{"id":221026,"date":"2025-05-29T06:07:48","date_gmt":"2025-05-29T06:07:48","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=221026"},"modified":"2025-05-29T06:07:51","modified_gmt":"2025-05-29T06:07:51","slug":"solve-each-equation-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/29\/solve-each-equation-2\/","title":{"rendered":"Solve each equation."},"content":{"rendered":"\n

ranscribed image text: ODDS Name: Unit 6: Radical Functions Date: Bell: Homework 6: Radical Equations ** This is a 2-page documents Directions: Solve each equation. Be sure to check for extraneous solutions. 1. 3-24 +17-20 2. 14-11-15-2 3. -7m+1 -14 4. -7+(16p+8)= -1 5. p+88–1 6. 17-2-3x+10 – 1 7. 36-2941-22 8. Gz-21 – 19-2<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

1. 3\u22122x+17=20\\sqrt{3 – 2x + 17} = 20<\/strong><\/h3>\n\n\n\n

Simplify inside the radical:<\/strong> 3\u22122x+17=20\u22122x=20\\sqrt{3 – 2x + 17} = \\sqrt{20 – 2x} = 20<\/p>\n\n\n\n

Square both sides:<\/strong> 20\u22122x=40020 – 2x = 400<\/p>\n\n\n\n

Solve for xx:<\/strong> \u22122x=380\u21d2x=\u2212190-2x = 380 \\Rightarrow x = -190<\/p>\n\n\n\n

Check for extraneous solutions:<\/strong> 3\u22122(\u2212190)+17=3+380+17=400=20\u21d2Valid\\sqrt{3 – 2(-190) + 17} = \\sqrt{3 + 380 + 17} = \\sqrt{400} = 20 \\Rightarrow \\text{Valid}<\/p>\n\n\n\n

\u2705 Final Answer: x=\u2212190\\boxed{x = -190}<\/p>\n\n\n\n

\n\n\n\n

3. \u22127m+1=\u221214-7\\sqrt{m + 1} = -14<\/strong><\/h3>\n\n\n\n

Divide both sides by -7:<\/strong> m+1=2\\sqrt{m + 1} = 2<\/p>\n\n\n\n

Square both sides:<\/strong> m+1=4\u21d2m=3m + 1 = 4 \\Rightarrow m = 3<\/p>\n\n\n\n

Check:<\/strong> \u221273+1=\u221274=\u22127(2)=\u221214\u21d2Valid-7\\sqrt{3 + 1} = -7\\sqrt{4} = -7(2) = -14 \\Rightarrow \\text{Valid}<\/p>\n\n\n\n

\u2705 Final Answer: m=3\\boxed{m = 3}<\/p>\n\n\n\n

\n\n\n\n

5. \u2212716p+83=\u22121-7\\sqrt[3]{16p + 8} = -1<\/strong><\/h3>\n\n\n\n

Divide both sides by -7:<\/strong> 16p+83=17\\sqrt[3]{16p + 8} = \\frac{1}{7}<\/p>\n\n\n\n

Cube both sides:<\/strong> 16p+8=(17)3=134316p + 8 = \\left(\\frac{1}{7}\\right)^3 = \\frac{1}{343}<\/p>\n\n\n\n

Solve for pp:<\/strong> 16p=1343\u22128=1\u22122744343=\u22122743343\u21d2p=\u22122743548816p = \\frac{1}{343} – 8 = \\frac{1 – 2744}{343} = \\frac{-2743}{343} \\Rightarrow p = \\frac{-2743}{5488}<\/p>\n\n\n\n

Check:<\/strong> Plug back into the original to confirm. It\u2019s valid.\\text{Plug back into the original to confirm. It’s valid.}<\/p>\n\n\n\n

\u2705 Final Answer: p=\u221227435488\\boxed{p = \\frac{-2743}{5488}}<\/p>\n\n\n\n

\n\n\n\n

7. 3k\u221229=41\u22122k\\sqrt{3k – 29} = \\sqrt{41 – 2k}<\/strong><\/h3>\n\n\n\n

Square both sides:<\/strong> 3k\u221229=41\u22122k3k – 29 = 41 – 2k<\/p>\n\n\n\n

Solve:<\/strong> 5k=70\u21d2k=145k = 70 \\Rightarrow k = 14<\/p>\n\n\n\n

Check:<\/strong> 3(14)\u221229=42\u221229=13and41\u22122(14)=13\u21d2Valid\\sqrt{3(14) – 29} = \\sqrt{42 – 29} = \\sqrt{13} \\quad \\text{and} \\quad \\sqrt{41 – 2(14)} = \\sqrt{13} \\Rightarrow \\text{Valid}<\/p>\n\n\n\n

\u2705 Final Answer: k=14\\boxed{k = 14}<\/p>\n\n\n\n

\n\n\n\n

Explanation (Summary):<\/h3>\n\n\n\n

To solve radical equations, isolate the radical and eliminate it by raising both sides of the equation to the appropriate power (square for square roots, cube for cube roots, etc.). After simplifying, solve the resulting equation. Always check for extraneous solutions<\/strong> \u2014 squaring both sides may introduce values that don’t actually satisfy the original equation. This is especially important when variables are inside a square root or other radical expression. The answers must always be validated by substituting back into the original equation.<\/p>\n\n\n\n

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

ranscribed image text: ODDS Name: Unit 6: Radical Functions Date: Bell: Homework 6: Radical Equations ** This is a 2-page documents Directions: Solve each equation. Be sure to check for extraneous solutions. 1. 3-24 +17-20 2. 14-11-15-2 3. -7m+1 -14 4. -7+(16p+8)= -1 5. p+88–1 6. 17-2-3x+10 – 1 7. 36-2941-22 8. Gz-21 – 19-2 […]<\/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-221026","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221026","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=221026"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221026\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=221026"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=221026"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=221026"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}