{"id":224821,"date":"2025-06-03T13:57:52","date_gmt":"2025-06-03T13:57:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224821"},"modified":"2025-06-03T13:57:54","modified_gmt":"2025-06-03T13:57:54","slug":"3x23x6-3x2xx232-3x23x2-32x-6x-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/3x23x6-3x2xx232-3x23x2-32x-6x-3\/","title":{"rendered":"3(x+2)=3x+6 3x+2x=x^2(3+2) 3x+2=3(x+2) -3(2+x)=-6x-3"},"content":{"rendered":"\n

3(x+2)=3x+6 3x+2x=x^2(3+2) 3x+2=3(x+2) -3(2+x)=-6x-3<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct equation that shows the distributive property<\/strong> is:<\/p>\n\n\n\n

3(x + 2) = 3x + 6<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation<\/h3>\n\n\n\n

The distributive property is a fundamental algebraic rule used to eliminate parentheses in expressions where a number is multiplied by a sum or difference. It states:<\/p>\n\n\n\n

a(b + c) = ab + ac<\/strong><\/p>\n\n\n\n

This means that when a number or variable is placed outside a set of parentheses and multiplied by the sum inside, you multiply the outside number with each term inside individually, then add or subtract the results.<\/p>\n\n\n\n

Let\u2019s apply the distributive property to the correct option:<\/p>\n\n\n\n

3(x + 2)<\/strong><\/p>\n\n\n\n

Using the distributive property:<\/p>\n\n\n\n

    \n
  • Multiply 3 by x \u2192 3x<\/li>\n\n\n\n
  • Multiply 3 by 2 \u2192 6<\/li>\n<\/ul>\n\n\n\n

    So:
    3(x + 2) = 3x + 6<\/strong><\/p>\n\n\n\n

    This matches the right-hand side of the equation in the first option<\/strong>:
    3(x + 2) = 3x + 6<\/strong><\/p>\n\n\n\n

    Let\u2019s quickly examine the other choices:<\/p>\n\n\n\n

      \n
    1. 3x + 2x = x\u00b2(3 + 2)<\/strong>
      This is not using the distributive property. It involves an incorrect assumption about powers and addition.<\/li>\n\n\n\n
    2. 3x + 2 = 3(x + 2)<\/strong>
      While this looks similar, it’s not a demonstration of the distributive property. Instead, it’s an equation you could solve, but not one that results directly from distribution.<\/li>\n\n\n\n
    3. \u20133(2 + x) = \u20136x \u2013 3<\/strong>
      Let\u2019s distribute:
      \u20133(2 + x) = \u20133\u00d72 + (\u20133)\u00d7x = \u20136 \u2013 3x
      This is not<\/strong> equal to \u20136x \u2013 3, so it is incorrect.<\/li>\n<\/ol>\n\n\n\n
      \n\n\n\n

      Summary:<\/h3>\n\n\n\n

      Only the first equation<\/strong> (3(x + 2) = 3x + 6) correctly applies the distributive property. It demonstrates how a number multiplies across a sum inside parentheses to simplify an algebraic expression.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      3(x+2)=3x+6 3x+2x=x^2(3+2) 3x+2=3(x+2) -3(2+x)=-6x-3 The Correct Answer and Explanation is: The correct equation that shows the distributive property is: 3(x + 2) = 3x + 6 Explanation The distributive property is a fundamental algebraic rule used to eliminate parentheses in expressions where a number is multiplied by a sum or difference. It states: a(b + […]<\/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-224821","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224821","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=224821"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224821\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224821"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224821"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224821"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}