{"id":"cb_question_bank:7083dee8-e403-4d1f-8868-7bfc3032ed55","source_id":"cb_question_bank","source_item_id":"7083dee8-e403-4d1f-8868-7bfc3032ed55","external_id":null,"ibn":"11289-DC","question_id":"b03adde3","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":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If u minus 3 equals, the fraction 6 over, t minus 2, end fraction , what is t in terms of u ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a7732b380316b9c3c62872d3b3953377c56ad0f0fc66cae355bed08fbf932ff6\" alt=\"u minus 3 equals, the fraction 6 over, t minus 2, end fraction \"></span></span>, what is <span class=\"italic\">t</span> in terms of <span class=\"italic\">u </span>?</p>\n","rationale_html":"<p>Choice D is correct. Multiplying both sides of the given equation by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/35ff98779f1e667edba31fb50372c5e2c46dcda2bd49b3a6090ffcd4383f3bff\" alt=\"t minus 2 \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e8de42a6aa6e73d8965e1b56b41c38d0a7086da016983436664729f812727266\" alt=\"open parenthesis, t minus 2, close parenthesis, times, open parenthesis, u minus 3, close parenthesis, equals 6\"></span>. Dividing both sides of this equation by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/314b8a44d4b22601b1721fbea685d536f549cfb9203032035d442f6687979fb7\" alt=\"u minus 3 \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fa979d0b52fcf4e88d0811048b73e63c1d2fd1f6e2589848c8a124f0a250879b\" alt=\"t minus 2, equals, the fraction with numerator 6, and denominator u minus 3, end fraction\"></span>. Adding 2 to both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ef6741626e0641ef0bd89ec63501e00d61818bc30dd020309634912a3ae9f332\" alt=\"t equals, the fraction with numerator 6, and denominator u minus 3, end fraction, plus 2\"></span>, which can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f33e0e2415d13031cc82f0d80fbec857d5e508f4e568fcdd33cd3f3496661b5c\" alt=\"t equals, the fraction with numerator 6, and denominator u minus 3, end fraction, plus, the fraction with numerator 2 times, open parenthesis, u minus 3, close parenthesis, and denominator u minus 3, end fraction\"></span>. Since the fractions on the right-hand side of this equation have a common denominator, adding the fractions yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4ea6efa2a0b3a4a66de17ceffbe0d760a67bb58dc3eff111b6c7fe895fd59fd4\" alt=\"t equals, the fraction with numerator 6 plus 2, times, open parenthesis, u minus 3, close parenthesis, and denominator u minus 3, end fraction\"></span>. Applying the distributive property to the numerator on the right-hand side of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6758f5c59374f09c4d2f1c4f9ef7ec24034e2097bbbb11c7371ea94932b3acc3\" alt=\"t equals, the fraction with numerator 6 plus 2 u, minus 6, and denominator u minus 3, end fraction\"></span>, which is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dba5b7c1dfb8c9090c2e8e9129188f0c0312c696edc422867c4e0173a3d83cc3\" alt=\"t equals, the fraction with numerator 2 u, and denominator u minus 3, end fraction\"></span>.</p><p>Choices A, B, and C are incorrect and may result from various misconceptions or miscalculations.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.639000+00:00","source_updated_at":"2023-08-02T20:25:59.639000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0d309218513b8d281663430fe3d5b3f84f69cdc5827cacf10eb56ec4388aefa6\" alt=\"t equals, the fraction 1 over u\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5a8ec72837dd780340a287c726efdf657f7df3f772662ddbd3e87e90cfca9d2f\" alt=\"t equals, the fraction 2 u plus 9, over u\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/61ba788026bba754bc9902d38687020026a36e7cdf46754c47680dc38e1c0b60\" alt=\"t equals, the fraction 1 over, u minus 3, end fraction \"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dba5b7c1dfb8c9090c2e8e9129188f0c0312c696edc422867c4e0173a3d83cc3\" alt=\"t equals, the fraction 2 u, over u minus 3, end fraction\"></span></span>\n          </p>\n","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}}