{"id":228731,"date":"2025-06-07T13:54:48","date_gmt":"2025-06-07T13:54:48","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228731"},"modified":"2025-06-07T13:54:50","modified_gmt":"2025-06-07T13:54:50","slug":"just-answer-the-last-one","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/just-answer-the-last-one\/","title":{"rendered":"Just answer the last one."},"content":{"rendered":"\n

Just answer the last one. Please Emilia pays $24 to rent a boat at the lake for up to 6 hours. She constructs the inequality and number line below to represent the number of hours, \u00e2\u201a\u00ac, she can use the boat: Emilia’s Model X \u00e2\u2030\u00a4 6 10 12 14 Are Emilia’s inequality and number line correct? Explain your reasoning by completing the statements. Click the arrows to choose an answer from each menu: Emilia’s inequality, \u00e2\u201a\u00ac 6 is Choose__ because the number of hours is Choose_ Emilia’s number line is Choose_ The endpoint Choose_ filled in and the number line Choose_ should be shaded to the left is correctly shaded to the right of the endpoint:<\/p>\n\n\n\n

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

Corrected Answer:<\/h3>\n\n\n\n

Emilia’s inequality, x \u2264 6<\/strong>, is correct<\/strong> because the number of hours is at most 6<\/strong>.
Emilia’s number line is incorrect<\/strong>.
The endpoint should be<\/strong> filled in and the number line should be shaded to the left<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/h3>\n\n\n\n

Emilia is renting a boat for up to 6 hours<\/strong> for $24. The phrase “up to 6 hours”<\/strong> means she can use the boat for any time from 0 hours up to and including 6 hours<\/strong>, but not more than 6 hours.<\/p>\n\n\n\n

The inequality x \u2264 6<\/strong> accurately represents this situation. In mathematics, “\u2264” means “less than or equal to.” Here, x<\/strong> stands for the number of hours Emilia uses the boat. So x \u2264 6<\/strong> means she can use the boat for 6 hours or any amount of time less than that<\/strong>\u2014such as 1, 3.5, or 5.9 hours. Therefore, Emilia\u2019s inequality is correct because it reflects the idea of a maximum allowed time<\/strong>.<\/p>\n\n\n\n

However, her number line representation<\/strong> has an issue. For an inequality like x \u2264 6<\/strong>, the number line should have:<\/p>\n\n\n\n

    \n
  • A filled-in (solid) circle<\/strong> at 6, because 6 is included in the allowed values.<\/li>\n\n\n\n
  • A shaded region to the left<\/strong> of 6, representing all values less than or equal to 6<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    If Emilia’s number line instead had an open circle<\/strong> at 6 or shaded to the right<\/strong>, it would incorrectly suggest that values greater than 6<\/strong> are allowed or that 6 is not included<\/strong>, both of which would be wrong.<\/p>\n\n\n\n

    In conclusion, while Emilia correctly wrote the inequality, her number line must be corrected to reflect the meaning of “x \u2264 6”: a solid point at 6 and shading to the left, capturing all values from 0 up to and including 6.<\/p>\n\n\n\n

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

    Just answer the last one. Please Emilia pays $24 to rent a boat at the lake for up to 6 hours. She constructs the inequality and number line below to represent the number of hours, \u00e2\u201a\u00ac, she can use the boat: Emilia’s Model X \u00e2\u2030\u00a4 6 10 12 14 Are Emilia’s inequality and number line […]<\/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-228731","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228731","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=228731"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228731\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228731"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228731"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}