{"id":113915,"date":"2022-02-15T16:28:14","date_gmt":"2022-02-15T22:28:14","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=113915"},"modified":"2026-05-05T09:08:37","modified_gmt":"2026-05-05T14:08:37","slug":"solving-equations-using-the-distributive-property","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/solving-equations-using-the-distributive-property\/","title":{"rendered":"Solving Equations Using the Distributive Property"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_ZkXLUUdJziY\" 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_ZkXLUUdJziY\" data-source-videoID=\"ZkXLUUdJziY\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Solving Equations Using the Distributive Property Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Solving Equations Using the Distributive Property\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_ZkXLUUdJziY:hover {cursor:pointer;} img#videoThumbnailImage_ZkXLUUdJziY {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/2177-thumbnail-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_ZkXLUUdJziY\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_ZkXLUUdJziY\" 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\",\"Solving Equations Using the Distributive Property\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_ZkXLUUdJziY\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_ZkXLUUdJziY\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_ZkXLUUdJziY\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction vQa_Function() {\n  var x = document.getElementById(\"vQa\");\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=\"vQa_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=\"vQa\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Review_of_the_Distributive_Property\" class=\"smooth-scroll\">Review of the Distributive Property<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_Distributing_on_One_Side\" class=\"smooth-scroll\">Example: Distributing on One Side<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_Distributing_on_Both_Sides\" class=\"smooth-scroll\">Example: Distributing on Both Sides<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Distributive_Property_Practice_Questions\" class=\"smooth-scroll\">Distributive Property 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>Hello! Welcome to this video about solving equations using the distributive property.<\/p>\n<h2><span id=\"Review_of_the_Distributive_Property\" class=\"m-toc-anchor\"><\/span>Review of the Distributive Property<\/h2>\n<p>\nAs a quick refresher, remember, if you have something like \\(3(5x+9)\\), the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/associative-property\/\">distributive property<\/a> says that you can multiply this first term, the outer term, by every term inside the parentheses.<\/p>\n<p>So, if we did this we would get:<\/p>\n<div class=\"examplesentence\">\\(3\\times 5x+3\\times 9\\)<br \/>\n\\(15x+27\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Example_Distributing_on_One_Side\" class=\"m-toc-anchor\"><\/span>Example: Distributing on One Side<\/h2>\n<p>\nSo, now that we&#8217;ve reviewed that, let&#8217;s use the distributive property to solve some equations. Let&#8217;s take a look at the equation:<\/p>\n<div class=\"examplesentence\">\\(2(3x-7)+x=21\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo our first step is to simplify the distributive part. The 2 right here is going to be distributed to the \\(3x\\) and to the \u22127. Notice that it&#8217;s not distributed to this \\(+x\\) over here. That&#8217;s because it&#8217;s not inside the parentheses. You only multiply the number outside by each term inside the parentheses; the rest of the part of the equation stays the same.<\/p>\n<div class=\"examplesentence\">\\(6x-14+x=21\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Combine_Like_Terms_and_Solve\" class=\"m-toc-anchor\"><\/span>Combine Like Terms and Solve<\/h3>\n<p>\nSo now we can combine like terms on the left side. So \\(6x\\) and \\(x\\) are like terms.<\/p>\n<div class=\"examplesentence\">\\(7x-14=21\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we can solve this just like a normal <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/solving-two-step-equations\/\">two-step equation<\/a>. We&#8217;ll start by adding 14 to both sides.<\/p>\n<div class=\"examplesentence\">\\(7x-14+14=21+14\\)<br \/>\n\\(7x=35\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd then all we have to do is divide by 7 on both sides.<\/p>\n<div class=\"examplesentence\">\\(\\dfrac{7x}{7}=\\dfrac{35}{7}\\)<br \/>\n\\(x=5\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd that\u2019s our answer! <\/p>\n<h2><span id=\"Example_Distributing_on_Both_Sides\" class=\"m-toc-anchor\"><\/span>Example: Distributing on Both Sides<\/h2>\n<p>\nLet&#8217;s look at another problem.<\/p>\n<div class=\"examplesentence\">\\(5(2x+6)=-2(3x+9)\\)<\/div>\n<p>\n&nbsp;<br \/>\nFor this one, we have to apply the distributive property to both sides of the equation, so we&#8217;re going to start by doing the left side.<\/p>\n<div class=\"examplesentence\">\\(10x+30=-2(3x+9)\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, our equal sign stays the same and we&#8217;re going to apply the distributive property to the right side of the equation.<\/p>\n<div class=\"examplesentence\">\\(10x+30=-6x-18\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Move_Variables_to_One_Side_and_Solve\" class=\"m-toc-anchor\"><\/span>Move Variables to One Side and Solve<\/h3>\n<p>\nNow we can <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/solving-equations-with-variables-on-both-sides\/\">solve it<\/a> like a regular equation. So, we&#8217;re going to start by adding \\(6x\\) to both sides.<\/p>\n<div class=\"examplesentence\">\\(10x+6x+30=-6x+6x-18\\)<\/div>\n<p>\n&nbsp;<br \/>\nRemember, we want to get all of our \\(x\\)-terms on one side, and all of our constants on the other side. However you do this is fine; if you wanted to subtract \\(10x\\) from both sides and get the \\(x\\)&#8217;s on the right side instead of the left side, that&#8217;s totally fine, it would work as well. This is the way I&#8217;m going to work it out though; we&#8217;re going to get the \\(x\\)&#8217;s on the left side and the constants on the right side.<\/p>\n<div class=\"examplesentence\">\\(16x+30=-18\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, we&#8217;re going to subtract 30 from both sides, to move this over to the right side of the equation.<\/p>\n<div class=\"examplesentence\">\\(16x+30-30=-18-30\\)<br \/>\n\\(16x=-48\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd finally, we divide by 16 on both sides.<\/p>\n<div class=\"examplesentence\">\\(\\dfrac{16x}{16}=\\dfrac{-48}{16}\\)<br \/>\n\\(x=-3\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd that\u2019s our answer! <\/p>\n<p>I hope that this video was helpful. Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Distributive_Property_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Distributive Property 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 the following equation:<\/p>\n<div class=\"yellow-math-quote\">\\(3(2x+4)-5=4x-9\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(x=8\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">\\(x=-8\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\(x=5\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(x=-5\\)<\/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>Using the distributive property, distribute 3 on the left side of the equation.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(3(2x+4)-5=4x-9\\)<br \/>\n\\(6x+12-5=4x-9\\)<\/p>\n<p>Now, combine like terms on the left side of the equation.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(6x+12-5=4x-9\\)<br \/>\n\\(6x+7=4x-9\\)<\/p>\n<p>To get the variable terms on the left side, subtract 4x from both sides of the equation.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(6x+7-4x=4x-9-4x\\)<br \/>\n\\(2x+7=-9\\)<\/p>\n<p>Now, solve the two-step equation for \\(x\\). Subtract 7 from both sides.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(2x+7-7=-9-7\\)<br \/>\n\\(2x=-16\\)<\/p>\n<p>Divide both sides of the equation by 2.<\/p>\n<p style=\"text-align: center; line-height: 55px\">\\(\\dfrac{2x}{2}=\\dfrac{-16}{2}\\)<br \/>\n\\(x=-8\\)<\/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 the following equation:<\/p>\n<div class=\"yellow-math-quote\">\\(-3(2x+6)+4x=3(x+4)\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">\\(x=-6\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(x=6\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(x=2\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(x=-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>Using the distributive property, distribute \u22123 on the left side and 3 on the right side of the equation.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(-3(2x+6)+4x=3(x+4)\\)<br \/>\n\\(-6x-18+4x=3x+12\\)<\/p>\n<p>Now, combine like terms on the left side of the equation.<\/p>\n<p style=\"text-align: center;\">\\(-2x-18=3x+12\\)<\/p>\n<p>To get the variable terms on the left side, subtract \\(3x\\) from both sides of the equation.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(-2x-18-3x=3x+12-3x\\)<br \/>\n\\(-5x-18=12\\)<\/p>\n<p>Now, solve the two-step equation for \\(x\\). Add 18 to both sides.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(-5x-18+18=12+18\\)<br \/>\n\\(-5x=30\\)<\/p>\n<p>Divide both sides of the equation by \u22125.<\/p>\n<p style=\"text-align: center; line-height: 55px\">\\(\\dfrac{-5x}{-5}=\\dfrac{30}{-5}\\)<br \/>\n\\(x=-6\\)<\/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 the following equation:<\/p>\n<div class=\"yellow-math-quote\">\\(-2(x+5)-3=2(3x+1)+2x\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(x=-\\frac{15}{8}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(x=-\\frac{8}{15}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(x=\\frac{2}{3}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">\\(x=-\\frac{3}{2}\\)<\/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>Using the distributive property, distribute \u22122 on the left side and 2 on the right side of the equation.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(-2(x+5)-3=2(3x+1)+2x\\)<br \/>\n\\(-2x-10-3=6x+2+2x\\)<\/p>\n<p>Now, combine like terms on the left side and right side of the equation.<\/p>\n<p style=\"text-align: center;\">\\(-2x-13=8x+2\\)<\/p>\n<p>To get the variable terms on the left side, subtract \\(8x\\) from both sides of the equation.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(-2x-13-8x=8x+2-8x\\)<br \/>\n\\(-10x-13=2\\)<\/p>\n<p>Now, solve the two-step equation for \\(x\\). Add 13 to both sides.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(-10x-13+13=2+13\\)<br \/>\n\\(-10x=15\\)<\/p>\n<p>Divide both sides of the equation by \u221210.<\/p>\n<p style=\"text-align: center; line-height: 55px\">\\(\\dfrac{-10x}{-10}=\\dfrac{15}{-10}\\)<br \/>\n\\(x=-\\dfrac{15}{10}\\)<\/p>\n<p>Reducing our answer by 5 gives the answer in simplest form.<\/p>\n<p style=\"text-align: center;\">\\(x=-\\dfrac{15\\div5}{10\\div5}=-\\dfrac{3}{2}\\)<\/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 \/>\nFour more than twice the sum of a number and 1 equals three times the difference between the number and 2. If \\(x\\) is the number, what is the value of \\(x\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\(x=9\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(x=5\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-3\">\\(x=12\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(x=-12\\)<\/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>The product of two and the sum of the number \\(x\\) and 1 can be written by the algebraic expression \\(2(x+1)\\). Four more than this expression is \\(2(x+1)+4\\). The product of three and the difference of \\(x\\) and 2 can be written by the expression \\(3(x-2)\\). Since the 2 algebraic expressions are the same, we have the following equation:<\/p>\n<p style=\"text-align: center;\">\\(2(x+1)+4=3(x-2)\\)<\/p>\n<p>To find the number, distribute 2 on the left side and 3 on the right side of the equation first.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(2(x+1)+4=3(x-2)\\)<br \/>\n\\(2x+2+4=3x-6\\)<\/p>\n<p>Combine like terms on the left side of the equation.<\/p>\n<p style=\"text-align: center;\">\\(2x+6=3x-6\\)<\/p>\n<p>To get the variable terms on the left side, subtract \\(3x\\) from both sides of the equation.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(2x+6-3x=3x-6-3x\\)<br \/>\n\\(-x+6=-6\\)<\/p>\n<p>Now, solve the two-step equation for \\(x\\). Subtract 6 from both sides.<\/p>\n<p style=\"text-align: center; line-height: 45px\">\\(-x+6-6=-6-6\\)<br \/>\n\\(\\large{\\frac{-x}{-1}}\\normalsize{\\,=\\,}\\large{\\frac{-12}{-1}}\\)<br \/>\n\\(x=12\\)<\/p>\n<p>So, the value of the number is \\(x=12\\).<\/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 \/>\nThe length of a rectangle is 3 more than the product of 2 and the sum of its width and 4. If the perimeter of the rectangle is 76 feet, what is its width?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">18 feet<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">9 feet<\/div><div class=\"PQ\"  id=\"PQ-5-3\">10 feet<\/div><div class=\"PQ\"  id=\"PQ-5-4\">6 feet<\/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>Let \\(x\\) be the width of the rectangle. Since the length of the rectangle is three more than the product of 2 and the sum of its width and 4, we can represent the length by the expression<br \/>\n\\(2(x+4)+3\\).<\/p>\n<p>Now, substitute \\(l=2(x+4)+3\\)\\), \\(w=x\\), and \\(P=76\\) into the equation for the perimeter of a rectangle.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(P=2l+2w\\)<br \/>\n\\(76=2[(2(x+4)+3]+2x\\)<\/p>\n<p>To find the width, distribute the 2 on the right side of the equation. Then, distribute 4.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(76=2[(2(x+4)+3]+2x\\)<br \/>\n\\(76=4(x+4)+2\\cdot3+2x\\)<br \/>\n\\(76=4x+16+6+2x\\)<\/p>\n<p>Combine like terms on the right side of the equation.<\/p>\n<p style=\"text-align: center;\">\\(76=6x+22\\)<\/p>\n<p>Now, solve the two-step equation for \\(x\\). Subtract 22 from both sides.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(76-22=6x+22-22\\)<br \/>\n\\(54=6x\\)<\/p>\n<p>Divide both sides of the equation by 6.<\/p>\n<p style=\"text-align: center; line-height: 50px\">\\(\\dfrac{54}{6}=\\dfrac{6x}{6}\\)<br \/>\n\\(9=x\\)<\/p>\n<p>So, the width is 9 feet.<\/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":22,"featured_media":113918,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-113915","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-practice-question-videos","7":"page_type-video","8":"content_type-practice-questions","9":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/113915","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=113915"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/113915\/revisions"}],"predecessor-version":[{"id":293174,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/113915\/revisions\/293174"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/113918"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=113915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}