{"id":"cb_question_bank:59007602-7ea9-4b62-8cee-b52f0cf410df","source_id":"cb_question_bank","source_item_id":"59007602-7ea9-4b62-8cee-b52f0cf410df","external_id":"c72f11a1-3ee5-4aee-a4eb-ef3be78817bb","ibn":null,"question_id":"1a621af4","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":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A number x is at most 2 less than 3 times the value of y . If the value of y is negative 4 , what is the greatest possible value of x ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A number <math alttext=\"x\"><mi>x</mi>\n</math> is at most <math alttext=\"2\"><mn>2</mn>\n</math> less than <math alttext=\"3\"><mn>3</mn>\n</math> times the value of <math alttext=\"y\"><mi>y</mi>\n</math>. If the value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"negative 4\"><mo>-</mo><mn>4</mn>\n</math>, what is the greatest possible value of <math alttext=\"x\"><mi>x</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"negative 14\"><mo>-</mo><mn>14</mn>\n</math>. It's given that a number <math alttext=\"x\"><mi>x</mi>\n</math> is at most <math alttext=\"2\"><mn>2</mn>\n</math> less than <math alttext=\"3\"><mn>3</mn>\n</math> times the value of <math alttext=\"y\"><mi>y</mi>\n</math>. Therefore, <math alttext=\"x\"><mi>x</mi>\n</math> is less than or equal to <math alttext=\"2\"><mn>2</mn>\n</math> less than <math alttext=\"3\"><mn>3</mn>\n</math> times the value of <math alttext=\"y\"><mi>y</mi>\n</math>. The expression <math alttext=\"3 y\"><mrow>\n\t<mn>3</mn>\n\t<mi>y</mi>\n</mrow>\n</math> represents <math alttext=\"3\"><mn>3</mn>\n</math> times the value of <math alttext=\"y\"><mi>y</mi>\n</math>. The expression <math alttext=\"3 y minus 2\"><mrow>\n\t<mrow>\n\t\t<mn>3</mn>\n\t\t<mi>y</mi>\n\t</mrow>\n\t<mo>-</mo>\n\t<mn>2</mn>\n</mrow>\n</math> represents <math alttext=\"2\"><mn>2</mn>\n</math> less than <math alttext=\"3\"><mn>3</mn>\n</math> times the value of <math alttext=\"y\"><mi>y</mi>\n</math>. Therefore, <math alttext=\"x\"><mi>x</mi>\n</math> is less than or equal to <math alttext=\"3 y minus 2\"><mrow>\n\t<mrow>\n\t\t<mn>3</mn>\n\t\t<mi>y</mi>\n\t</mrow>\n\t<mo>-</mo>\n\t<mn>2</mn>\n</mrow>\n</math>. This can be shown by the inequality <math alttext=\"x less than or equals 3 y minus 2\"><mi>x</mi><mo>≤</mo><mn>3</mn><mi>y</mi><mo>-</mo><mn>2</mn></math>. Substituting <math alttext=\"negative 4\"><mo>-</mo><mn>4</mn>\n</math> for <math alttext=\"y\"><mi>y</mi>\n</math> in this inequality yields <math alttext=\"x less than or equals 3 left parenthesis negative 4 right parenthesis minus 2\"><mi>x</mi><mo>≤</mo><mn>3</mn><mfenced><mrow><mo>-</mo><mn>4</mn></mrow></mfenced><mo>-</mo><mn>2</mn></math>&nbsp;or, <math alttext=\"x less than or equals negative 14\"><mi>x</mi><mo>≤</mo><mo>-</mo><mn>14</mn></math>. Therefore, if the value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"negative 4\"><mo>-</mo><mn>4</mn>\n</math>, the greatest possible value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"negative 14\"><mo>-</mo><mn>14</mn>\n</math>.</p>","correct_answer":["-14"],"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":[],"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}}