{"id":"cb_question_bank:b7b798da-bdcc-45c0-a9fa-585125e16f36","source_id":"cb_question_bank","source_item_id":"b7b798da-bdcc-45c0-a9fa-585125e16f36","external_id":null,"ibn":"14894-DC","question_id":"9ff10b3b","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If one half x, minus one sixth x, equals 1 , what is the value of x ?","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/d1a3fb92c90b328281e916e73d316c03155def57dc7931115464d1c2715a529d\" alt=\"one half x, minus one sixth x, equals 1\"></span></span>, what is the value of <span class=\"italic\">x</span> ?</p>\n","rationale_html":"<p>Choice C is correct. To make it easier to add like terms on the left-hand side of the given equation, both sides of the equation can be multiplied by 6, which is the lowest common denominator of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/acd304db4db3ee4a427462753769f86b9941b320104a3856da731c39db5d894c\" alt=\"one half\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b937562b5a18b41892a0bc0ac044c109853b95b8f6ec9136a2a341d8e007bf07\" alt=\"one sixth\"></span>. This yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/08bbfd222f2c09c1d650d016c6e62d4f217ee46aa46cc11a1715eebe5753efad\" alt=\"3 x minus x, equals 6\"></span>, which can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a7ab1ad27f4f1f0a4cbafe24c1a2be7cb4539394491d95a5bb84c3e6020cb624\" alt=\"2 x equals 6\"></span>. Dividing both sides of this equation by 2 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ceba1165e53a8baa1cf03f75cde85da34750b8ab2728ef25385d77f80f8276c5\" alt=\"x equals 3\"></span>.</p><p>Choice A is incorrect and may result from subtracting the denominators instead of numerators with common denominators to get <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/df816fb2e9d4a2d52f68d3a0342aad3d7cec875afb25d9ac971f5758cff3754d\" alt=\"negative one fourth x\"></span>, rather than <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cf8399d8f4d85f5f3569b2502ad79aa59c450b1727a398a0266f1badc051007a\" alt=\"one third x\"></span>, on the left-hand side of the equation. Choice B is incorrect and may result from rewriting the given equation as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8893706e0d3382f3be9622d0daccc10259d19ac2e6f2b4d6676dc3839ce1718a\" alt=\"one half x, equals one sixth\"></span> instead of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a7ab1ad27f4f1f0a4cbafe24c1a2be7cb4539394491d95a5bb84c3e6020cb624\" alt=\"2 x equals 6\"></span>. Choice D is incorrect and may result from conceptual or computational errors.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.639000+00:00","source_updated_at":"2023-08-02T20:25:59.639000+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/bc0609d3d5523eaf8e35097c2a9c872ba31206db61297d0a21597123b1c843d7\" alt=\"negative 4\"></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/fce26b7f770543c2e33190a4ea311aa1f4d8da39df9b43ef0ea5dfff882a8571\" alt=\"one third\"></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/b35ae18904fb781bd47e663cf02b992965491e4f50b31194e7d69870143879cd\" alt=\"3\"></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/3ba1d0c351ba804f1e264fab3db5d1fb3d2696b974be16e1a3b091433eb096d6\" alt=\"6\"></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}}