{"id":"cb_question_bank:98687b37-39db-45fa-9411-74c44778f07d","source_id":"cb_question_bank","source_item_id":"98687b37-39db-45fa-9411-74c44778f07d","external_id":null,"ibn":"070623-DC","question_id":"a391ed22","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The expression above is equivalent to a, x squared, plus b x, plus c , where a , b , and c are constants. What is the value of b ?","stimulus":"open parenthesis, one half x, plus three halves, close parenthesis, times, open parenthesis, three halves x, plus one half, close parenthesis","stimulus_html":"<div class=\"stimulus_reference \">\n\t\t\t\t<p class=\"standalone_statement style:1 \">\n\t\t\t\t\t<span class=\"math_expression \">\n\t\t\t\t\t\t<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/74feaea29b5e80ccaa3092a474e4e08dea0a21b3f5849155d6de1155217f6ca1\" alt=\"open parenthesis, one half x, plus three halves, close parenthesis, times, open parenthesis, three halves x, plus one half, close parenthesis\"></span></span>\n\t\t\t\t</p>\n\t\t\t</div>\n","stem_html":"<p class=\"stem_paragraph \">The expression above is equivalent to <span class=\"math_expression \">\n\t\t\t\t\t\t<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/934e21781a6f763f949024aa31fdfc0cda125720480046286c0b1333e65e0310\" alt=\"a, x squared, plus b x, plus c \"></span></span>, where <span class=\"italic\">a</span>, <span class=\"italic\">b</span>, and <span class=\"italic\">c</span> are constants. What is the value <span class=\"formatted_line_break delivery_mode:PPT \"></span>of <span class=\"italic\">b</span>?</p>\n","rationale_html":"<p>The correct answer is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c07dd1b3634a62972e13523df568fe0411662f40a588412490b6b3c77df4e541\" alt=\"five halves\"></span>. The expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/74feaea29b5e80ccaa3092a474e4e08dea0a21b3f5849155d6de1155217f6ca1\" alt=\"open parenthesis, one half x, plus three halves, close parenthesis, times, open parenthesis, three halves x, plus one half, close parenthesis\"></span> can be written in the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/934e21781a6f763f949024aa31fdfc0cda125720480046286c0b1333e65e0310\" alt=\"a, x squared, plus b x, plus c\"></span>, where <span class=\"italic\">a</span>, <span class=\"italic\">b</span>, and <span class=\"italic\">c</span> are constants, by multiplying out the expression using the distributive property of multiplication over addition. The result is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/77b7ec94ae2c2285b27fdbc66783d75f5dd63f6cff430114e4e368d9ba981183\" alt=\"one half x, times three halves x, plus, one half x, times one half, plus, three halves times three halves x, plus, three halves times one half\"></span>. This expression can be rewritten by multiplying as indicated to give <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/15658947e335a9e620e617784426d6b45c8eaada1e2b9a596b90e4280b39a7b8\" alt=\"three fourths x squared, plus, one fourth x, plus, nine fourths x, plus, three fourths\"></span>, which can be simplified to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/73f23bc44f0599676e317ed2e05ef3a4dc2f18812af5489371f5140ba3ab04d3\" alt=\"three fourths x squared, plus, ten fourths x, plus, three fourths\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c696d3df66eb909b14164a8772874c8876e7bc8a1f9b64a7a84ed4805e199412\" alt=\"three fourths x squared, plus, five halves x, plus, three fourths\"></span>. This is in the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/934e21781a6f763f949024aa31fdfc0cda125720480046286c0b1333e65e0310\" alt=\"a, x squared, plus b x, plus c\"></span>, where the value of <span class=\"italic\">b</span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c07dd1b3634a62972e13523df568fe0411662f40a588412490b6b3c77df4e541\" alt=\"five halves\"></span>. Note that 5/2 and 2.5 are examples of ways to enter a correct answer.</p>\n","correct_answer":["5/2"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.631000+00:00","source_updated_at":"2023-08-02T20:25:59.631000+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}}