{"id":214985,"date":"2025-05-16T06:03:07","date_gmt":"2025-05-16T06:03:07","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=214985"},"modified":"2025-05-17T02:58:18","modified_gmt":"2025-05-17T02:58:18","slug":"select-all-the-equations-that-have-the-same-solution-as-the-equation-3x-1224","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/16\/select-all-the-equations-that-have-the-same-solution-as-the-equation-3x-1224\/","title":{"rendered":"Select all the equation that have the same solution as the equation 3x-12=24"},"content":{"rendered":"\n<p>Select all the equation that have the same solution as the equation 3x-12=24<\/p>\n\n\n\n<p>A: 15 x -60=120<br>b: 3x=12<br>c: 3 x =36<br>d: x-4=8<br>e: 12x -12=24<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine which equations have the <strong>same solution<\/strong> as the equation:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Original Equation:<\/h3>\n\n\n\n<p><strong>3x &#8211; 12 = 24<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Solve the original equation<\/strong><\/h3>\n\n\n\n<p>We\u2019ll solve for <strong>x<\/strong>: 3x\u221212=243x &#8211; 12 = 24<\/p>\n\n\n\n<p>Add 12 to both sides: 3x=363x = 36<\/p>\n\n\n\n<p>Now divide both sides by 3: x=12x = 12<\/p>\n\n\n\n<p>So the solution to the original equation is: x=12x = 12<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Check which other equations also have the solution x = 12<\/strong><\/h3>\n\n\n\n<p>Let\u2019s test each option:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>A. 15x &#8211; 60 = 120<\/strong><\/p>\n\n\n\n<p>Substitute x = 12: 15(12)\u221260=180\u221260=120\u271315(12) &#8211; 60 = 180 &#8211; 60 = 120 \u2713<\/p>\n\n\n\n<p>\u2705 True, so <strong>A is correct<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>B. 3x = 12<\/strong><\/p>\n\n\n\n<p>Substitute x = 12: 3(12)=36\u226012\u27173(12) = 36 \u2260 12 \u2717<\/p>\n\n\n\n<p>\u274c False, so <strong>B is incorrect<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>C. 3x = 36<\/strong><\/p>\n\n\n\n<p>Substitute x = 12: 3(12)=36\u27133(12) = 36 \u2713<\/p>\n\n\n\n<p>\u2705 True, so <strong>C is correct<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>D. x &#8211; 4 = 8<\/strong><\/p>\n\n\n\n<p>Substitute x = 12: 12\u22124=8\u271312 &#8211; 4 = 8 \u2713<\/p>\n\n\n\n<p>\u2705 True, so <strong>D is correct<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>E. 12x &#8211; 12 = 24<\/strong><\/p>\n\n\n\n<p>Substitute x = 12: 12(12)\u221212=144\u221212=132\u226024\u271712(12) &#8211; 12 = 144 &#8211; 12 = 132 \u2260 24 \u2717<\/p>\n\n\n\n<p>\u274c False, so <strong>E is incorrect<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Final Answer: A, C, and D<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\udde0 Explanation (300+ words):<\/h3>\n\n\n\n<p>To find all equations that share the <strong>same solution<\/strong> as a given equation, we begin by solving the original equation for <strong>x<\/strong>. The equation <strong>3x &#8211; 12 = 24<\/strong> is a linear equation, and solving it involves isolating the variable:<\/p>\n\n\n\n<p>First, we add 12 to both sides to eliminate the constant on the left-hand side: 3x\u221212+12=24+12\u21d23x=363x &#8211; 12 + 12 = 24 + 12 \\Rightarrow 3x = 36<\/p>\n\n\n\n<p>Then divide both sides by 3: x=12x = 12<\/p>\n\n\n\n<p>This means that any other equation that is also true when <strong>x = 12<\/strong> has the same solution.<\/p>\n\n\n\n<p>For example, in option <strong>A<\/strong>, the equation is <strong>15x &#8211; 60 = 120<\/strong>. Plugging in x = 12 gives us: 15(12)\u221260=180\u221260=12015(12) &#8211; 60 = 180 &#8211; 60 = 120<\/p>\n\n\n\n<p>Which is true, so A has the same solution.<\/p>\n\n\n\n<p>Option <strong>C<\/strong> is already simplified to <strong>3x = 36<\/strong>, which matches the transformed version of our original equation\u2014clearly, it has the same solution.<\/p>\n\n\n\n<p>Option <strong>D<\/strong> says <strong>x &#8211; 4 = 8<\/strong>, which simplifies to x = 12 when solved. So it also matches.<\/p>\n\n\n\n<p>On the other hand, <strong>option B<\/strong> results in <strong>3x = 12<\/strong>, and solving this gives x = 4\u2014not a match.<\/p>\n\n\n\n<p>Option <strong>E<\/strong> results in <strong>12x &#8211; 12 = 24<\/strong>. Solving this: 12x=36\u21d2x=312x = 36 \\Rightarrow x = 3<\/p>\n\n\n\n<p>Again, not equal to 12.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Select all the equation that have the same solution as the equation 3x-12=24 A: 15 x -60=120b: 3x=12c: 3 x =36d: x-4=8e: 12x -12=24 The Correct Answer and Explanation is: To determine which equations have the same solution as the equation: Original Equation: 3x &#8211; 12 = 24 Step 1: Solve the original equation We\u2019ll [&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-214985","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214985","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=214985"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214985\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=214985"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=214985"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=214985"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}