{"id":165903,"date":"2024-11-13T04:58:34","date_gmt":"2024-11-13T04:58:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=165903"},"modified":"2024-11-13T04:58:37","modified_gmt":"2024-11-13T04:58:37","slug":"simplify-4x-8x-using-the-properties-of-operations","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/13\/simplify-4x-8x-using-the-properties-of-operations\/","title":{"rendered":"Simplify 4x + 8x using the properties of operations"},"content":{"rendered":"\n<p>Simplify 4x + 8x using the properties of operations.<br>A 4x + 8<br>B 12x\u00b2<br>C 4 + 8x<br>D 12x<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The correct answer is <strong>D: 12x<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To simplify the expression ( 4x + 8x ), we can apply the <strong>properties of operations<\/strong>, particularly the <strong>commutative property of addition<\/strong> and <strong>distributive property<\/strong>.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Commutative Property of Addition<\/strong>: This property states that the order of addition does not change the sum. So, we can rewrite the expression as:<br>[<br>4x + 8x = 8x + 4x<br>]<br>(Although this step is not strictly necessary, it&#8217;s helpful to understand that the terms can be reordered.)<\/li>\n\n\n\n<li><strong>Combining Like Terms<\/strong>: Both ( 4x ) and ( 8x ) are &#8220;like terms,&#8221; meaning they both contain the variable ( x ). To combine them, we add the coefficients (the numbers in front of ( x )) together. The coefficients are 4 and 8. So:<br>[<br>4x + 8x = (4 + 8)x<br>]<br>[<br>4x + 8x = 12x<br>]<br>This shows that the expression simplifies to ( 12x ).<\/li>\n\n\n\n<li><strong>Distributive Property<\/strong>: Another way to approach this is by factoring out the common factor of ( x ) from both terms:<br>[<br>4x + 8x = (4 + 8)x<br>]<br>This simplifies to:<br>[<br>12x<br>]<br>The distributive property states that you can factor out a common factor from terms that have it, and then multiply it by the sum of the remaining terms.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Why the Other Options Are Incorrect:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A: ( 4x + 8 )<\/strong>: This is not correct because it represents adding ( 4x ) to a constant, but the original expression doesn&#8217;t have a constant term like 8; both terms are multiples of ( x ).<\/li>\n\n\n\n<li><strong>B: ( 12x^2 )<\/strong>: This is incorrect because the terms ( 4x ) and ( 8x ) do not involve squaring the variable. We are simply adding the ( x )-terms, not multiplying them.<\/li>\n\n\n\n<li><strong>C: ( 4 + 8x )<\/strong>: This is not correct because it changes the order of the terms, and the variable ( x ) is not combined in the proper way.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the correct simplified form of ( 4x + 8x ) is <strong>12x<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Simplify 4x + 8x using the properties of operations.A 4x + 8B 12x\u00b2C 4 + 8xD 12x The Correct Answer and Explanation is : The correct answer is D: 12x. Explanation: To simplify the expression ( 4x + 8x ), we can apply the properties of operations, particularly the commutative property of addition and distributive [&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-165903","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165903","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=165903"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165903\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=165903"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=165903"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=165903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}