{"id":"cb_question_bank:3b6d1415-beb6-4c9b-ab45-5d531a6e160b","source_id":"cb_question_bank","source_item_id":"3b6d1415-beb6-4c9b-ab45-5d531a6e160b","external_id":"98dc96db-8257-4f49-95af-515712d5e4e3","ibn":null,"question_id":"25e1cfed","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"How many solutions does the equation 10 left parenthesis 15 x minus 9 right parenthesis equals minus 15 left parenthesis 6 minus 10 x right parenthesis have?","stimulus":"","stimulus_html":null,"stem_html":"<p>How many solutions does the equation <math alttext=\"10 left parenthesis 15 x minus 9 right parenthesis equals minus 15 left parenthesis 6 minus 10 x right parenthesis\"><mrow><mn>10</mn></mrow><mfenced><mrow><mrow><mn>15</mn></mrow><mi>x</mi><mo>-</mo><mrow><mn>9</mn></mrow></mrow></mfenced><mo>=</mo><mo>-</mo><mrow><mn>15</mn></mrow><mfenced><mrow><mrow><mn>6</mn></mrow><mo>-</mo><mrow><mn>10</mn></mrow><mi>x</mi></mrow></mfenced></math> have?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. Applying the distributive property to each side of the given equation yields <math alttext=\"150 x minus 90 equals negative 90 plus 150 x\"><mn>150</mn><mi>x</mi><mo>-</mo><mn>90</mn><mo>=</mo><mo>-</mo><mn>90</mn><mo>+</mo><mn>150</mn><mi>x</mi></math>. Applying the commutative property of addition to the right-hand side of this equation yields <math alttext=\"150 x minus 90 equals 150 x minus 90\"><mn>150</mn><mi>x</mi><mo>-</mo><mn>90</mn><mo>=</mo><mn>150</mn><mi>x</mi><mo>-</mo><mn>90</mn></math>. Since the two sides of the equation are equivalent, this equation is true for any value of <math alttext=\"x\"><mi>x</mi>\n</math>. Therefore, the given equation has infinitely many solutions.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</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 D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.809000+00:00","source_updated_at":"2023-08-02T20:25:59.809000+00:00","options":[{"label":"A","content_html":"<p style=\"text-align: left;\">Exactly one</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">Exactly two</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">Infinitely many</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">Zero</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}}