{"id":235055,"date":"2025-06-14T19:10:29","date_gmt":"2025-06-14T19:10:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235055"},"modified":"2025-06-14T19:10:31","modified_gmt":"2025-06-14T19:10:31","slug":"simplify-the-expression-use-the-distributive-property-to-remove-parentheses-first","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/simplify-the-expression-use-the-distributive-property-to-remove-parentheses-first\/","title":{"rendered":"Simplify the expression: Use the distributive property to remove parentheses first"},"content":{"rendered":"\n<p>Simplify the expression: Use the distributive property to remove parentheses first: 2(3s 1) &#8211; 7(s 11) 2(3s 1) &#8211; 7(s 11) = (Simplify your answer:)<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Simplified Expression:<\/strong><\/p>\n\n\n\n<p>Given:2(3s+1)\u22127(s+11)2(3s + 1) &#8211; 7(s + 11)2(3s+1)\u22127(s+11)<\/p>\n\n\n\n<p><strong>Step 1: Apply the distributive property to each term.<\/strong><\/p>\n\n\n\n<p>Distribute the <strong>2<\/strong> across <strong>(3s + 1)<\/strong>:2\u22c53s=6s,2\u22c51=22 \\cdot 3s = 6s,\\quad 2 \\cdot 1 = 22\u22c53s=6s,2\u22c51=2<\/p>\n\n\n\n<p>So,2(3s+1)=6s+22(3s + 1) = 6s + 22(3s+1)=6s+2<\/p>\n\n\n\n<p>Distribute the <strong>-7<\/strong> across <strong>(s + 11)<\/strong>:\u22127\u22c5s=\u22127s,\u22127\u22c511=\u221277-7 \\cdot s = -7s,\\quad -7 \\cdot 11 = -77\u22127\u22c5s=\u22127s,\u22127\u22c511=\u221277<\/p>\n\n\n\n<p>So,\u22127(s+11)=\u22127s\u221277-7(s + 11) = -7s &#8211; 77\u22127(s+11)=\u22127s\u221277<\/p>\n\n\n\n<p><strong>Step 2: Combine all parts.<\/strong>6s+2\u22127s\u2212776s + 2 &#8211; 7s &#8211; 776s+2\u22127s\u221277<\/p>\n\n\n\n<p><strong>Step 3: Combine like terms.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Combine <strong>6s &#8211; 7s<\/strong> = <strong>-s<\/strong><\/li>\n\n\n\n<li>Combine <strong>2 &#8211; 77<\/strong> = <strong>-75<\/strong><\/li>\n<\/ul>\n\n\n\n<p><strong>Final Answer:<\/strong>\u2212s\u221275-s &#8211; 75\u2212s\u221275<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation <\/strong><\/p>\n\n\n\n<p>To simplify expressions involving parentheses, the distributive property plays a key role. This property states that a number multiplied by a sum (or difference) inside parentheses must be distributed to each term within the parentheses. Begin by identifying the two sets of parentheses: <strong>2(3s + 1)<\/strong> and <strong>-7(s + 11)<\/strong>.<\/p>\n\n\n\n<p>The first part, <strong>2(3s + 1)<\/strong>, involves multiplying 2 by both 3s and 1. Multiplying 2 by 3s results in 6s, and 2 by 1 gives 2. So, the expression becomes <strong>6s + 2<\/strong>.<\/p>\n\n\n\n<p>Next, look at the second part, <strong>-7(s + 11)<\/strong>. Here, the -7 must be distributed to both s and 11. Multiply -7 by s to get -7s, and -7 by 11 to get -77. This results in <strong>-7s &#8211; 77<\/strong>.<\/p>\n\n\n\n<p>Now, substitute these new expressions back into the original expression:<br><strong>6s + 2 &#8211; 7s &#8211; 77<\/strong><\/p>\n\n\n\n<p>To simplify, combine like terms. First, group the terms with the variable <strong>s<\/strong>. Combine <strong>6s<\/strong> and <strong>-7s<\/strong>, which gives <strong>-s<\/strong>. Then, group the constant terms <strong>2<\/strong> and <strong>-77<\/strong>; combining these gives <strong>-75<\/strong>.<\/p>\n\n\n\n<p>Putting the simplified terms together results in the final simplified expression:<br><strong>-s &#8211; 75<\/strong><\/p>\n\n\n\n<p>This expression no longer contains parentheses, and all like terms have been combined correctly, giving a fully simplified form.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-550.jpeg\" alt=\"\" class=\"wp-image-235056\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Simplify the expression: Use the distributive property to remove parentheses first: 2(3s 1) &#8211; 7(s 11) 2(3s 1) &#8211; 7(s 11) = (Simplify your answer:) The Correct Answer and Explanation is: Simplified Expression: Given:2(3s+1)\u22127(s+11)2(3s + 1) &#8211; 7(s + 11)2(3s+1)\u22127(s+11) Step 1: Apply the distributive property to each term. Distribute the 2 across (3s + [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-235055","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235055","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=235055"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235055\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235055"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235055"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235055"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}