{"id":245855,"date":"2025-07-06T13:52:14","date_gmt":"2025-07-06T13:52:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245855"},"modified":"2025-07-06T13:52:22","modified_gmt":"2025-07-06T13:52:22","slug":"solving-graphing-inequalities-solve-each-inequality-and-graph-the-solution","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/solving-graphing-inequalities-solve-each-inequality-and-graph-the-solution\/","title":{"rendered":"Solving & Graphing Inequalities Solve each inequality and graph the solution."},"content":{"rendered":"\n

Solving & Graphing Inequalities Solve each inequality and graph the solution. 1) 9x ? 54 2) x+1<9 3) x-7>8 4) \\frac{x}{3} ? 6 5) 12+x?24 6) 5x < 15 7) \\frac{x}{9} > 4 8) x-2?13<\/p>\n\n\n\n

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

<\/p>\n\n\n\n

Let’s go through each inequality one by one and solve them. After solving, I’ll explain how to graph each solution.<\/p>\n\n\n\n

    \n
  1. 9x \u2264 54<\/strong>\n
      \n
    • Divide both sides by 9:\n
        \n
      • x \u2264 6<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Graph<\/strong>: A solid dot on 6 with a shaded region extending to the left.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • x + 1 < 9<\/strong>\n
          \n
        • Subtract 1 from both sides:\n
            \n
          • x < 8<\/li>\n<\/ul>\n<\/li>\n\n\n\n
          • Graph<\/strong>: An open dot on 8 with a shaded region extending to the left.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
          • x – 7 \u2265 8<\/strong>\n
              \n
            • Add 7 to both sides:\n
                \n
              • x \u2265 15<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • Graph<\/strong>: A solid dot on 15 with a shaded region extending to the right.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • x \/ 3 \u2265 6<\/strong>\n
                  \n
                • Multiply both sides by 3:\n
                    \n
                  • x \u2265 18<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                  • Graph<\/strong>: A solid dot on 18 with a shaded region extending to the right.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                  • 12 + x \u2265 24<\/strong>\n
                      \n
                    • Subtract 12 from both sides:\n
                        \n
                      • x \u2265 12<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                      • Graph<\/strong>: A solid dot on 12 with a shaded region extending to the right.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                      • 5x < 15<\/strong>\n
                          \n
                        • Divide both sides by 5:\n
                            \n
                          • x < 3<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                          • Graph<\/strong>: An open dot on 3 with a shaded region extending to the left.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                          • x \/ 9 > 4<\/strong>\n
                              \n
                            • Multiply both sides by 9:\n
                                \n
                              • x > 36<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                              • Graph<\/strong>: An open dot on 36 with a shaded region extending to the right.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                              • x – 2 \u2264 13<\/strong>\n
                                  \n
                                • Add 2 to both sides:\n
                                    \n
                                  • x \u2264 15<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                  • Graph<\/strong>: A solid dot on 15 with a shaded region extending to the left.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

                                    Explanation of Graphing:<\/h3>\n\n\n\n
                                      \n
                                    • The solid dot<\/strong> indicates that the number is included in the solution (i.e., \u2264 or \u2265).<\/li>\n\n\n\n
                                    • The open dot<\/strong> indicates that the number is not included in the solution (i.e., < or >).<\/li>\n\n\n\n
                                    • The shaded region shows the range of values that satisfy the inequality. It extends to the left for inequalities with “less than” and to the right for inequalities with “greater than.”<\/li>\n<\/ul>\n\n\n\n
                                      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

                                      Solving & Graphing Inequalities Solve each inequality and graph the solution. 1) 9x ? 54 2) x+1<9 3) x-7>8 4) \\frac{x}{3} ? 6 5) 12+x?24 6) 5x < 15 7) \\frac{x}{9} > 4 8) x-2?13 Let’s go through each inequality one by one and solve them. After solving, I’ll explain how to graph each solution. […]<\/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-245855","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245855","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=245855"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245855\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245855"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245855"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245855"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}