{"id":"cb_question_bank:307d3be2-c903-4943-8e6c-d5cb417992cd","source_id":"cb_question_bank","source_item_id":"307d3be2-c903-4943-8e6c-d5cb417992cd","external_id":"16d897b1-c597-4b7a-b4ee-ecba3515085e","ibn":null,"question_id":"433184f1","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which expression is equivalent to StartFraction 4 Over 4 x minus 5 EndFraction minus StartFraction 1 Over x plus 1 EndFraction ?","stimulus":"","stimulus_html":null,"stem_html":"

Which expression is equivalent to \n\t\n\t\t\n\t\t\t4\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t4\n\t\t\t\t\tx\n\t\t\t\t\n\t\t\t\t-\n\t\t\t\t5\n\t\t\t\n\t\t\n\t\n\t-\n\t\n\t\t1\n\t\t\n\t\t\tx\n\t\t\t+\n\t\t\t1\n\t\t\n\t\n\n?

","rationale_html":"

Choice D is correct. The expression 44x-5-1x+1 can be rewritten as 44x-5+-1x+1. To add the two terms of this expression, the terms can be rewritten with a common denominator. Since x+1x+1=1, the expression 44x-5 can be rewritten as x+14x+14x-5. Since 4x-54x-5=1, the expression -1x+1 can be rewritten as 4x-5-14x-5x+1. Therefore, the expression 44x-5+-1x+1 can be rewritten as x+14x+14x-5+4x-5-14x-5x+1, which is equivalent to x+14+4x-5-1x+14x-5. Applying the distributive property to each term of the numerator yields 4x+4+-4x+5x+14x-5, or  4x+-4x+4+5x+14x-5. Adding like terms in the numerator yields 9x+14x-5.

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Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.821000+00:00","source_updated_at":"2023-08-02T20:25:59.821000+00:00","options":[{"label":"A","content_html":"

\n\t\n\t\t1\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t+\n\t\t\t\t\t1\n\t\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t4\n\t\t\t\t\t\tx\n\t\t\t\t\t\n\t\t\t\t\t-\n\t\t\t\t\t5\n\t\t\t\t\n\t\t\t\n\t\t\n\t\n\n

","ord":0},{"label":"B","content_html":"

\n\t\n\t\t3\n\t\t\n\t\t\t\n\t\t\t\t3\n\t\t\t\tx\n\t\t\t\n\t\t\t-\n\t\t\t6\n\t\t\n\t\n\n

","ord":1},{"label":"C","content_html":"

\n\t-\n\t\n\t\t1\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t+\n\t\t\t\t\t1\n\t\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t4\n\t\t\t\t\t\tx\n\t\t\t\t\t\n\t\t\t\t\t-\n\t\t\t\t\t5\n\t\t\t\t\n\t\t\t\n\t\t\n\t\n\n

","ord":2},{"label":"D","content_html":"

\n\t\n\t\t9\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t+\n\t\t\t\t\t1\n\t\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t4\n\t\t\t\t\t\tx\n\t\t\t\t\t\n\t\t\t\t\t-\n\t\t\t\t\t5\n\t\t\t\t\n\t\t\t\n\t\t\n\t\n\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}}