{"id":"cb_question_bank:c97a3b2c-7810-4e1e-aa79-a67f0ef2a518","source_id":"cb_question_bank","source_item_id":"c97a3b2c-7810-4e1e-aa79-a67f0ef2a518","external_id":"9dc23c3a-e1d2-402a-9e2a-4085bbba4933","ibn":null,"question_id":"73b5f330","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function f is defined by f left parenthesis x right parenthesis equals 5 x plus 8 . For what value of x does f left parenthesis x right parenthesis equals 58 ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The function <math alttext=\"f\"><mi>f</mi>\n</math> is defined by&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals 5 x plus 8\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>5</mn></mrow><mi>x</mi><mo>+</mo><mrow><mn>8</mn></mrow></math>. For what value of <math alttext=\"x\"><mi>x</mi>\n</math> does&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals 58\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>58</mn></mrow></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It's given that the function <math alttext=\"f\"><mi>f</mi>\n</math> is defined by <math alttext=\"f left parenthesis x right parenthesis equals 5 x plus 8\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>8</mn></math>. Substituting <math alttext=\"58\"><mn>58</mn>\n</math> for <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in this equation yields <math alttext=\"58 equals 5 x plus 8\"><mn>58</mn><mo>=</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>8</mn></math>. Subtracting <math alttext=\"8\"><mn>8</mn>\n</math> from both sides of this equation yields <math alttext=\"50 equals 5 x\"><mrow>\n\t<mn>50</mn>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>5</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n</mrow>\n</math>. Dividing both sides of this equation by <math alttext=\"5\"><mn>5</mn>\n</math> yields <math alttext=\"10 equals x\"><mrow>\n\t<mn>10</mn>\n\t<mo>=</mo>\n\t<mi>x</mi>\n</mrow>\n</math>. Therefore, the value of <math alttext=\"x\"><mi>x</mi>\n</math> when <math alttext=\"f left parenthesis x right parenthesis equals 58\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>58</mn></math> is <math alttext=\"10\"><mn>10</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is the value of&nbsp;<math alttext=\"f left parenthesis 58 right parenthesis\"><mi>f</mi><mfenced><mn>58</mn></mfenced></math>, not the value of <math alttext=\"x\"><mi>x</mi>\n</math> when&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals 58\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>58</mn></math>.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.813000+00:00","source_updated_at":"2023-08-02T20:25:59.813000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"10\"><mn>10</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"13\"><mn>13</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"50\"><mn>50</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"298\"><mn>298</mn>\n</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}}