3(x \u2013 4) = 2(\u20132x + 1)<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve the equation ( 3(x – 4) = 2(-2x + 1) ), let’s break it down step by step:<\/p>\n\n\n\n Distribute the 3 on the left-hand side and the 2 on the right-hand side:<\/p>\n\n\n\n [ Distribute:<\/p>\n\n\n\n [ Simplifying both sides:<\/p>\n\n\n\n [ To get all the terms with ( x ) on one side, add ( 4x ) to both sides:<\/p>\n\n\n\n [ Simplifying:<\/p>\n\n\n\n [ Now, add 12 to both sides to isolate the term with ( x ):<\/p>\n\n\n\n [ Simplifying:<\/p>\n\n\n\n [ Now divide both sides of the equation by 7 to solve for ( x ):<\/p>\n\n\n\n [ Simplifying:<\/p>\n\n\n\n [ The solution to the equation is ( x = 2 ).<\/p>\n\n\n\n The process we used is the method of solving linear equations. We started by applying the distributive property to eliminate parentheses. Next, we collected all terms involving ( x ) on one side of the equation and constants on the other side. Finally, we solved for ( x ) by performing simple arithmetic (addition and division). This method is widely used to solve linear equations, ensuring that the value of ( x ) satisfies both sides of the original equation.<\/p>\n","protected":false},"excerpt":{"rendered":" 3(x \u2013 4) = 2(\u20132x + 1) The Correct Answer and Explanation is : To solve the equation ( 3(x – 4) = 2(-2x + 1) ), let’s break it down step by step: Step 1: Distribute the constants on both sides Distribute the 3 on the left-hand side and the 2 on the right-hand […]<\/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-170590","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170590","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=170590"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170590\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=170590"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=170590"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=170590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Distribute the constants on both sides<\/h3>\n\n\n\n
3(x – 4) = 2(-2x + 1)
]<\/p>\n\n\n\n
3 \\cdot x – 3 \\cdot 4 = 2 \\cdot (-2x) + 2 \\cdot 1
]<\/p>\n\n\n\n
3x – 12 = -4x + 2
]<\/p>\n\n\n\nStep 2: Move all terms with ( x ) to one side<\/h3>\n\n\n\n
3x + 4x – 12 = 2
]<\/p>\n\n\n\n
7x – 12 = 2
]<\/p>\n\n\n\nStep 3: Move the constant term to the other side<\/h3>\n\n\n\n
7x – 12 + 12 = 2 + 12
]<\/p>\n\n\n\n
7x = 14
]<\/p>\n\n\n\nStep 4: Solve for ( x )<\/h3>\n\n\n\n
x = \\frac{14}{7}
]<\/p>\n\n\n\n
x = 2
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n