To solve for xxx, we use the formula for the midsegment of a trapezoid<\/strong>:Midsegment=12(base1+base2)\\text{Midsegment} = \\frac{1}{2} (\\text{base}_1 + \\text{base}_2)Midsegment=21\u200b(base1\u200b+base2\u200b)<\/p>\n\n\n\n From the problem:<\/p>\n\n\n\n 14.5=12((3x\u22121)+19)14.5 = \\frac{1}{2} \\left( (3x – 1) + 19 \\right)14.5=21\u200b((3x\u22121)+19)<\/p>\n\n\n\n 14.5=12(3x+18)14.5 = \\frac{1}{2} (3x + 18)14.5=21\u200b(3x+18)<\/p>\n\n\n\n 2\u22c514.5=3x+182 \\cdot 14.5 = 3x + 182\u22c514.5=3x+1829=3x+1829 = 3x + 1829=3x+18<\/p>\n\n\n\n 29\u221218=3×29 – 18 = 3×29\u221218=3×11=3×11 = 3×11=3xx=113x = \\frac{11}{3}x=311\u200b<\/p>\n\n\n\n x=113\\boxed{x = \\frac{11}{3}}x=311\u200b\u200b<\/p>\n\n\n\n In a trapezoid, the midsegment<\/strong> (also called the median) is the line segment that connects the midpoints of the two non-parallel sides. This segment is always parallel to the two bases and its length is the average<\/strong> of the lengths of the two bases. The formula to calculate the length of the midsegment is:Midsegment=12(base1+base2)\\text{Midsegment} = \\frac{1}{2} (\\text{base}_1 + \\text{base}_2)Midsegment=21\u200b(base1\u200b+base2\u200b)<\/p>\n\n\n\n In this problem, you are given the lengths of the two bases and the midsegment, with one base expressed in terms of the variable xxx. Specifically, base 1 is 3x\u221213x – 13x\u22121, base 2 is 19, and the midsegment is 14.5.<\/p>\n\n\n\n To find the value of xxx, substitute these values into the midsegment formula:14.5=12((3x\u22121)+19)14.5 = \\frac{1}{2} \\left((3x – 1) + 19\\right)14.5=21\u200b((3x\u22121)+19)<\/p>\n\n\n\n Combine like terms inside the parentheses:14.5=12(3x+18)14.5 = \\frac{1}{2} (3x + 18)14.5=21\u200b(3x+18)<\/p>\n\n\n\n Then, multiply both sides by 2 to remove the fraction:29=3x+1829 = 3x + 1829=3x+18<\/p>\n\n\n\n Isolate the variable by subtracting 18 from both sides:11=3×11 = 3×11=3x<\/p>\n\n\n\n Finally, divide both sides by 3:x=113x = \\frac{11}{3}x=311\u200b<\/p>\n\n\n\n This is the value of xxx that makes the length of the midsegment equal to 14.5, based on the formula derived from trapezoid geometry.<\/p>\n\n\n\n The formula for the midsegment of a trapezoid is midsegment = 1\/2(base1 + base2). Find the value of x. 3x – 1 145 19 14.5 = \u00e2\u02c6\u0161(3x + 1 + 19) Solve for x. Back Next Type here to search The Correct Answer and Explanation is: To solve for xxx, we use the formula for […]<\/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-232368","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232368","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=232368"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232368\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
Step 1: Plug into the formula<\/h3>\n\n\n\n
Step 2: Simplify the expression inside the parentheses<\/h3>\n\n\n\n
Step 3: Eliminate the fraction by multiplying both sides by 2<\/h3>\n\n\n\n
Step 4: Solve for xxx<\/h3>\n\n\n\n
\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
\n\n\n\nExplanation (like in a textbook, ~300 words):<\/h3>\n\n\n\n
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<\/figure>\n","protected":false},"excerpt":{"rendered":"