{"id":"cb_question_bank:9ed0d9cc-9a9c-496f-ab91-dafcefa5d2b6","source_id":"cb_question_bank","source_item_id":"9ed0d9cc-9a9c-496f-ab91-dafcefa5d2b6","external_id":"ae0f3b56-b349-4863-90be-5dfd21f6eebd","ibn":null,"question_id":"5ae186b4","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"M","score_band":4,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"StartFraction negative 54 Over w EndFraction equals 6 What is the solution to the given equation?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"StartFraction negative 54 Over w EndFraction equals 6\"><mfrac><mrow><mo>-</mo><mn>54</mn></mrow><mi>w</mi></mfrac><mo>=</mo><mrow><mn>6</mn></mrow></math></p>\n<p style=\"text-align: left;\">What is the solution to the given equation?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"negative 9\"><mo>-</mo><mn>9</mn>\n</math>. Since <math alttext=\"w\"><mi>w</mi>\n</math> is in the denominator of a fraction in the given equation, <math alttext=\"w\"><mi>w</mi>\n</math> can't be equal to <math alttext=\"0\"><mn>0</mn>\n</math>. Since <math alttext=\"w\"><mi>w</mi>\n</math> isn't equal to <math alttext=\"0\"><mn>0</mn>\n</math>, multiplying both sides of the given equation by <math alttext=\"w\"><mi>w</mi>\n</math> yields an equivalent equation, <math alttext=\"negative 54 equals 6 w\"><mrow>\n\t<mo>-</mo><mn>54</mn>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>6</mn>\n\t\t<mi>w</mi>\n\t</mrow>\n</mrow>\n</math>. Dividing both sides of this equation by <math alttext=\"6\"><mn>6</mn>\n</math> yields <math alttext=\"negative 9 equals w\"><mrow>\n\t<mo>-</mo><mn>9</mn>\n\t<mo>=</mo>\n\t<mi>w</mi>\n</mrow>\n</math>. Therefore, <math alttext=\"negative 9\"><mo>-</mo><mn>9</mn>\n</math> is the solution to the given equation.</p>","correct_answer":["-9"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.823000+00:00","source_updated_at":"2023-08-02T20:25:59.823000+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}}