{"id":228830,"date":"2025-06-07T16:16:22","date_gmt":"2025-06-07T16:16:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228830"},"modified":"2025-06-07T16:16:24","modified_gmt":"2025-06-07T16:16:24","slug":"solve-the-equation-for-a-k-4a-9ab","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/solve-the-equation-for-a-k-4a-9ab\/","title":{"rendered":"solve the equation for a. K =4a +9ab"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><br>solve the equation for a. K =4a +9ab<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><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 class=\"wp-block-paragraph\">K=4a+9ab<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Our goal is to <strong>solve for<\/strong> aaa, which means we want to isolate aaa on one side of the equation.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Given:K=4a+9abK = 4a + 9abK=4a+9ab<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Factor out aaa from the right-hand side:K=a(4+9b)K = a(4 + 9b)K=a(4+9b)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now, divide both sides of the equation by (4+9b)(4 + 9b)(4+9b) to isolate aaa:a=K4+9ba = \\frac{K}{4 + 9b}a=4+9bK\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">a=K4+9b\\boxed{a = \\frac{K}{4 + 9b}}a=4+9bK\u200b\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">To solve an equation for a variable means we want to rearrange the equation so that the target variable stands alone on one side, typically the left side. In this case, we\u2019re solving for aaa in the equation K=4a+9abK = 4a + 9abK=4a+9ab, where KKK and bbb are considered constants or other known values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The first step is to observe how aaa appears in the expression. Notice that both terms on the right-hand side\u20144a4a4a and 9ab9ab9ab\u2014include aaa as a common factor. This suggests we can <strong>factor out<\/strong> aaa. Factoring is a useful algebraic technique where we express a common term (in this case, aaa) outside a set of parentheses. So:K=4a+9ab\u21d2K=a(4+9b)K = 4a + 9ab \\Rightarrow K = a(4 + 9b)K=4a+9ab\u21d2K=a(4+9b)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now the equation is much simpler. We have aaa multiplied by the expression (4+9b)(4 + 9b)(4+9b). To isolate aaa, we simply divide both sides of the equation by the quantity (4+9b)(4 + 9b)(4+9b). This step uses the <strong>division property of equality<\/strong>, which allows us to divide both sides of an equation by the same non-zero quantity:a=K4+9ba = \\frac{K}{4 + 9b}a=4+9bK\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This form expresses aaa purely in terms of KKK and bbb, which is the desired solution. It\u2019s important to note that 4+9b4 + 9b4+9b must not be equal to zero, since division by zero is undefined. Therefore, the solution is valid for all b\u2260\u221249b \\neq -\\frac{4}{9}b\ue020=\u221294\u200b.<\/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-banner4-632.jpeg\" alt=\"\" class=\"wp-image-228831\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>solve the equation for a. K =4a +9ab The Correct Answer and Explanation is: K=4a+9ab Our goal is to solve for aaa, which means we want to isolate aaa on one side of the equation. Step-by-step Solution Given:K=4a+9abK = 4a + 9abK=4a+9ab Factor out aaa from the right-hand side:K=a(4+9b)K = a(4 + 9b)K=a(4+9b) Now, divide [&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-228830","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228830","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=228830"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228830\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228830"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228830"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228830"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}