{"id":228085,"date":"2025-06-07T02:59:54","date_gmt":"2025-06-07T02:59:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228085"},"modified":"2025-06-07T02:59:57","modified_gmt":"2025-06-07T02:59:57","slug":"solve-for-g-give-an-exact-answer-100-4-0-5g-4g","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/solve-for-g-give-an-exact-answer-100-4-0-5g-4g\/","title":{"rendered":"Solve for g. Give an exact answer. 10(0.4 + 0.5g) = 4g"},"content":{"rendered":"\n<p>Solve for g. Give an exact answer. 10(0.4 + 0.5g) = 4g<\/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>10(0.4+0.5g)=4g<\/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 1: Distribute the 10 on the left side<\/strong><\/h3>\n\n\n\n<p>Apply the distributive property:10\u22c50.4+10\u22c50.5g=4g10 \\cdot 0.4 + 10 \\cdot 0.5g = 4g10\u22c50.4+10\u22c50.5g=4g4+5g=4g4 + 5g = 4g4+5g=4g<\/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 2: Move all terms to one side<\/strong><\/h3>\n\n\n\n<p>Subtract 4g4g4g from both sides to get all ggg terms on one side:4+5g\u22124g=04 + 5g &#8211; 4g = 04+5g\u22124g=04+g=04 + g = 04+g=0<\/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: Solve for ggg<\/strong><\/h3>\n\n\n\n<p>Subtract 4 from both sides:g=\u22124g = -4g=\u22124<\/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<p>g=\u22124\\boxed{g = -4}g=\u22124\u200b<\/p>\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>This problem is a linear equation in one variable. The goal is to isolate the variable ggg and solve for its exact value.<\/p>\n\n\n\n<p>We start by using the <strong>distributive property<\/strong>, which allows us to eliminate parentheses by multiplying the number outside (in this case, 10) with each term inside the parentheses. That turns the left-hand side of the equation into two terms: 10\u00d70.4=410 \\times 0.4 = 410\u00d70.4=4 and 10\u00d70.5g=5g10 \\times 0.5g = 5g10\u00d70.5g=5g. So we simplify the expression to:4+5g=4g4 + 5g = 4g4+5g=4g<\/p>\n\n\n\n<p>Next, we aim to get all terms involving ggg on one side. To do this, subtract 4g4g4g from both sides:4+g=04 + g = 04+g=0<\/p>\n\n\n\n<p>Now, we isolate ggg by subtracting 4 from both sides:g=\u22124g = -4g=\u22124<\/p>\n\n\n\n<p>This is the solution. It&#8217;s important to check your answer to confirm accuracy. Substituting g=\u22124g = -4g=\u22124 back into the original equation:10(0.4+0.5(\u22124))=10(0.4\u22122)=10(\u22121.6)=\u22121610(0.4 + 0.5(-4)) = 10(0.4 &#8211; 2) = 10(-1.6) = -1610(0.4+0.5(\u22124))=10(0.4\u22122)=10(\u22121.6)=\u221216<\/p>\n\n\n\n<p>On the right side:4(\u22124)=\u2212164(-4) = -164(\u22124)=\u221216<\/p>\n\n\n\n<p>Both sides equal \u221216-16\u221216, so our solution g=\u22124g = -4g=\u22124 is correct.<\/p>\n\n\n\n<p>This equation showcases the importance of distributive property and simple algebraic manipulation, which are foundational in solving real-world and mathematical problems involving unknowns.<\/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-banner4-586.jpeg\" alt=\"\" class=\"wp-image-228086\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Solve for g. Give an exact answer. 10(0.4 + 0.5g) = 4g The Correct Answer and Explanation is: 10(0.4+0.5g)=4g Step 1: Distribute the 10 on the left side Apply the distributive property:10\u22c50.4+10\u22c50.5g=4g10 \\cdot 0.4 + 10 \\cdot 0.5g = 4g10\u22c50.4+10\u22c50.5g=4g4+5g=4g4 + 5g = 4g4+5g=4g Step 2: Move all terms to one side Subtract 4g4g4g from [&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-228085","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228085","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=228085"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228085\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}