{"id":280745,"date":"2025-08-05T05:25:10","date_gmt":"2025-08-05T05:25:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=280745"},"modified":"2025-08-05T05:25:13","modified_gmt":"2025-08-05T05:25:13","slug":"jackson-is-building-a-small-rectangular-basketball-section-in-his-backyard","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/05\/jackson-is-building-a-small-rectangular-basketball-section-in-his-backyard\/","title":{"rendered":"\u00a0Jackson is building a small rectangular basketball section in his backyard."},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

Based on the blurry text in the image, the problem is to solve the compound inequality: x + 8 \u2265 9 AND 2x – 1 < 5.<\/p>\n\n\n\n

Correct Answer:<\/strong> 1 \u2264 x < 3<\/p>\n\n\n\n

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

The problem presented is a compound inequality, which consists of two separate inequalities joined by the word “AND”. For a value of x to be a solution, it must satisfy both inequalities simultaneously. The process involves solving each inequality independently and then finding the intersection, or the overlapping portion, of their respective solution sets.<\/p>\n\n\n\n

First, let’s solve the inequality x + 8 \u2265 9. The goal is to isolate the variable x on one side. To achieve this, we can subtract 8 from both sides of the inequality. This operation gives us x + 8 – 8 \u2265 9 – 8, which simplifies to x \u2265 1. This result means that any valid solution for x must be a number that is greater than or equal to 1. In interval notation, this solution set is represented as [1, \u221e).<\/p>\n\n\n\n

Next, we solve the second inequality, 2x – 1 < 5. This is a two step process. First, we need to isolate the term containing x, which is 2x. We do this by adding 1 to both sides of the inequality, resulting in 2x – 1 + 1 < 5 + 1, which simplifies to 2x < 6. The second step is to completely isolate x by dividing both sides by 2. This gives us x < 3. This result tells us that any valid solution for x must also be a number strictly less than 3. In interval notation, this solution set is written as (-\u221e, 3).<\/p>\n\n\n\n

Finally, we must combine these two solutions. Since the inequalities are connected by “AND”, we are looking for the numbers that are both greater than or equal to 1 AND less than 3. Visualizing this on a number line, we find the intersection of the two sets. The final solution is all numbers between 1 and 3, including 1 but not including 3. This is written as the compound inequality 1 \u2264 x < 3.<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: Based on the blurry text in the image, the problem is to solve the compound inequality: x + 8 \u2265 9 AND 2x – 1 < 5. Correct Answer: 1 \u2264 x < 3 Explanation The problem presented is a compound inequality, which consists of two separate inequalities joined by the […]<\/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-280745","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280745","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=280745"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280745\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=280745"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=280745"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=280745"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}