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\n<p>Subtract [latex]105[\/latex] from both sides to isolate the term with the variable.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}5y+105=65\\,\\,\\,\\\\ \\underline{\\,\\,\\,\\,\\,\\,-105\\,-105} \\\\5y=-40\\end{array}[\/latex]<\/p>\r\n<p>Divide both sides by [latex]5[\/latex] to isolate the [latex]y[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\underline{5y}=\\underline{-40}\\\\ 5\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,5\\,\\,\\\\ y=-8\\,\\,\\end{array}[\/latex]<\/p>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>","rendered":"<h2>Solving Multi-Step Equations With Parentheses<\/h2>\n<p>If an equation you encounter contains parentheses, you\u2019ll need to clear them from the equations before attempting to combine like terms. To clear parentheses from an equation, use the distributive property to multiply the number in front of the parentheses by each term inside of the parentheses. If the number in front of the parentheses is negative, multiply the negative against each term inside the parentheses.<\/p>\n<section class=\"textbox recall\">\n<p><strong>The Distributive Property of Multiplication<\/strong><\/p>\n<p>For all real numbers [latex]a, b[\/latex] and [latex]c[\/latex],\u00a0[latex]a(b+c)=ab+ac[\/latex].<\/p>\n<\/section>\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 to isolate the variable and solve the equation.<\/p>\n<section class=\"textbox example\">Solve the following for [latex]a[\/latex]:<\/p>\n<div style=\"text-align: center;\">[latex]4\\left(2a+3\\right)=28[\/latex]<\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q372387\">Show Solution<\/button><\/p>\n<div id=\"q372387\" class=\"hidden-answer\" style=\"display: none\">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 [latex]12[\/latex]\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 [latex]8[\/latex] to get a coefficient of [latex]1[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\underline{8a}=\\underline{16}\\\\8\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,8\\,\\,\\\\a\\,=\\,\\,2\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<p>In the next example, there are parentheses on both sides of the equal sign. To clear them, you\u2019ll need to use the distributive property on both sides of the equation.<\/p>\n<section class=\"textbox example\">Solve the following for  [latex]t[\/latex]:\u00a0<\/p>\n<div style=\"text-align: center;\">[latex]2\\left(4t-5\\right)=-3\\left(2t+1\\right)[\/latex]<\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q302387\">Show Solution<\/button><\/p>\n<div id=\"q302387\" class=\"hidden-answer\" style=\"display: none\">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 [latex]10[\/latex] to both sides of the equation to isolate [latex]t[\/latex].<\/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 [latex]14[\/latex] to completely isolate [latex]t[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\Large\\frac{14t}{14}\\normalsize=\\Large\\frac{7}{14}\\end{array}[\/latex]<\/p>\n<p>We simplify the fraction [latex]\\Large\\frac{7}{14}[\/latex] into the final answer of [latex]t=\\Large\\frac{1}{2}[\/latex]<\/p><\/div>\n<\/div>\n<\/section>\n<h2>Clearing Fractions and Decimals from Equations<\/h2>\n<p>Sometimes, you will encounter a multi-step equation containing fractions. Before attempting to solve the equation, first 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. It is acceptable to simply do the operations on the fractions without clearing them first, but the technique used here will apply to more complicated situations you\u2019ll encounter later, so it is worthwhile to practice it. 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<section class=\"textbox example\">Solve \u00a0[latex]\\Large\\frac{1}{2}\\normalsize x-3=2-\\Large\\frac{3}{4}\\normalsize x[\/latex] by clearing the fractions in the equation first.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q129951\">Show Solution<\/button><\/p>\n<div id=\"q129951\" class=\"hidden-answer\" style=\"display: none\">Multiply both sides of the equation by [latex]4[\/latex], the common denominator of the fractional coefficients.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\Large\\frac{1}{2}\\normalsize{x-3=2-}\\Large\\frac{3}{4}\\normalsize{x}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\\\\\\\ 4\\left(\\Large\\frac{1}{2}\\normalsize{x-3}\\right)=4\\left(2-\\Large\\frac{3}{4}\\normalsize{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(\\Large\\frac{1}{2}\\normalsize{x}\\right)-4\\left(3\\right)=4\\left(2\\right)-4\\left(-\\Large\\frac{3}{4}\\normalsize{x}\\right)\\\\\\\\ \\Large\\frac{4}{2}\\normalsize{x}-12=8-\\Large\\frac{12}{4}\\normalsize{x}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\\\\\\\ 2x-12=8-3x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\end{array}[\/latex]<\/p>\n<p>Add [latex]3x[\/latex] to both sides to move the variable terms 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 [latex]12[\/latex] 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{20}\\\\ 5\\,\\,\\,\\,\\,\\,\\,\\,\\,5\\,\\,\\\\ x=4\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<p>Sometimes, you will encounter a multi-step equation with decimals. To clear the decimals from the equation, use the multiplication property of equality to multiply both sides of the equation by a factor of [latex]10[\/latex], that will help clear the decimals.<\/p>\n<section class=\"textbox example\">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\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q159951\">Show Solution<\/button><\/p>\n<div id=\"q159951\" class=\"hidden-answer\" style=\"display: none\">Since the smallest decimal place value represented in the equation is [latex]0.10[\/latex], we want to multiply by [latex]10[\/latex] to 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 [latex]105[\/latex] 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 [latex]5[\/latex] to isolate the [latex]y[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}\\underline{5y}=\\underline{-40}\\\\ 5\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,5\\,\\,\\\\ y=-8\\,\\,\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n","protected":false},"author":15,"menu_order":29,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and 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