{"id":165975,"date":"2024-11-13T07:51:36","date_gmt":"2024-11-13T07:51:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=165975"},"modified":"2024-11-13T07:51:39","modified_gmt":"2024-11-13T07:51:39","slug":"2x-1-2x-1-how-many-solutions","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/13\/2x-1-2x-1-how-many-solutions\/","title":{"rendered":"2x + 1 = 2x – 1 how many solutions"},"content":{"rendered":"\n

2x + 1 = 2x – 1 how many solutions?<\/p>\n\n\n\n

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

To solve the equation ( 2x + 1 = 2x – 1 ), let\u2019s try to isolate ( x ) by simplifying both sides.<\/p>\n\n\n\n

    \n
  1. Subtract ( 2x ) from both sides: [
    2x + 1 – 2x = 2x – 1 – 2x
    ] This simplifies to: [
    1 = -1
    ]<\/li>\n\n\n\n
  2. We end up with the statement ( 1 = -1 ), which is a contradiction. This statement is false and has no possible solutions.<\/li>\n<\/ol>\n\n\n\n

    Explanation<\/h3>\n\n\n\n

    An equation with no solutions is called an inconsistent equation<\/strong>. In this case, after simplifying the equation, we encountered a contradictory statement, ( 1 = -1 ). Since no value of ( x ) will ever make ( 1 = -1 ) true, there is no possible solution for ( x ).<\/p>\n\n\n\n

    When solving equations, if the variable terms cancel each other out, you may be left with one of two cases:<\/p>\n\n\n\n

      \n
    • True statement (identity):<\/strong> If the remaining equation is always true (like ( 0 = 0 )), the original equation has infinitely many solutions<\/strong> because it holds for all values of the variable.<\/li>\n\n\n\n
    • False statement (contradiction):<\/strong> If the remaining equation is always false (like ( 1 = -1 )), the original equation has no solutions<\/strong> because no value of the variable will satisfy it.<\/li>\n<\/ul>\n\n\n\n

      In this case, ( 2x + 1 = 2x – 1 ) simplifies to a contradiction. Hence, the equation has no solutions<\/strong>.<\/p>\n\n\n\n

      In summary, this equation is inconsistent and has no solutions because, after isolating the variable terms, we are left with a false statement that cannot be satisfied by any value of ( x ).<\/p>\n","protected":false},"excerpt":{"rendered":"

      2x + 1 = 2x – 1 how many solutions? The Correct Answer and Explanation is: To solve the equation ( 2x + 1 = 2x – 1 ), let\u2019s try to isolate ( x ) by simplifying both sides. Explanation An equation with no solutions is called an inconsistent equation. In this case, after […]<\/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-165975","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165975","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=165975"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165975\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=165975"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=165975"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=165975"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}