{"id":"cb_question_bank:95bf49fe-456b-468a-9722-37b223d534cb","source_id":"cb_question_bank","source_item_id":"95bf49fe-456b-468a-9722-37b223d534cb","external_id":"e82ae7c1-3cdb-480b-8a7b-5d3fe9c18b84","ibn":null,"question_id":"f2bbd43d","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"y greater than 14 4 x plus y less than 18 The point left parenthesis x comma 53 right parenthesis is a solution to the system of inequalities in the xy -plane. Which of the following could be the value of x ?","stimulus":"","stimulus_html":null,"stem_html":"

y>14

\n

4x+y<18

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The point x,53 is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of x\n?

","rationale_html":"

Choice A is correct. It’s given that the point x,53 is a solution to the given system of inequalities in the xy-plane. This means that the coordinates of the point, when substituted for the variables x\n and y\n, make both of the inequalities in the system true. Substituting 53\n for y\n in the inequality y>14 yields 53>14, which is true. Substituting 53\n for y\n in the inequality 4x+y<18 yields 4x+53<18. Subtracting 53\n from both sides of this inequality yields 4x<-35. Dividing both sides of this inequality by 4\n yields x<-8.75. Therefore, x\n must be a value less than -8.75\n. Of the given choices, only -9\n is less than -8.75\n.

\n

Choice B is incorrect. Substituting -5\n for x\n and 53\n for y\n in the inequality 4x+y<18 yields 4-5+53<18, or 33<18, which is not true.

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Choice C is incorrect. Substituting 5\n for x\n and 53\n for y\n in the inequality 4x+y<18 yields 45+53<18, or 73<18, which is not true.

\n

Choice D is incorrect. Substituting 9\n for x\n and 53\n for y\n in the inequality 4x+y<18 yields 49+53<18, or 89<18, which is not true.

","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.820000+00:00","source_updated_at":"2023-08-02T20:25:59.820000+00:00","options":[{"label":"A","content_html":"

-9\n

","ord":0},{"label":"B","content_html":"

-5\n

","ord":1},{"label":"C","content_html":"

5\n

","ord":2},{"label":"D","content_html":"

9\n

","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}