To solve the equation:12(4x\u22128)+3x=36\\frac{1}{2}(4x – 8) + 3x = 3621\u200b(4x\u22128)+3x=36<\/p>\n\n\n\n
Step 1: Distribute the 12\\frac{1}{2}21\u200b<\/h3>\n\n\n\n
Apply the distributive property to the expression inside the parentheses:12\u22c54x=2xand12\u22c5(\u22128)=\u22124\\frac{1}{2} \\cdot 4x = 2x \\quad \\text{and} \\quad \\frac{1}{2} \\cdot (-8) = -421\u200b\u22c54x=2xand21\u200b\u22c5(\u22128)=\u22124<\/p>\n\n\n\n
So the equation becomes:2x\u22124+3x=362x – 4 + 3x = 362x\u22124+3x=36<\/p>\n\n\n\n
Step 2: Combine like terms<\/h3>\n\n\n\n
Now combine the terms with xxx:(2x+3x)\u22124=36\u21d25x\u22124=36(2x + 3x) – 4 = 36 \\Rightarrow 5x – 4 = 36(2x+3x)\u22124=36\u21d25x\u22124=36<\/p>\n\n\n\n
Step 3: Solve for xxx<\/h3>\n\n\n\n
Add 4 to both sides:5x\u22124+4=36+4\u21d25x=405x – 4 + 4 = 36 + 4 \\Rightarrow 5x = 405x\u22124+4=36+4\u21d25x=40<\/p>\n\n\n\n
Now divide both sides by 5:x=405=8x = \\frac{40}{5} = 8x=540\u200b=8<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
8\\boxed{8}8\u200b<\/p>\n\n\n\n
\n\n\n\n
Explanation <\/h3>\n\n\n\n
This problem involves solving a linear equation with one variable. The original equation contains a fraction and parentheses, indicating that the distributive property must be applied. The goal is to isolate the variable xxx and determine its value.<\/p>\n\n\n\n
The first step is to simplify the expression 12(4x\u22128)\\frac{1}{2}(4x – 8)21\u200b(4x\u22128) by distributing the 12\\frac{1}{2}21\u200b across both terms inside the parentheses. Multiplying 12\\frac{1}{2}21\u200b by 4x4x4x results in 2x2x2x, and multiplying 12\\frac{1}{2}21\u200b by \u22128-8\u22128 gives \u22124-4\u22124. The expression now reads:2x\u22124+3x=362x – 4 + 3x = 362x\u22124+3x=36<\/p>\n\n\n\n
Next, like terms are combined. The terms 2x2x2x and 3x3x3x are both coefficients of xxx, and they add up to 5x5x5x. The equation is now simplified to:5x\u22124=365x – 4 = 365x\u22124=36<\/p>\n\n\n\n
The next step is to isolate the variable term. This involves eliminating the constant term on the left-hand side by adding 4 to both sides of the equation, yielding:5x=405x = 405x=40<\/p>\n\n\n\n
Finally, divide both sides of the equation by 5 to solve for xxx, resulting in:x=8x = 8x=8<\/p>\n\n\n\n
This value of xxx satisfies the original equation, as substituting it back in would yield a true statement. This step-by-step method emphasizes the importance of applying algebraic operations consistently and logically to arrive at a correct solution.<\/p>\n\n\n\n Enter the value for X that makes the equation 1\/2 (4x-8) + 3x = 36 true The Correct Answer and Explanation is: To solve the equation:12(4x\u22128)+3x=36\\frac{1}{2}(4x – 8) + 3x = 3621\u200b(4x\u22128)+3x=36 Step 1: Distribute the 12\\frac{1}{2}21\u200b Apply the distributive property to the expression inside the parentheses:12\u22c54x=2xand12\u22c5(\u22128)=\u22124\\frac{1}{2} \\cdot 4x = 2x \\quad \\text{and} \\quad \\frac{1}{2} […]<\/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-232349","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232349","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=232349"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232349\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232349"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232349"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232349"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner9-264.jpeg\")
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