{"id":165475,"date":"2024-11-12T10:20:22","date_gmt":"2024-11-12T10:20:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=165475"},"modified":"2024-11-12T10:20:24","modified_gmt":"2024-11-12T10:20:24","slug":"what-is-the-solution-to-the-inequality-2x-3-7","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/12\/what-is-the-solution-to-the-inequality-2x-3-7\/","title":{"rendered":"What is the solution to the inequality |2x + 3| < 7"},"content":{"rendered":"\n

What is the solution to the inequality |2x + 3| < 7? 4 < x < 10 \u20135 < x < 2 x < 4 or x > 10
x < \u20135 or x > 2<\/p>\n\n\n\n

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

We are given the inequality ( |2x + 3| < 7 ) and need to find the solution. Here’s the step-by-step process to solve it:<\/p>\n\n\n\n

Step 1: Understanding the Absolute Value Inequality<\/h3>\n\n\n\n

The absolute value inequality ( |A| < B ) means that the expression inside the absolute value, ( A ), must lie between ( -B ) and ( B ), i.e.,
[
-B < A < B
]
In this case, the expression inside the absolute value is ( 2x + 3 ), and the inequality is ( |2x + 3| < 7 ). Therefore, we can rewrite it as:
[
-7 < 2x + 3 < 7
]<\/p>\n\n\n\n

Step 2: Solving the Compound Inequality<\/h3>\n\n\n\n

Now, we solve the compound inequality ( -7 < 2x + 3 < 7 ).<\/p>\n\n\n\n

    \n
  1. Isolate ( 2x ):<\/strong> Subtract 3 from all parts of the inequality:
    [
    -7 – 3 < 2x < 7 – 3
    ]
    [
    -10 < 2x < 4
    ]<\/li>\n\n\n\n
  2. Solve for ( x ):<\/strong> Divide all parts of the inequality by 2:
    [
    \\frac{-10}{2} < x < \\frac{4}{2}
    ]
    [
    -5 < x < 2
    ]<\/li>\n<\/ol>\n\n\n\n

    Step 3: Conclusion<\/h3>\n\n\n\n

    The solution to the inequality is ( -5 < x < 2 ).<\/p>\n\n\n\n

    Thus, the correct answer is:
    [
    \\boxed{-5 < x < 2}
    ]<\/p>\n\n\n\n

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

    This solution means that for the absolute value expression ( |2x + 3| ) to be less than 7, ( x ) must be a number between ( -5 ) and ( 2 ). If ( x ) is outside this range (i.e., less than ( -5 ) or greater than ( 2 )), the expression ( 2x + 3 ) would exceed 7 or be less than -7, making the absolute value greater than 7. Hence, the valid values for ( x ) are confined to this interval.<\/p>\n","protected":false},"excerpt":{"rendered":"

    What is the solution to the inequality |2x + 3| < 7? 4 < x < 10 \u20135 < x < 2 x < 4 or x > 10x < \u20135 or x > 2 The Correct Answer and Explanation is: We are given the inequality ( |2x + 3| < 7 ) and need […]<\/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-165475","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165475","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=165475"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165475\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=165475"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=165475"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=165475"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}