{"id":150183,"date":"2024-10-08T14:01:01","date_gmt":"2024-10-08T14:01:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=150183"},"modified":"2024-10-08T14:01:07","modified_gmt":"2024-10-08T14:01:07","slug":"solve-negative-two-thirds-n-less-than-or-equal-to-16","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/08\/solve-negative-two-thirds-n-less-than-or-equal-to-16\/","title":{"rendered":"Solve Negative two-thirds n less-than-or-equal-to 16"},"content":{"rendered":"\n<p>Solve Negative two-thirds n less-than-or-equal-to 16. Which of the following must be true about the inequality and the resulting graph? Select three options. n less-than-or-equal-to negative 24 n greater-than-or-equal-to negative 24 The circle is open. The circle is closed. The arrow points right.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The given inequality is:<br>[<br>-\\frac{2}{3}n \\leq 16<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Solve the inequality<\/h3>\n\n\n\n<p>To solve this inequality, the goal is to isolate (n). First, we eliminate the fraction by multiplying both sides of the inequality by (-\\frac{3}{2}) (the reciprocal of (-\\frac{2}{3})). However, since we are multiplying by a negative number, we need to <strong>flip the inequality<\/strong>.<\/p>\n\n\n\n<p>[<br>n \\geq 16 \\times \\left(-\\frac{3}{2}\\right)<br>]<br>[<br>n \\geq -24<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Interpret the solution<\/h3>\n\n\n\n<p>The solution to the inequality is:<br>[<br>n \\geq -24<br>]<\/p>\n\n\n\n<p>This means that (n) can be any number greater than or equal to (-24).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Analyze the options<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>n less-than-or-equal-to negative 24<\/strong>: This option is incorrect because the inequality we derived shows that (n) is <strong>greater than or equal to<\/strong> (-24), not less than.<\/li>\n\n\n\n<li><strong>n greater-than-or-equal-to negative 24<\/strong>: This is correct based on the solution.<\/li>\n\n\n\n<li><strong>The circle is open<\/strong>: This option is incorrect. Since the inequality includes (n \\geq -24), the circle on the graph would be <strong>closed<\/strong>, indicating that (-24) is included in the solution.<\/li>\n\n\n\n<li><strong>The circle is closed<\/strong>: This is correct because (-24) is part of the solution, and the graph should have a closed circle at (-24).<\/li>\n\n\n\n<li><strong>The arrow points right<\/strong>: This is correct because the inequality is (n \\geq -24), meaning the values of (n) are greater than or equal to (-24), which is represented by an arrow pointing to the right on a number line.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Correct options:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>n greater-than-or-equal-to negative 24<\/li>\n\n\n\n<li>The circle is closed<\/li>\n\n\n\n<li>The arrow points right<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Solve Negative two-thirds n less-than-or-equal-to 16. Which of the following must be true about the inequality and the resulting graph? Select three options. n less-than-or-equal-to negative 24 n greater-than-or-equal-to negative 24 The circle is open. The circle is closed. The arrow points right. The Correct Answer and Explanation is : The given inequality is:[-\\frac{2}{3}n \\leq [&hellip;]<\/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-150183","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150183","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=150183"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150183\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=150183"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=150183"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=150183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}