{"id":"cb_question_bank:069dfdcf-e062-4c12-8d4c-27b606e2809a","source_id":"cb_question_bank","source_item_id":"069dfdcf-e062-4c12-8d4c-27b606e2809a","external_id":null,"ibn":"022234-DC","question_id":"b8caaf84","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If p equals, 3 x, plus 4 and v equals, x plus 5 , which of the following is equivalent to p v, minus 2 p, plus v ?","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/97a99f8bdca7c6b8dce1e38f1a12880569608b1841aa70260252275b6a03316f\" alt=\"p equals, 3 x, plus 4 \"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/19f921d4c733bf439ff68f8a4b4c00337f89277c230875a24ae32c371677f026\" alt=\"v equals, x plus 5\"></span></span>, which of the following is equivalent to <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/13ecb38256cb4848a65d6bd48a11e1b71ed11dde67771c5bc07f9fd146a2172d\" alt=\"p v, minus 2 p, plus v\"></span></span> ?</p>\n","rationale_html":"<p>Choice B is correct. It’s given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/97a99f8bdca7c6b8dce1e38f1a12880569608b1841aa70260252275b6a03316f\" alt=\"p equals, 3 x plus 4 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/19f921d4c733bf439ff68f8a4b4c00337f89277c230875a24ae32c371677f026\" alt=\"v equals, x plus 5\"></span>. Substituting the values for <span class=\"italic\">p</span> and <span class=\"italic\">v</span> into the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/13ecb38256cb4848a65d6bd48a11e1b71ed11dde67771c5bc07f9fd146a2172d\" alt=\"p v, minus 2 p, plus v \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5dab34b930d66de8e790f4608e2eb25d24d588a56d6cff2afa1c5fc30b105fa0\" alt=\"open parenthesis, 3 x plus 4, close parenthesis, times, open parenthesis, x plus 5, close parenthesis, minus, 2 times, open parenthesis, 3 x plus 4, close parenthesis, plus x, plus 5\"></span>. Multiplying the terms <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5ec835d948609b0e4f9c0e453441cbd2294c5d796dc9725834607517080d1ee6\" alt=\"open parenthesis, 3 x plus 4, close parenthesis, times, open parenthesis, x plus 5, close parenthesis\"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/949aba382aab826c44ad4fd9bc78866a9293bbe3a77847024432bf8b859a2d72\" alt=\"3 x squared, plus 4 x, plus 15 x, plus 20\"></span>. Using the distributive property to rewrite <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5996c07deb81e1342541fba89525088b85c49264d78922819374ad924893cc01\" alt=\"negative 2 times, open parenthesis, 3 x plus 4, close parenthesis\"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cd04c59da9686d97755e90ac9e17c027e293a9d6de74cf9c5a3c836b2d32f684\" alt=\"negative 6 x minus 8\"></span>. Therefore, the entire expression can be represented as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d38c6c453f471f15568d9c03ca1703b24518e060cb39941e177fe8ee1d29dc1e\" alt=\"3 x squared, plus 4 x, plus 15 x, plus 20, minus 6 x, minus 8, plus x, plus 5\"></span>. Combining like terms yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2759366031afdb49d41ec0fdda7a9b6bdc493a699f0e0fe3525e7230a03c4482\" alt=\"3 x squared, plus 14 x, plus 17\"></span>.</p><p>Choice A is incorrect and may result from subtracting, instead of adding, the term <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f774c766794ca6883d8aa2c0e5603f5668852b808fcfb2f4940cd18d6758cb03\" alt=\"x plus 5\"></span>. Choice C is incorrect. This is the result of multiplying the terms <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5ec835d948609b0e4f9c0e453441cbd2294c5d796dc9725834607517080d1ee6\" alt=\"open parenthesis, 3 x plus 4, close parenthesis, times, open parenthesis, x plus 5, close parenthesis\"></span>. Choice D is incorrect and may result from distributing 2, instead of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a546b5be2c97283e2d1e93605f422844d5a87f3418a61a7d23019eb596b64f17\" alt=\"negative 2\"></span>, to the term <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7b887198aa73d3c2d465660a33501c2303ca68f2f17d82b6f4935f98c6866b61\" alt=\"3 x plus 4\"></span>.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.617000+00:00","source_updated_at":"2023-08-02T20:25:59.617000+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/b1655223073ccd41778f6530854358e8f63a020b82cfac5a002228f9747240b2\" alt=\"3 x squared, plus, 12 x, plus 7\"></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/2759366031afdb49d41ec0fdda7a9b6bdc493a699f0e0fe3525e7230a03c4482\" alt=\"3 x squared, plus, 14 x, plus 17\"></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/19deaac33119af228d1fbee1a93e62800af2d3f74878d92d96a34d5939907f86\" alt=\"3 x squared, plus, 19 x, plus 20\"></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/77720d22a0e29d25ea106120af9a5b3bb701817379f75f1fc08e911678a184d9\" alt=\"3 x squared, plus, 26 x, plus 33\"></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}}