{"id":254412,"date":"2025-07-12T13:29:29","date_gmt":"2025-07-12T13:29:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=254412"},"modified":"2025-07-12T13:29:31","modified_gmt":"2025-07-12T13:29:31","slug":"is-dashed-or-solid","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/12\/is-dashed-or-solid\/","title":{"rendered":"Is dashed or solid"},"content":{"rendered":"\n

is dashed or solid? C) Which of the following is the feasible region? i) the upper left ii) the upper right iii) the lower right iv) the lower left
Consider the inequality: 3X + 7Y > 21 A) List the Intercepts of the border line B) Write whether the border line is dashed or solid? C) Which of the following is the feasible region? i) the upper left ii) the upper right iii) the lower right iv) the lower left<\/p>\n\n\n\n

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

To solve this inequality problem, we need to go step by step:<\/p>\n\n\n\n

A) List the intercepts of the border line<\/h3>\n\n\n\n

The inequality is:
3X + 7Y > 21<\/strong><\/p>\n\n\n\n

To find the intercepts, first rewrite the inequality as an equation:
3X + 7Y = 21<\/strong><\/p>\n\n\n\n

    \n
  1. X-Intercept:<\/strong> Set Y = 0<\/strong> and solve for X<\/strong>. 3X+7(0)=21\u2005\u200a\u27f9\u2005\u200a3X=21\u2005\u200a\u27f9\u2005\u200aX=73X + 7(0) = 21 \\implies 3X = 21 \\implies X = 73X+7(0)=21\u27f93X=21\u27f9X=7 So, the X-intercept<\/strong> is (7, 0)<\/strong>.<\/li>\n\n\n\n
  2. Y-Intercept:<\/strong> Set X = 0<\/strong> and solve for Y<\/strong>. 3(0)+7Y=21\u2005\u200a\u27f9\u2005\u200a7Y=21\u2005\u200a\u27f9\u2005\u200aY=33(0) + 7Y = 21 \\implies 7Y = 21 \\implies Y = 33(0)+7Y=21\u27f97Y=21\u27f9Y=3 So, the Y-intercept<\/strong> is (0, 3)<\/strong>.<\/li>\n<\/ol>\n\n\n\n

    B) Dashed or Solid Line?<\/h3>\n\n\n\n

    Since the inequality is 3X + 7Y > 21<\/strong>, the boundary line should be dashed<\/strong>. This is because the inequality is strict (i.e., “>” instead of “\u2265”). A dashed line indicates that the points on the line are not included<\/strong> in the solution set.<\/p>\n\n\n\n

    C) Feasible Region<\/h3>\n\n\n\n

    To determine the feasible region, we need to look at which side of the boundary line satisfies the inequality.<\/p>\n\n\n\n

      \n
    1. Start by testing a point not on the line, like (0, 0)<\/strong> (the origin).
      Substitute X = 0<\/strong> and Y = 0<\/strong> into the inequality: 3(0)+7(0)>21\u2005\u200a\u27f9\u2005\u200a0>213(0) + 7(0) > 21 \\implies 0 > 213(0)+7(0)>21\u27f90>21 This is false<\/strong>, so the origin is not<\/strong> in the feasible region. The feasible region must lie on the opposite side of the line.<\/li>\n\n\n\n
    2. The boundary line 3X + 7Y = 21<\/strong> divides the plane into two half-planes. The feasible region is where the inequality 3X + 7Y > 21<\/strong> holds, which is above<\/strong> the boundary line (since the origin is not a solution, the solution lies above the line).<\/li>\n<\/ol>\n\n\n\n

      Conclusion<\/h3>\n\n\n\n
        \n
      • A)<\/strong> The intercepts of the border line are (7, 0)<\/strong> and (0, 3)<\/strong>.<\/li>\n\n\n\n
      • B)<\/strong> The border line is dashed<\/strong> because the inequality is strict.<\/li>\n\n\n\n
      • C)<\/strong> The feasible region is in the upper right<\/strong> portion of the graph, meaning ii) the upper right<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        This process shows how to identify intercepts, determine the nature of the boundary line, and find the feasible region based on the inequality.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        is dashed or solid? C) Which of the following is the feasible region? i) the upper left ii) the upper right iii) the lower right iv) the lower leftConsider the inequality: 3X + 7Y > 21 A) List the Intercepts of the border line B) Write whether the border line is dashed or solid? C) […]<\/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-254412","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/254412","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=254412"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/254412\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=254412"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=254412"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=254412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}