Additive property of length 7RA
You have prizes to reveal! Go to your game board. X
If EF = 2x, FG = 8, and EG = 4x, what is ER?
E
F
G
2x
4x
Simplify your answer and write it as a proper fraction, mixed number, or integer.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve for ( ER ) given the segments ( EF = 2x ), ( FG = 8 ), and ( EG = 4x ), we can utilize the additive property of length, which states that the total length of a line segment is equal to the sum of its parts.<\/p>\n\n\n\n We are given three segments along a line:<\/p>\n\n\n\n According to the additive property, we can write the relationship as: Now we can solve for ( x ):<\/p>\n\n\n\n Now that we have the value of ( x ), we can find the lengths of each segment:<\/p>\n\n\n\n Now, to find ( ER ), we notice that ( ER ) is actually equal to ( EG ), since ( E ) and ( G ) are the endpoints of the entire segment. Thus, Therefore, the value of ( ER ) is ( \\boxed{16} ).<\/p>\n\n\n\n The additive property of length helps us understand how segments relate to each other on a number line. By setting up an equation based on these segments and solving for ( x ), we can easily calculate the lengths of the individual segments and ultimately find the desired total length. This approach exemplifies how algebra can simplify geometric problems, making it a valuable tool in various mathematical applications.<\/p>\n","protected":false},"excerpt":{"rendered":" Additive property of length 7RAYou have prizes to reveal! Go to your game board. XIf EF = 2x, FG = 8, and EG = 4x, what is ER?EFG2x4xSimplify your answer and write it as a proper fraction, mixed number, or integer. The Correct Answer and Explanation is : To solve for ( ER ) given […]<\/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-146955","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146955","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=146955"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146955\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Understand the Relationships<\/h3>\n\n\n\n
\n
[
EG = EF + FG
]
Substituting the known expressions into this equation gives:
[
4x = 2x + 8
]<\/p>\n\n\n\nStep 2: Solve for ( x )<\/h3>\n\n\n\n
\n
[
4x – 2x = 8
]
[
2x = 8
]<\/li>\n\n\n\n
[
x = 4
]<\/li>\n<\/ol>\n\n\n\nStep 3: Find the Lengths of Each Segment<\/h3>\n\n\n\n
\n
[
EF = 2x = 2(4) = 8
]<\/li>\n\n\n\n
[
FG = 8
]<\/li>\n\n\n\n
[
EG = 4x = 4(4) = 16
]<\/li>\n<\/ol>\n\n\n\nStep 4: Find ( ER )<\/h3>\n\n\n\n
[
ER = EG = 16
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n
Explanation<\/h3>\n\n\n\n