{"id":"cb_question_bank:953a2965-c80f-4df3-b9d2-60c75971a42d","source_id":"cb_question_bank","source_item_id":"953a2965-c80f-4df3-b9d2-60c75971a42d","external_id":null,"ibn":"070610-DC","question_id":"4f669597","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"What value of p is the solution of the equation above?","stimulus":"2 times, open parenthesis, p plus 1, close parenthesis, plus, 8 times, open parenthesis, p minus 1, close parenthesis, equals, 5 p","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-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/805dcf5b11d874b9930c9e860a5fec6f065c4905d468a2ee12e36cf1dd8c1af4\" alt=\"2 times, open parenthesis, p plus 1, close parenthesis, plus, 8 times, open parenthesis, p minus 1, close parenthesis, equals, 5 p\"></span></p>\n\t\t\t</div>\n","stem_html":"<p class=\"stem_paragraph \">What value of <span class=\"italic\">p</span> is the solution of the equation above?</p>\n","rationale_html":"<p>The correct answer is 1.2. One way to solve the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/805dcf5b11d874b9930c9e860a5fec6f065c4905d468a2ee12e36cf1dd8c1af4\" alt=\"2 times, open parenthesis, p plus 1, close parenthesis, plus, 8 times, open parenthesis, p minus 1, close parenthesis, equals 5 p\"></span> is to first distribute the terms outside the parentheses to the terms inside the parentheses: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fe4c1530752bc247b0298ff5a7cb9a057144b63ff6e52ce2e85b47608d7365cf\" alt=\"2 p plus 2, plus 8 p, minus 8, equals 5 p\"></span>. Next, combine like terms on the left side of the equal sign: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1e5efd53abab057dd9d20db54b48029719bc6c9606b3fb70f1094557d8a50c58\" alt=\"10 p minus 6, equals 5 p\"></span> . Subtracting 10<span class=\"italic\">p</span> from both sides yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8a9f6b6b19525b15141569d2db10e3f7eae78372fcb2cbe3d71bc82ae5f84b40\" alt=\"negative 6 equals negative 5 p\"></span> . Finally, dividing both sides by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8d84f0934ecb7d96090b9c086b990db006ef3ed6d80c6aa9d1f4b6324479d5b8\" alt=\"negative 5\"></span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f589632858cc0911043e9f81381d4bd7f1486f9242754b301b6e5311e4db82ab\" alt=\"p equals six fifths\"></span>, which is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/494d90a8d1b979a550b8174ecf2ad350b8cce17277bf5255ec8ebc66bcc69804\" alt=\"p equals 1 point 2\"></span>. Note that 1.2 and 6/5 are examples of ways to enter a correct answer.</p>\n","correct_answer":["1.2"],"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}}