{"id":"cb_question_bank:9e2c4648-810b-488b-96d6-691820ec14fe","source_id":"cb_question_bank","source_item_id":"9e2c4648-810b-488b-96d6-691820ec14fe","external_id":"40946085-fbf1-4c4a-977f-931fd79ef80c","ibn":null,"question_id":"d8539e09","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"y less than 6 x plus 2 For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?","stimulus":"","stimulus_html":null,"stem_html":"

y<6x+2

\n

For which of the following tables are all the values of x\n and their corresponding values of y\n solutions to the given inequality?

","rationale_html":"

Choice C is correct. All the tables in the choices have the same three values of x\n, so each of the three values of x\n can be substituted in the given inequality to compare the corresponding values of y\n in each of the tables. Substituting 3\n for x\n in the given inequality yields y<63+2, or y<20. Therefore, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is less than 20\n. Substituting 5\n for x\n in the given inequality yields y<65+2, or y<32. Therefore, when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is less than 32\n. Substituting 7\n for x\n in the given inequality yields y<67+2, or y<44. Therefore, when \n\tx\n\t=\n\t7\n\n, the corresponding value of y\n is less than 44\n. For the table in choice C, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is 16\n, which is less than 20\n; when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 28\n, which is less than 32\n; when \n\tx\n\t=\n\t7\n\n, the corresponding value of y\n is 40\n, which is less than 44\n. Therefore, the table in choice C gives values of x\n and their corresponding values of y\n that are all solutions to the given inequality.

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Choice A is incorrect. In the table for choice A, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is 20\n, which is not less than 20\n; when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 32\n, which is not less than 32\n; when \n\tx\n\t=\n\t7\n\n, the corresponding value of y\n is 44\n, which is not less than 44\n.

\n

Choice B is incorrect. In the table for choice B, when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 36\n, which is not less than 32\n.

\n

Choice D is incorrect. In the table for choice D, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is 24\n, which is not less than 20\n; when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 36\n, which is not less than 32\n; when \n\tx\n\t=\n\t7\n\n, the corresponding value of y\n is 48\n, which is not less than 44\n.

","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":true,"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":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
3\n20\n
5\n32\n
7\n44\n
","ord":0},{"label":"B","content_html":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
3\n16\n
5\n36\n
7\n40\n
","ord":1},{"label":"C","content_html":"
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x\ny\n
3\n16\n
5\n28\n
7\n40\n
","ord":2},{"label":"D","content_html":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
3\n24\n
5\n36\n
7\n48\n
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