Which of the following are solutions to |x-1|= 5x + 2? Check all that apply.
A: x=3\/4
B: x=3\/4, 1\/6
C: x= -1\/6
D: x= 1\/6<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve the absolute value equation ( |x-1| = 5x + 2 ), we must first recall that an absolute value equation can lead to two possible cases, depending on whether the expression inside the absolute value is positive or negative. Therefore, we need to consider both:<\/p>\n\n\n\n For this case, the absolute value function ( |x-1| ) is simply ( x – 1 ). So, we set up the equation as: For this case, the absolute value function ( |x-1| ) is ( -(x – 1) ), or ( 1 – x ). The equation becomes: We now check which of the provided options are correct:<\/p>\n\n\n\n The correct solution is Option C: x = -\\frac{1}{6}<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Which of the following are solutions to |x-1|= 5x + 2? Check all that apply.A: x=3\/4B: x=3\/4, 1\/6C: x= -1\/6D: x= 1\/6 The Correct Answer and Explanation is: To solve the absolute value equation ( |x-1| = 5x + 2 ), we must first recall that an absolute value equation can lead to two possible […]<\/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-167422","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167422","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=167422"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167422\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167422"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167422"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167422"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Solve for Case 1 (When ( x-1 \\geq 0 ))<\/h3>\n\n\n\n
[
x – 1 = 5x + 2
]
Now, solve for ( x ):
[
x – 1 = 5x + 2 \\quad \\Rightarrow \\quad x – 5x = 2 + 1 \\quad \\Rightarrow \\quad -4x = 3 \\quad \\Rightarrow \\quad x = -\\frac{3}{4}
]
However, this solution must satisfy the condition ( x – 1 \\geq 0 ), meaning ( x \\geq 1 ). The solution ( x = -\\frac{3}{4} ) does not meet this condition, so it is not valid<\/strong>.<\/p>\n\n\n\nStep 2: Solve for Case 2 (When ( x-1 < 0 ))<\/h3>\n\n\n\n
[
1 – x = 5x + 2
]
Now, solve for ( x ):
[
1 – x = 5x + 2 \\quad \\Rightarrow \\quad 1 – 2 = 5x + x \\quad \\Rightarrow \\quad -1 = 6x \\quad \\Rightarrow \\quad x = -\\frac{1}{6}
]
This solution does satisfy the condition ( x – 1 < 0 ) (since ( -\\frac{1}{6} – 1 = -\\frac{7}{6} ), which is indeed less than 0). Therefore, ( x = -\\frac{1}{6} ) is a valid solution<\/strong>.<\/p>\n\n\n\nStep 3: Check the Provided Options<\/h3>\n\n\n\n
\n
Correct Answer:<\/h3>\n\n\n\n