{"id":230291,"date":"2025-06-09T06:30:57","date_gmt":"2025-06-09T06:30:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230291"},"modified":"2025-06-09T06:30:59","modified_gmt":"2025-06-09T06:30:59","slug":"which-expression-is-equivalent-to-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/09\/which-expression-is-equivalent-to-3\/","title":{"rendered":"Which expression is equivalent to"},"content":{"rendered":"\n<p>Which expression is equivalent to<br>?<\/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\/image-316.png\" alt=\"\" class=\"wp-image-230292\"\/><\/figure>\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>The problem is asking:<\/p>\n\n\n\n<p><strong>Which expression is equivalent to<\/strong>\u221214\u221235d?-14 &#8211; 35d?\u221214\u221235d?<\/p>\n\n\n\n<p>Let\u2019s analyze each answer choice and see which one simplifies to \u221214\u221235d-14 &#8211; 35d\u221214\u221235d.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Factor \u221214\u221235d-14 &#8211; 35d\u221214\u221235d<\/h3>\n\n\n\n<p>We look for a common factor of both terms.<br>\u221214=\u22127\u22c52-14 = -7 \\cdot 2\u221214=\u22127\u22c52<br>\u221235d=\u22127\u22c55d-35d = -7 \\cdot 5d\u221235d=\u22127\u22c55d<\/p>\n\n\n\n<p>So we factor out <strong>-7<\/strong>:\u221214\u221235d=\u22127(2+5d)-14 &#8211; 35d = -7(2 + 5d)\u221214\u221235d=\u22127(2+5d)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Match with the options<\/h3>\n\n\n\n<p>Let\u2019s examine each choice:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>-7(2 + 5d)<\/strong> \u2705<br>This matches our factorization exactly.<\/li>\n\n\n\n<li><strong>7(2 \u2212 5d)<\/strong><br>Distributing gives 14\u221235d14 &#8211; 35d14\u221235d, which is <strong>not<\/strong> the same.<\/li>\n\n\n\n<li><strong>7(\u22122 + 5d)<\/strong><br>Distributing gives \u221214+35d-14 + 35d\u221214+35d, which is also <strong>not<\/strong> correct.<\/li>\n\n\n\n<li><strong>-7(2 \u2212 5d)<\/strong><br>Distributing gives \u221214+35d-14 + 35d\u221214+35d, which is also <strong>not<\/strong> correct.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Correct Answer:<\/h3>\n\n\n\n<p><strong>-7(2 + 5d)<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"> Explanation:<\/h3>\n\n\n\n<p>To find which expression is equivalent to \u221214\u221235d-14 &#8211; 35d\u221214\u221235d, we use factoring. Factoring is a technique that rewrites a mathematical expression as a product of its greatest common factor (GCF) and a remaining expression inside parentheses.<\/p>\n\n\n\n<p>In this case, we look at the terms \u221214-14\u221214 and \u221235d-35d\u221235d. Both numbers have a common factor of \u22127-7\u22127:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u221214=\u22127\u00d72-14 = -7 \\times 2\u221214=\u22127\u00d72<\/li>\n\n\n\n<li>\u221235d=\u22127\u00d75d-35d = -7 \\times 5d\u221235d=\u22127\u00d75d<\/li>\n<\/ul>\n\n\n\n<p>So we can factor \u22127-7\u22127 out of both terms:\u221214\u221235d=\u22127(2+5d)-14 &#8211; 35d = -7(2 + 5d)\u221214\u221235d=\u22127(2+5d)<\/p>\n\n\n\n<p>This tells us that the expression is equivalent to <strong>-7(2 + 5d)<\/strong>.<\/p>\n\n\n\n<p>Let\u2019s check this by distributing:\u22127(2+5d)=\u22127\u22c52+(\u22127\u22c55d)=\u221214\u221235d-7(2 + 5d) = -7 \\cdot 2 + (-7 \\cdot 5d) = -14 &#8211; 35d\u22127(2+5d)=\u22127\u22c52+(\u22127\u22c55d)=\u221214\u221235d<\/p>\n\n\n\n<p>This confirms the factorization is correct.<\/p>\n\n\n\n<p>The other options do not match because when you distribute them, you get different signs or values. For example, 7(2\u22125d)7(2 &#8211; 5d)7(2\u22125d) becomes 14\u221235d14 &#8211; 35d14\u221235d, which is not the same as \u221214\u221235d-14 &#8211; 35d\u221214\u221235d.<\/p>\n\n\n\n<p>In conclusion, factoring helps simplify and understand algebraic expressions by identifying common factors. The correct choice is the one that, when expanded, gives the original expression. Thus, <strong>-7(2 + 5d)<\/strong> is the correct and equivalent expression.<\/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-banner7-372.jpeg\" alt=\"\" class=\"wp-image-230293\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which expression is equivalent to? The Correct Answer and Explanation is: The problem is asking: Which expression is equivalent to\u221214\u221235d?-14 &#8211; 35d?\u221214\u221235d? Let\u2019s analyze each answer choice and see which one simplifies to \u221214\u221235d-14 &#8211; 35d\u221214\u221235d. Step 1: Factor \u221214\u221235d-14 &#8211; 35d\u221214\u221235d We look for a common factor of both terms.\u221214=\u22127\u22c52-14 = -7 \\cdot 2\u221214=\u22127\u22c52\u221235d=\u22127\u22c55d-35d [&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-230291","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230291","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=230291"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230291\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}