Solve each inequality x+8>18<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve the inequality ( x + 8 > 18 ), we can follow these steps:<\/p>\n\n\n\n The goal is to solve for ( x ), so we need to isolate ( x ) on one side of the inequality.<\/p>\n\n\n\n Start with the original inequality: To isolate ( x ), subtract 8 from both sides of the inequality: The solution to the inequality is ( x > 10 ). This means that ( x ) can be any value greater than 10, but not equal to 10.<\/p>\n\n\n\n In other words, the solution is the set of all real numbers greater than 10, expressed in interval notation as: To verify, choose a value for ( x ) that is greater than 10 and substitute it back into the original inequality.<\/p>\n\n\n\n For example, let\u2019s choose ( x = 11 ): Now, let\u2019s test with a value less than 10, say ( x = 9 ): Thus, the solution to the inequality ( x + 8 > 18 ) is ( x > 10 ), which can be written in interval notation as ( (10, \\infty) ).<\/p>\n","protected":false},"excerpt":{"rendered":" Solve each inequality x+8>18 The Correct Answer and Explanation is: To solve the inequality ( x + 8 > 18 ), we can follow these steps: Step 1: Isolate the variable ( x ) The goal is to solve for ( x ), so we need to isolate ( x ) on one side of […]<\/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 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1: Isolate the variable ( x )<\/h3>\n\n\n\n
[
x + 8 > 18
]<\/p>\n\n\n\n
[
x + 8 – 8 > 18 – 8
]
Simplifying both sides:
[
x > 10
]<\/p>\n\n\n\nStep 2: Interpret the solution<\/h3>\n\n\n\n
[
(10, \\infty)
]
This interval notation represents all numbers starting just after 10 and extending infinitely to the right.<\/p>\n\n\n\nStep 3: Verify the solution<\/h3>\n\n\n\n
[
x + 8 = 11 + 8 = 19
]
Since 19 is greater than 18, the inequality holds true, confirming that the solution is correct.<\/p>\n\n\n\n
[
x + 8 = 9 + 8 = 17
]
Since 17 is not greater than 18, the inequality is not satisfied for ( x = 9 ), which further confirms that ( x > 10 ) is the correct solution.<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n