{"id":225816,"date":"2025-06-04T15:56:50","date_gmt":"2025-06-04T15:56:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225816"},"modified":"2025-06-04T15:56:52","modified_gmt":"2025-06-04T15:56:52","slug":"what-is-the-solution-to-three-fourths-a-greater-than-negative-16","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/what-is-the-solution-to-three-fourths-a-greater-than-negative-16\/","title":{"rendered":"What is the solution to Three-fourths a greater-than negative 16"},"content":{"rendered":"\n<p>What is the solution to Three-fourths a greater-than negative 16? a greater-than negative 21 and one-third a less-than negative 21 and one-third a greater-than 21 and one-third a less-than 21 and one-third<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Let&#8217;s break down and solve the inequality:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Given:<\/strong><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Three-fourths <em>a<\/em> &gt; -16<br>This is written as:<br><strong>(3\/4)\u00b7a &gt; -16<\/strong><\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Solve the inequality<\/strong><\/h3>\n\n\n\n<p>To isolate <strong>a<\/strong>, multiply both sides of the inequality by the <strong>reciprocal<\/strong> of 3\/4, which is <strong>4\/3<\/strong>: a&gt;\u221216\u22c543a &gt; \\frac{-16 \\cdot 4}{3} a&gt;\u2212643a &gt; \\frac{-64}{3}<\/p>\n\n\n\n<p>So the solution is:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>a &gt; -64\/3<\/strong><\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Interpret the answer<\/strong><\/h3>\n\n\n\n<p>Now convert <strong>-64\/3<\/strong> into a mixed number: \u221264\u00f73=\u221221&nbsp;remainder&nbsp;1\u21d2\u22122113-64 \\div 3 = -21 \\text{ remainder } 1 \\Rightarrow -21 \\frac{1}{3}<\/p>\n\n\n\n<p>So:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>a &gt; -21\u2153<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p>This means the value of <strong>a<\/strong> must be <strong>greater than -21\u2153<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Choose the correct option<\/strong><\/h3>\n\n\n\n<p>Now evaluate the given choices:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>a > -21\u2153<\/strong> \u2705<\/li>\n\n\n\n<li><strong>a &lt; -21\u2153<\/strong> \u274c<\/li>\n\n\n\n<li><strong>a > 21\u2153<\/strong> \u274c<\/li>\n\n\n\n<li><strong>a &lt; 21\u2153<\/strong> \u274c<\/li>\n<\/ul>\n\n\n\n<p>Only one choice correctly represents the solution.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Final Answer:<\/strong><\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>a &gt; -21 and one-third<\/strong><\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation<\/strong><\/h3>\n\n\n\n<p>To solve the inequality &#8220;Three-fourths a greater than -16&#8221;, we begin by translating this into algebraic form: (3\/4)\u00b7a &gt; -16. The goal is to isolate the variable <strong>a<\/strong> so we can determine which values satisfy the inequality. Since <strong>a<\/strong> is being multiplied by 3\/4, we eliminate this fraction by multiplying both sides by the reciprocal of 3\/4, which is 4\/3. This operation is valid because multiplying both sides of an inequality by a <strong>positive number<\/strong> does not change the direction of the inequality.<\/p>\n\n\n\n<p>So, we multiply both sides by 4\/3:<br>(4\/3) \u00d7 (3\/4)\u00b7a &gt; (4\/3) \u00d7 -16.<br>This simplifies to: a &gt; -64\/3.<\/p>\n\n\n\n<p>The fraction -64\/3 is then converted into a mixed number for easier understanding. Dividing 64 by 3 gives 21 with a remainder of 1, so -64\/3 is equal to -21 and 1\/3 (or -21\u2153). Therefore, the final solution is <strong>a &gt; -21\u2153<\/strong>.<\/p>\n\n\n\n<p>We then examine the multiple-choice options to find which one correctly matches our solution. The only option that expresses <strong>a greater than -21\u2153<\/strong> is <strong>a &gt; -21 and one-third<\/strong>. All other options either incorrectly reverse the inequality sign or point to positive values of 21\u2153, which are irrelevant to the actual solution.<\/p>\n\n\n\n<p>Thus, the correct answer is <strong>a > -21 and one-third<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-359.jpeg\" alt=\"\" class=\"wp-image-225817\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>What is the solution to Three-fourths a greater-than negative 16? a greater-than negative 21 and one-third a less-than negative 21 and one-third a greater-than 21 and one-third a less-than 21 and one-third The Correct Answer and Explanation is: Let&#8217;s break down and solve the inequality: Given: Three-fourths a &gt; -16This is written as:(3\/4)\u00b7a &gt; -16 [&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-225816","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225816","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=225816"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225816\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225816"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225816"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225816"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}