{"id":257948,"date":"2025-07-17T18:46:46","date_gmt":"2025-07-17T18:46:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=257948"},"modified":"2025-07-17T18:46:52","modified_gmt":"2025-07-17T18:46:52","slug":"6x-4-4-6x-b-4x-6-4x-3-c-2x-4-3x-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/17\/6x-4-4-6x-b-4x-6-4x-3-c-2x-4-3x-4\/","title":{"rendered":"6x – 4 = -4 + 6x b. 4x – 6 = 4x + 3 c. -2x + 4 = -3x + 4"},"content":{"rendered":"\n

a. 6x – 4 = -4 + 6x b. 4x – 6 = 4x + 3 c. -2x + 4 = -3x + 4<\/p>\n\n\n\n

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

Let’s solve each equation step by step:<\/p>\n\n\n\n

a. 6x\u22124=\u22124+6x6x – 4 = -4 + 6x6x\u22124=\u22124+6x<\/h3>\n\n\n\n
    \n
  1. Start by simplifying both sides of the equation. In this case, the terms involving xxx are already on both sides, so we’ll move the terms with xxx to one side.<\/li>\n\n\n\n
  2. Subtract 6x6x6x from both sides: 6x\u22124\u22126x=\u22124+6x\u22126x6x – 4 – 6x = -4 + 6x – 6x6x\u22124\u22126x=\u22124+6x\u22126x This simplifies to: \u22124=\u22124-4 = -4\u22124=\u22124 This is a true statement, which means the equation has infinitely many solutions<\/strong>. This is called an identity<\/strong>.<\/li>\n<\/ol>\n\n\n\n

    b. 4x\u22126=4x+34x – 6 = 4x + 34x\u22126=4x+3<\/h3>\n\n\n\n
      \n
    1. To eliminate xxx from one side, subtract 4x4x4x from both sides: 4x\u22126\u22124x=4x+3\u22124x4x – 6 – 4x = 4x + 3 – 4x4x\u22126\u22124x=4x+3\u22124x This simplifies to: \u22126=3-6 = 3\u22126=3 This is a contradiction<\/strong>. Since the statement is false, the equation has no solution<\/strong>.<\/li>\n<\/ol>\n\n\n\n

      c. \u22122x+4=\u22123x+4-2x + 4 = -3x + 4\u22122x+4=\u22123x+4<\/h3>\n\n\n\n
        \n
      1. Move the terms involving xxx to one side by adding 3x3x3x to both sides: \u22122x+4+3x=\u22123x+4+3x-2x + 4 + 3x = -3x + 4 + 3x\u22122x+4+3x=\u22123x+4+3x Simplifying both sides: x+4=4x + 4 = 4x+4=4<\/li>\n\n\n\n
      2. Subtract 4 from both sides: x+4\u22124=4\u22124x + 4 – 4 = 4 – 4x+4\u22124=4\u22124 This simplifies to: x=0x = 0x=0 So, the solution to the equation is x=0x = 0x=0.<\/li>\n<\/ol>\n\n\n\n

        Summary:<\/h3>\n\n\n\n
          \n
        • Equation (a) has infinitely many solutions<\/strong>.<\/li>\n\n\n\n
        • Equation (b) has no solution<\/strong>.<\/li>\n\n\n\n
        • Equation (c) has the solution x=0x = 0x=0.<\/li>\n<\/ul>\n\n\n\n
          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          a. 6x – 4 = -4 + 6x b. 4x – 6 = 4x + 3 c. -2x + 4 = -3x + 4 The Correct Answer and Explanation is: Let’s solve each equation step by step: a. 6x\u22124=\u22124+6x6x – 4 = -4 + 6x6x\u22124=\u22124+6x b. 4x\u22126=4x+34x – 6 = 4x + 34x\u22126=4x+3 c. \u22122x+4=\u22123x+4-2x […]<\/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-257948","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257948","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=257948"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257948\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=257948"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=257948"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=257948"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}