{"id":262774,"date":"2025-07-20T18:59:22","date_gmt":"2025-07-20T18:59:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=262774"},"modified":"2025-07-20T18:59:24","modified_gmt":"2025-07-20T18:59:24","slug":"given-the-equation-5-x-12-2x-7","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/20\/given-the-equation-5-x-12-2x-7\/","title":{"rendered":"Given the equation 5 + x -12 = 2x – 7."},"content":{"rendered":"\n

Given the equation 5 + x -12 = 2x – 7. Part A. Solve the equation 5 + x – 12 = 2x – 7. In your final answer, be sure to state the solution and include all of your work. Part B. Use the values x = -0.5,0,1 to prove your solution to the equation 5 + x – 12 = 2x – 7 . In your final answer, include all of your calculations.<\/p>\n\n\n\n

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

Part A: Solve the equation<\/h3>\n\n\n\n

We are given the equation:
5+x\u221212=2x\u221275 + x – 12 = 2x – 75+x\u221212=2x\u22127<\/p>\n\n\n\n

Step 1: Combine like terms on the left-hand side of the equation.
5\u221212+x=2x\u221275 – 12 + x = 2x – 75\u221212+x=2x\u22127
\u22127+x=2x\u22127-7 + x = 2x – 7\u22127+x=2x\u22127<\/p>\n\n\n\n

Step 2: Move the terms involving xxx to one side by subtracting xxx from both sides.
\u22127=x\u22127-7 = x – 7\u22127=x\u22127<\/p>\n\n\n\n

Step 3: To isolate xxx, add 7 to both sides.
0=x0 = x0=x<\/p>\n\n\n\n

Thus, the solution to the equation is:
x=0x = 0x=0<\/p>\n\n\n\n

Part B: Verify the solution using x=\u22120.5x = -0.5x=\u22120.5, x=0x = 0x=0, and x=1x = 1x=1<\/h3>\n\n\n\n

1. Test x=\u22120.5x = -0.5x=\u22120.5:<\/h4>\n\n\n\n

Substitute x=\u22120.5x = -0.5x=\u22120.5 into the original equation:
5+(\u22120.5)\u221212=2(\u22120.5)\u221275 + (-0.5) – 12 = 2(-0.5) – 75+(\u22120.5)\u221212=2(\u22120.5)\u22127
Simplify both sides:
5\u22120.5\u221212=\u22121\u221275 – 0.5 – 12 = -1 – 75\u22120.5\u221212=\u22121\u22127
\u22127.5=\u22128-7.5 = -8\u22127.5=\u22128<\/p>\n\n\n\n

Since \u22127.5\u2260\u22128-7.5 \\neq -8\u22127.5\ue020=\u22128, x=\u22120.5x = -0.5x=\u22120.5 is not<\/strong> a solution.<\/p>\n\n\n\n

2. Test x=0x = 0x=0:<\/h4>\n\n\n\n

Substitute x=0x = 0x=0 into the original equation:
5+0\u221212=2(0)\u221275 + 0 – 12 = 2(0) – 75+0\u221212=2(0)\u22127
Simplify both sides:
5\u221212=0\u221275 – 12 = 0 – 75\u221212=0\u22127
\u22127=\u22127-7 = -7\u22127=\u22127<\/p>\n\n\n\n

Since both sides are equal, x=0x = 0x=0 is a solution<\/strong>.<\/p>\n\n\n\n

3. Test x=1x = 1x=1:<\/h4>\n\n\n\n

Substitute x=1x = 1x=1 into the original equation:
5+1\u221212=2(1)\u221275 + 1 – 12 = 2(1) – 75+1\u221212=2(1)\u22127
Simplify both sides:
6\u221212=2\u221276 – 12 = 2 – 76\u221212=2\u22127
\u22126=\u22125-6 = -5\u22126=\u22125<\/p>\n\n\n\n

Since \u22126\u2260\u22125-6 \\neq -5\u22126\ue020=\u22125, x=1x = 1x=1 is not<\/strong> a solution.<\/p>\n\n\n\n

Conclusion:<\/h3>\n\n\n\n

The solution to the equation is x=0x = 0x=0. The only value that satisfies the equation is x=0x = 0x=0, as shown by the verification steps.<\/p>\n\n\n\n

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

Given the equation 5 + x -12 = 2x – 7. Part A. Solve the equation 5 + x – 12 = 2x – 7. In your final answer, be sure to state the solution and include all of your work. Part B. Use the values x = -0.5,0,1 to prove your solution to the […]<\/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-262774","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262774","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=262774"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262774\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=262774"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=262774"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=262774"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}