{"id":63841,"date":"2020-12-10T17:33:51","date_gmt":"2020-12-10T17:33:51","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=63841"},"modified":"2026-03-28T11:07:08","modified_gmt":"2026-03-28T16:07:08","slug":"rules-for-manipulating-equations","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/rules-for-manipulating-equations\/","title":{"rendered":"Rules for Manipulating Equations"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_AUy7Kto55s0\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_AUy7Kto55s0\" data-source-videoID=\"AUy7Kto55s0\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Rules for Manipulating Equations Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Rules for Manipulating Equations\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_AUy7Kto55s0:hover {cursor:pointer;} img#videoThumbnailImage_AUy7Kto55s0 {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/1708-rules-for-manipulating-equations-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_AUy7Kto55s0\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_AUy7Kto55s0\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Rules for Manipulating Equations\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_AUy7Kto55s0\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_AUy7Kto55s0\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_AUy7Kto55s0\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction dso_Function() {\n  var x = document.getElementById(\"dso\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"dso_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"dso\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Reviewing_the_Basics\" class=\"smooth-scroll\">Reviewing the Basics<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Carrying_Operations\" class=\"smooth-scroll\">Carrying Operations<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Combining_Like_Terms\" class=\"smooth-scroll\">Combining Like Terms<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Canceling_Terms\" class=\"smooth-scroll\">Canceling Terms<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Review_Questions\" class=\"smooth-scroll\">Review Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Manipulating_Equation_Practice_Questions\" class=\"smooth-scroll\">Manipulating Equation Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video about <strong>manipulating equations<\/strong>! In this video, we\u2019ll be discussing these three main concepts, seeing what each is, why we need to know it, and how we use it:<\/p>\n<ul>\n<li>Carrying out the Same Operation on Both Sides of the Equation<\/li>\n<li>The Advantage of Combining Like Terms<\/li>\n<li>Canceling Terms on Opposite Sides of an Equation<\/li>\n<\/ul>\n<p>Let\u2019s get started!<\/p>\n<h2><span id=\"Reviewing_the_Basics\" class=\"m-toc-anchor\"><\/span>Reviewing the Basics<\/h2>\n<p>\nBefore we jump into it, let\u2019s quickly review some background info to ensure we\u2019re on the same page. <\/p>\n<p>Remember that an equation is a statement of equality. The equation \\(2x\\) plus 4 equals \\(10 [2x + 4 = 10]\\) tells us that the expression \\(2x\\) plus \\(4\\text{ }2x + 4\\) is equivalent to the expression 10. It also tells us there is some value of \\(x\\) that will make the expression \\(2x\\) plus 4 actually equal 10 and, therefore, make the statement true. In this case, \\(x\\) would be 3: 2 times 3, plus 4 equals \\(10 [2(3) + 4 = 10]\\). <\/p>\n<p>All other values of \\(x\\) make the statement false. For instance, if we tried to say that \\(x=5\\), the left side of the equation would equal 14 and therefore not be equal to 10.<\/p>\n<p>Okay, now let\u2019s get into the first concept: carrying out the same operation on both sides of the equation.<\/p>\n<h2><span id=\"Carrying_Operations\" class=\"m-toc-anchor\"><\/span>Carrying Operations<\/h2>\n<p>\nSince the two expressions on either side of the equals sign are in fact equal, we can use any operation we want on one expression as long as we do the exact same thing to the other expression. This is generally known as keeping equations balanced. It produces equivalent expressions and does not change the value of \\(x\\) that makes the original statement true.<\/p>\n<p>For example, we can subtract 7 from both sides, which would give us \\(2x-3=3\\).<\/p>\n<div class=\"examplesentence\">\\(2x + 4 = 10\\)<br \/>\n\\( -7\\text{        }-7\\)<br \/>\n\\(2x \u2013 3 = 3\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe statement is still true when \\(x=3\\): 2 times 3, minus 3 does in fact equal 3.<\/p>\n<p>Or we can divide all the terms on both sides by 2. So, we have our original again \\(2x\\) plus 4 equals 10. And if we divide each part by 2, that gives us \\(x\\) plus 2 equals 5.<\/p>\n<div class=\"examplesentence\">\\((2x)\/2+4\/2 = 10\/2\\)<br \/>\n\\(x+2=5\\)<\/div>\n<p>\n&nbsp;<br \/>\nAgain, when \\(x=3\\), the statement is true, and all other values make it false: 3 plus 2 equals 5. \\(3+2=5\\)<\/p>\n<p>Typically, when given an equation, we want to isolate \\(x\\) using addition, subtraction, multiplication, or division so we can see its value. So, even though we can manipulate an equation using any terms we want, there are certain operations in every equation that help us reach a solution.<\/p>\n<p>Now that we\u2019ve got that down, let\u2019s discuss our next concept: combining like terms.<\/p>\n<h2><span id=\"Combining_Like_Terms\" class=\"m-toc-anchor\"><\/span>Combining Like Terms<\/h2>\n<p>\nCombining like terms is an important equation-solving step that is usually done before any actual solving begins as a way to simplify the equation. To combine like terms, add or subtract all of the terms with the same variable.<\/p>\n<p>For example, consider the equation \\(2(x+3)+3(2+x+3)=-4\\). The 2 and the 3 in the second set of parentheses are like terms, so we can combine them. Doing so gives us 2 times (\\(x\\) plus 3), plus 3 times (\\(x\\) plus 4) equals negative 4. \\(2(x+3)+3(x+5)=-4\\). Now, we can carry out the multiplications that are implied by the parentheses, distributing the outer 2 and 3 accordingly: 2 times \\(x\\) is \\(2x\\), plus 2 times 3 is 6, plus 3 times \\(x\\) is \\(3x\\), plus 3 times 5 is 15, equals negative 4.<\/p>\n<div class=\"examplesentence\">\\(2x+6+3x+15=-4\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe \\(2x\\) and the \\(3x\\) terms are like terms, so we can add them together to get \\(5x\\) plus 6, plus 15, equals negative 4. \\(5x+6+15=-4\\). Now, the constants 6, 15, and \\(\u20134\\) are also like terms, and we can combine them as well. Subtracting 6 and 15 from both sides of the equation, will give us this: \\(5x\\)  equals negative 25, which simplifies further (by dividing by 5 on both sides) to \\(x=-5\\).<\/p>\n<p>Let\u2019s look at another example. In the equation \\(2x+4=16\u2013x\\), we need to get the \\(x\\)-terms on one side and the numbers on the other.<\/p>\n<p>We can add \\(x\\) and subtract 4. This will gives us \\(3x=12\\).<\/p>\n<div class=\"examplesentence\">\\(2x+4=16\u2013x\\)<br \/>\n\\(2x+4+x=16\u2013x+x\\)<br \/>\n\\(3x+4\u20134=16\u20134\\)<br \/>\n\\(3x=12\\)<\/div>\n<p>\n&nbsp;<br \/>\nOr we can subtract \\(2x\\) and subtract 16. So, if we try this one again, we have \\(2x+4=16-x\\) and if we subtract \\(2x\\) from both sides, and subtract 16, that will leave us with \\(-12=-3x\\).<\/p>\n<div class=\"examplesentence\">\\(2x+4=16\u2013x\\)<br \/>\n\\(2x+4\u20132x=16\u2013x\u20132x\\)<br \/>\n\\(4\u201316=16\u20133x\u201316\\)<br \/>\n\\(-12=-3x\\)<\/div>\n<p>\n&nbsp;<br \/>\nRegardless of the steps to combine the like terms, the solution is the same: \\(x\\) equals 4. Divide by 3 on both sides and we get that \\(x\\) equals 4, and here divide by negative 3 on both sides again gives us that \\(x\\) equals 4 (since dividing a negative by a negative results in a positive.<\/p>\n<p>Now onto the third and final concept we\u2019re going to cover: canceling terms on opposite sides of an equation.<\/p>\n<h2><span id=\"Canceling_Terms\" class=\"m-toc-anchor\"><\/span>Canceling Terms<\/h2>\n<p>\nSometimes, manipulating terms in an equation is called \u201ccanceling\u201d or \u201ccanceling out\u201d. Two terms on opposite sides of an equation can be canceled if and only if they exactly match each other. They must have the same variable raised to the same power and the same coefficient. <\/p>\n<p>Canceling can be done using any of <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/addition-subtraction-multiplication-and-division\/\">the four operations<\/a>, but there is a more specific way to think about what we\u2019re doing.<\/p>\n<p>When we add or subtract a term to both sides of an equation, we\u2019re making a zero by adding the opposite of a term.<\/p>\n<p>In the equation \\(x+6=13\\), we would solve by subtracting 6 from both sides.<\/p>\n<div class=\"examplesentence\">\\(x+6=13\\)<br \/>\n\\(-6\\text{     }-6\\)<br \/>\n\\(x=7\\)<\/div>\n<p>\n&nbsp;<br \/>\nBy subtracting 6 from both sides, we made 0 on the left side, since 6 minus 6 equals 0, allowing us to solve the equation.<\/p>\n<p>By the same token, in the equation \\(x\\) minus 5 equals negative \\(4x\\) \\(x\u20135=-4x\\), we might subtract \\(x\\) from both sides to make a 0 and find the solution. Then we\u2019ll divide by negative 5 on both sides to get that \\(x\\) equals 1.<\/p>\n<div class=\"examplesentence\">\\(x\u20135=-4x\\)<br \/>\n\\(-x\\text{      }-x\\)<br \/>\n\\(-5=-5x\\)<br \/>\n\\(1=x\\)<\/div>\n<p>\n&nbsp;<br \/>\nWith multiplication and division, the goal is to make a 1. In the equation \\(3x\\) equals 9 \\(3x=9\\), we need to make that \\(3x\\) a single \\(x\\) by dividing both sides by 3.<\/p>\n<div class=\"examplesentence\">\\(3x=9\\)<br \/>\n\\(3x\/3=9\/3\\)<br \/>\n\\(x=3\\)<\/div>\n<p>\n&nbsp;<br \/>\nSince  3 over 3 equals 1 \\(3\/3=1\\), we were able to solve the equation.<\/p>\n<h2><span id=\"Review_Questions\" class=\"m-toc-anchor\"><\/span>Review Questions<\/h2>\n<p>\nThinking about manipulation in terms of making zeros and making ones will help you determine the path to finding a solution to any equation. Let\u2019s practice a couple before we go!<\/p>\n<h3><span id=\"Question_1\" class=\"m-toc-anchor\"><\/span>Question #1<\/h3>\n<p>\nSolve: \\( \\frac{x-3}{2}=6\\\\\\)<\/p>\n<p>Make a one by multiplying both sides by 2: \\(x-3=12\\).<\/p>\n<div class=\"examplesentence\">\\(2(x-3)\/2=6(2)\\)<br \/>\n\\(x\u20133=12\\)<\/div>\n<p>\n&nbsp;<br \/>\nMake a zero by adding 3 to both sides: \\(x=15\\).<\/p>\n<div class=\"examplesentence\">\\(x\u20133+3=12+3\\)<br \/>\n\\(x = 15\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Question_2\" class=\"m-toc-anchor\"><\/span>Question #2<\/h3>\n<p>\nSolve: \\(8x+7=-11\u2013x\\)<\/p>\n<p>Make a zero by subtracting 7 from both sides: \\(8x=-18-x\\)<\/p>\n<div class=\"examplesentence\">\\(8x+7\u20137=-11\u2013x\u20137\\)<br \/>\n\\(8x=-18\u2013x\\)<\/div>\n<p>\n&nbsp;<br \/>\nMake another zero by adding x to both sides: \\(9x=-18\\).<\/p>\n<div class=\"examplesentence\">\\(8x+x=-18\u2013x+x\\)<br \/>\n&nbsp;<br \/>\n\\(9x=-18\\)<\/div>\n<p>\n&nbsp;<\/p>\n<p>Make a one by dividing both sides by 9: \\(x=-2\\).<\/p>\n<div class=\"examplesentence\">\\(9x\/9=-18\/9\\)<br \/>\n\\(x=-2\\)<\/div>\n<p>\n&nbsp;<br \/>\nI hope that this video increased your equation manipulation skills! Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Manipulating_Equation_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Manipulating Equation Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for \\(x\\):<\/p>\n<div class=\"yellow-math-quote\">\\(3x+6=33\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(x=27\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(x=81\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">\\(x=9\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(x=13\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>We only need to carry out two steps to solve the equation:<\/p>\n<p>First, subtract 6 from both sides to isolate the term with \\(x\\):<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(3x+6=33\\)<br \/>\n\\(3x+6-6=33-6\\)<\/p>\n<p>Then, divide both sides by 3 to solve fr \\(x\\):<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(3x=27\\)<br \/>\n\\(3x\\div3=27\\div3\\)<br \/>\n\\(x=9\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for \\(x\\) by cancelling out terms on both sides of the following equation:<\/p>\n<div class=\"yellow-math-quote\">\\(-x+8=10x-14\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">\\(x=2\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(x=\\large{\\frac{6}{11}}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(x=\\large{\\frac{2}{3}}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(x=-\\large{\\frac{2}{3}}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>We will need to cancel out a regular, integer term and we will need to cancel out an \\(x\\)-term. We can do this at least two different ways.<\/p>\n<h4 style=\"margin-bottom: 0.15em; font-weight: 600 !important; font-size: 105%\">Method 1: Cancel the \\(x\\)-Term on the Left First<\/h4>\n<p>First, add \\(x\\) to both sides to cancel the \\(-x\\).<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(-x+8=10x-14\\)<br \/>\n\\(-x+8+x=10x-14+x\\)<br \/>\n\\(8=11x-14\\)<\/p>\n<p>Then, add 14 to both sides to move the number term.<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(8+14=11x-14+14\\)<br \/>\n\\(22=11x\\)<\/p>\n<p>Finally, divide both sides by 11 to solve for \\(x\\).<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(22\\div11=11x\\div11\\)<br \/>\n\\(2=x\\)<\/p>\n<h4 style=\"margin-bottom: 0.15em; font-weight: 600 !important; font-size: 105%\">Method 2: Cancel the \\(x\\)-Term on the Right First<\/h4>\n<p>First, subtract \\(10x\\) from both sides to cancel the \\(10x\\).<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(-x+8-10x=10x-14-10x\\)<br \/>\n\\(-11x+8=-14\\)<\/p>\n<p>Then, subtract 8 from both sides to move the number term.<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(-11x+8-8=-14-8\\)<br \/>\n\\(-11x=-22\\)<\/p>\n<p>Finally, divide both sides by \u221211 to solve for \\(x\\).<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(-11x\\div(-11)=-22\\div(-11)\\)<br \/>\n\\(x=2\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for \\(x\\) in the equation below by combining like terms and then cancelling out terms on both sides.<\/p>\n<div class=\"yellow-math-quote\">\\(2(3+x-2)+5(x+5)=132\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(x=14\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(x=21\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(x=16\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">\\(x=15\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The first step that we want to do is combine like terms. We want to make things look as simple and neat as possible.<\/p>\n<p>First, combine the 3 and \u22122 in the leftmost set of parentheses:<\/p>\n<p style=\"text-align: center;\">\\(2(x+1)+5(x+5)=132\\)<\/p>\n<p>Then, distribute the 2 and the 5 through their respective parentheses:<\/p>\n<p style=\"text-align: center;\">\\(2x+2+5x+25=132\\)<\/p>\n<p>Now we have more like terms to combine.<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(2x+5x+2+25=132\\)<br \/>\n\\(7x+27=132\\)<\/p>\n<p>Finally, subtract 27 from both sides and divide by 7 on both sides.<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(7x+27=132\\)<br \/>\n\\(7x+27-27=132-27\\)<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(7x=105\\)<br \/>\n\\(7x\\div7=105\\div7\\)<\/p>\n<p style=\"text-align: center\">\\(x=15\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for \\(x\\):<\/p>\n<div class=\"yellow-math-quote\">\\(3(x+3)-2(x-1)=-10x\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">\\(x=-1\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(x=-\\large{\\frac{7}{11}}\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(x=-3\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(x=-\\large{\\frac{1}{11}}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>First, distribute the 3 and the \u22122 through their respective parentheses. Then, we\u2019ll combine like terms and cancel out certain terms.<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(3(x+3)-2(x-1)=-10x\\)<br \/>\n\\(3x+9-2x+2=-10x\\)<br \/>\n\\(x+11=-10x\\)<br \/>\n\\(11=-11x\\)<br \/>\n\\(-1=x\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for \\(x\\):<\/p>\n<div class=\"yellow-math-quote\" style=\"line-height: 35px\">\\(10(x+4)-3(x+1)\\)\\(\\:=-3+8x+34\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(x=9\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">\\(x=6\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\(x=-5\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(x=-7\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>First, combine like terms. Then, distribute the 10 and the \u22123. Finally, combine like terms again and do some cancelling.<\/p>\n<p style=\"text-align: center; line-height: 35px;\">\\(10(x+4)-3(x+1)=-3+8x+34\\)<br \/>\n\\(10(x+4)-3(x+1)=8x+31\\)<br \/>\n\\(10x+40-3x-3=8x+31\\)<br \/>\n\\(7x+37=8x+31\\)<br \/>\n\\(37=x+31\\)<br \/>\n\\(6=x\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-i\/\">Return to Algebra I Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Algebra I Videos<\/p>\n","protected":false},"author":1,"featured_media":100690,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-63841","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-algebra-i-videos","7":"page_category-manipulating-expressions-1","8":"page_category-math-advertising-group","9":"page_type-video","10":"subject_matter-math"},"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO Pro 4.9.9 - aioseo.com -->\n\t<meta name=\"description\" content=\"Manipulation of equations is a vital math skill. 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