{"id":226037,"date":"2025-06-04T20:14:14","date_gmt":"2025-06-04T20:14:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226037"},"modified":"2025-06-04T20:14:16","modified_gmt":"2025-06-04T20:14:16","slug":"which-graph-shows-the-solution-set-for","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/which-graph-shows-the-solution-set-for\/","title":{"rendered":"Which graph shows the solution set for"},"content":{"rendered":"\n

Which graph shows the solution set for
?<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

We are given the inequality:<\/p>\n\n\n\n

2x + 3 > -9<\/strong><\/p>\n\n\n\n

Let\u2019s solve it step by step:<\/p>\n\n\n\n

Step 1: Subtract 3 from both sides:<\/h3>\n\n\n\n

2x+3\u22123>\u22129\u221232x>\u2212122x + 3 – 3 > -9 – 3 \\\\ 2x > -12<\/p>\n\n\n\n

Step 2: Divide both sides by 2:<\/h3>\n\n\n\n

x>\u22126x > -6<\/p>\n\n\n\n

So, the solution set is all real numbers greater than -6<\/strong>, which we write as: x>\u22126x > -6<\/p>\n\n\n\n

Step 3: Graph interpretation<\/h3>\n\n\n\n

We are looking for a number line graph that:<\/p>\n\n\n\n

    \n
  • Has an open circle<\/strong> at -6<\/strong> (because the inequality is strict<\/strong>, not \u2265<\/strong>).<\/li>\n\n\n\n
  • Has a ray pointing to the right<\/strong>, indicating all numbers greater than -6.<\/li>\n<\/ul>\n\n\n\n

    Analysis of the given graphs:<\/h3>\n\n\n\n
      \n
    • Option A<\/strong>: Open circle at -6, arrow pointing left<\/strong> \u2192 Incorrect (this represents x<\u22126x < -6)<\/li>\n\n\n\n
    • Option B<\/strong>: Closed<\/strong> circle at -6, arrow right \u2192 Incorrect (represents x\u2265\u22126x \\geq -6)<\/li>\n\n\n\n
    • Option C<\/strong>: Open<\/strong> circle at -6, arrow right \u2192 Correct<\/strong> (represents x>\u22126x > -6)<\/li>\n\n\n\n
    • Option D<\/strong>: Closed<\/strong> circle at -6, arrow right \u2192 Again, represents x\u2265\u22126x \\geq -6 \u2192 Incorrect<\/li>\n<\/ul>\n\n\n\n

      \u2705 Correct answer: Option C<\/strong><\/h3>\n\n\n\n

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

      The inequality given is 2x+3>\u221292x + 3 > -9. To solve this, we isolate the variable xx. First, subtract 3 from both sides to get 2x>\u2212122x > -12. Then divide both sides by 2, resulting in x>\u22126x > -6. This means that the solution includes all numbers greater than -6 but not<\/strong> -6 itself.<\/p>\n\n\n\n

      In graphing inequalities on a number line, an open circle<\/strong> represents values not included<\/strong> in the solution (for strict inequalities like > or <), while a closed circle<\/strong> represents values included<\/strong> (for \u2265 or \u2264). Since -6 is not part of the solution, we must use an open circle<\/strong> at -6. Additionally, since the inequality is \u201cgreater than,\u201d we shade or draw an arrow to the right<\/strong> of -6, representing all values larger than -6.<\/p>\n\n\n\n

      Only Option C<\/strong> meets both of these criteria: an open circle at -6 and a ray extending to the right. The other options either point the wrong way or include -6, which changes the meaning of the inequality. Therefore, Option C<\/strong> is the correct graphical representation of the solution set to the inequality 2x+3>\u221292x + 3 > -9.<\/p>\n\n\n\n

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

      Which graph shows the solution set for? The Correct Answer and Explanation is: We are given the inequality: 2x + 3 > -9 Let\u2019s solve it step by step: Step 1: Subtract 3 from both sides: 2x+3\u22123>\u22129\u221232x>\u2212122x + 3 – 3 > -9 – 3 \\\\ 2x > -12 Step 2: Divide both sides by […]<\/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-226037","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226037","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=226037"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226037\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226037"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226037"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226037"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}