{"id":"cb_question_bank:cd5cd2de-5e06-4ff0-bbbf-b4918e8761fd","source_id":"cb_question_bank","source_item_id":"cd5cd2de-5e06-4ff0-bbbf-b4918e8761fd","external_id":null,"ibn":"05487-DC","question_id":"b47419f4","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following is equivalent to the expression above?","stimulus":"open parenthesis, one-half x, plus 3, close parenthesis, minus, open parenthesis, two-thirds x, minus 5, close parenthesis","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/42ebc4f304f7516d0d8bcbf157bb5106227cb001d23d97972a58787415a8c313\" alt=\"open parenthesis, one-half x, plus 3, close parenthesis, minus, open parenthesis, two-thirds x, minus 5, close parenthesis\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following is equivalent to the expression above?</p>\n","rationale_html":"<p class=\"tcp-1f880b6e-38f9-491c-967b-0a0203d4c894\">Choice A is correct. By distributing the minus sign through the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8e7d0f86f844d02edafd39e02a43cdd2f84dcc07d950069812dcb83e2fad9fad\" alt=\"two thirds x minus 5\"></span>, the given expression can be rewritten as&nbsp;<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cf28743a82103b9acd6791ffd9614ce1de2a2b855c8b4e65ad708c7e80b26c9f\" alt=\"open parenthesis, one half x plus 3, close parenthesis, minus two thirds x, plus 5\"></span>, which is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9de4cc906312f51eb153acc55f2bdb10a024cdea9cf9522d37674c514a1d0fd5\" alt=\"one half x, minus two thirds x, plus 3, plus 5\"></span>. Combining like terms gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c7f94543f0e87c1c5ecf76c348f99cb823e6b9b11657d4f265995f81592be18e\" alt=\"open parenthesis, one half minus two thirds, close parenthesis, times x, plus, open parenthesis, 3 plus 5, close parenthesis\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/28df93cbd05ee7dd88b202914b27f6639045cb491cf20ee5bea7d11c186da814\" alt=\"negative one sixth x plus 8\"></span>.</p><p>Choice B is incorrect and may be the result of failing to distribute the minus sign appropriately through the second term and simplifying the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/017d6862076bd2937d2462506ad391d5e4fd20b04f30293ace9d08b7d120b4e7\" alt=\"one half x, plus 3, minus two thirds x, minus 5\"></span>. Choice C is incorrect and may be the result of multiplying the expressions&nbsp;<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6c2d6580b563413ed8a039f892f084daba5891ae8c3921a4661f0d292250b3d6\" alt=\"one half x plus 3 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8dd21e4d422defbc8afb189e7767318125c2df853e01a282723e35dce9978e5a\" alt=\"negative two thirds x plus 5\"></span>. Choice D is incorrect and may be the result of multiplying the expressions <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6c2d6580b563413ed8a039f892f084daba5891ae8c3921a4661f0d292250b3d6\" alt=\"one half x plus 3 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f660036e98902a879bb48820a84f93c8626cc38f6647f2daf248aa7562295750\" alt=\"negative two thirds x minus 5\"></span>.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.629000+00:00","source_updated_at":"2023-08-02T20:25:59.629000+00:00","options":[{"label":"A","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/42c822e6113a7beb88ccf828ecb270daacaf2eb0bddd6979fa5d598fef743c8c\" alt=\"negative one sixth x, plus 8\"></span></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f1fa3423c85eeb7fc4d6140ecd26c98a3debc684a8e2ef748ed63284d6a9ec3a\" alt=\"negative one sixth x, minus 2\"></span></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/41d02b4b5d286520734def8130f98c2dd3b10b4ada195e9cd0220a5431c38d20\" alt=\"negative one-third x squared, plus one-half x, plus 15\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/56fc1234edc9572c3560131a7324517457ed8acfd7b573cfc8db5c7c102bce54\" alt=\"negative one-third x squared, minus nine halves x, minus 15\"></span></span>\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}}