{"id":"cb_question_bank:dc50b354-b03f-4fae-8ebf-bd19e023cdda","source_id":"cb_question_bank","source_item_id":"dc50b354-b03f-4fae-8ebf-bd19e023cdda","external_id":"4d535a61-d332-4981-961c-a1bf2488438f","ibn":null,"question_id":"8f0c82e2","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":"The minimum value of x is 12 less than 6 times another number n . Which inequality shows the possible values of x ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The minimum value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"12\"><mn>12</mn>\n</math> less than <math alttext=\"6\"><mn>6</mn>\n</math> times another number <math alttext=\"n\"><mi>n</mi>\n</math>. Which inequality shows the possible values of <math alttext=\"x\"><mi>x</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. It’s given that the minimum value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"12\"><mn>12</mn>\n</math> less than <math alttext=\"6\"><mn>6</mn>\n</math> times another number <math alttext=\"n\"><mi>n</mi>\n</math>. Therefore, the possible values of <math alttext=\"x\"><mi>x</mi>\n</math> are all greater than or equal to the value of <math alttext=\"12\"><mn>12</mn>\n</math> less than <math alttext=\"6\"><mn>6</mn>\n</math> times <math alttext=\"n\"><mi>n</mi>\n</math>. The value of <math alttext=\"6\"><mn>6</mn>\n</math> times <math alttext=\"n\"><mi>n</mi>\n</math> is given by the expression <math alttext=\"6 n\"><mrow>\n\t<mn>6</mn>\n\t<mi>n</mi>\n</mrow>\n</math>. The value of <math alttext=\"12\"><mn>12</mn>\n</math> less than <math alttext=\"6 n\"><mrow>\n\t<mn>6</mn>\n\t<mi>n</mi>\n</mrow>\n</math> is given by the expression <math alttext=\"6 n minus 12\"><mrow>\n\t<mrow>\n\t\t<mn>6</mn>\n\t\t<mi>n</mi>\n\t</mrow>\n\t<mo>-</mo>\n\t<mn>12</mn>\n</mrow>\n</math>. Therefore, the possible values of <math alttext=\"x\"><mi>x</mi>\n</math> are all greater than or equal to <math alttext=\"6 n minus 12\"><mrow>\n\t<mrow>\n\t\t<mn>6</mn>\n\t\t<mi>n</mi>\n\t</mrow>\n\t<mo>-</mo>\n\t<mn>12</mn>\n</mrow>\n</math>. This can be shown by the inequality <math alttext=\"x greater than or equals 6 n minus 12\"><mi>x</mi><mo>≥</mo><mn>6</mn><mi>n</mi><mo>-</mo><mn>12</mn></math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This inequality shows the possible values of <math alttext=\"x\"><mi>x</mi>\n</math> if the maximum, not the minimum, value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"12\"><mn>12</mn>\n</math> less than <math alttext=\"6\"><mn>6</mn>\n</math> times <math alttext=\"n\"><mi>n</mi>\n</math>.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This inequality shows the possible values of <math alttext=\"x\"><mi>x</mi>\n</math> if the maximum, not the minimum, value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"6\"><mn>6</mn>\n</math> times <math alttext=\"n\"><mi>n</mi>\n</math> less than <math alttext=\"12\"><mn>12</mn>\n</math>, not <math alttext=\"12\"><mn>12</mn>\n</math> less than <math alttext=\"6\"><mn>6</mn>\n</math> times <math alttext=\"n\"><mi>n</mi>\n</math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This inequality shows the possible values of <math alttext=\"x\"><mi>x</mi>\n</math> if the minimum value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"6\"><mn>6</mn>\n</math>&nbsp;times <math alttext=\"n\"><mi>n</mi>\n</math>&nbsp;less than <math alttext=\"12\"><mn>12</mn>\n</math>, not <math alttext=\"12\"><mn>12</mn>\n</math> less than <math alttext=\"6\"><mn>6</mn>\n</math> times <math alttext=\"n\"><mi>n</mi>\n</math>.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.819000+00:00","source_updated_at":"2023-08-02T20:25:59.819000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"x less than or equals 6 n minus 12\"><mi>x</mi><mo>≤</mo><mrow><mn>6</mn></mrow><mi>n</mi><mo>-</mo><mrow><mn>12</mn></mrow></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"x greater than or equals 6 n minus 12\"><mi>x</mi><mo>≥</mo><mrow><mn>6</mn></mrow><mi>n</mi><mo>-</mo><mrow><mn>12</mn></mrow></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"x less than or equals 12 minus 6 n\"><mi>x</mi><mo>≤</mo><mrow><mn>12</mn></mrow><mo>-</mo><mrow><mn>6</mn></mrow><mi>n</mi></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"x greater than or equals 12 minus 6 n\"><mi>x</mi><mo>≥</mo><mrow><mn>12</mn></mrow><mo>-</mo><mrow><mn>6</mn></mrow><mi>n</mi></math></p>","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}}