{"id":"cb_question_bank:343e0d95-dc77-4891-a3eb-83399e016a7b","source_id":"cb_question_bank","source_item_id":"343e0d95-dc77-4891-a3eb-83399e016a7b","external_id":null,"ibn":"025700-DC","question_id":"b80d10d7","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"What is the solution to the equation above?","stimulus":"the fraction with numerator 2 times, open parenthesis, x plus 1, close parenthesis, and denominator x plus 5, end fraction, equals 1 minus the fraction with numerator 1, and denominator x plus 5, end fraction","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/fe431dd04e8f686a8d3aa37bab7ee43d50d164bb234a55379736f3c285499d0e\" alt=\"the fraction with numerator 2 times, open parenthesis, x plus 1, close parenthesis, and denominator x plus 5, end fraction, equals 1 minus the fraction with numerator 1, and denominator x plus 5, end fraction\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">What is the solution to the equation above?</p>\n","rationale_html":"<p>Choice B is correct. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c11358252e2181bf0f59a4dbe534d4a542e3d975d0ed19337250fb0e5eea312e\" alt=\"the fraction with numerator x plus 5, and denominator x plus 5, end fraction\"></span> is equivalent to 1, the right-hand side of the given equation can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fbf81c508bf8ffa16da19d7caa4e9ac4b21a12cce4b6f8568998584e7e920d5b\" alt=\"the fraction with numerator x plus 5, and denominator x plus 5, end fraction, minus, the fraction 1 over, x plus 5, end fraction \"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9e00e7562ca660e1330a0c73c1b13cfaeff67e454d779e95dd1a388f289c473e\" alt=\"the fraction with numerator x plus 4, and denominator x plus 5, end fraction\"></span>. Since the left- and right-hand sides of the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/51a31c76798724aca90d386de54607dac1e56298d156d43e866cd458466021f8\" alt=\"the fraction with numerator 2 times, open parenthesis, x plus 1, close parenthesis, and denominator x plus 5, end fraction, equals, the fraction with numerator x plus 4, and denominator x plus 5, end fraction \"></span> have the same denominator, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a7d7503ad3a702abafd1705e06d4155460058b967ca54bcbdc40e006f1cc2d87\" alt=\"2 times, open parenthesis, x plus 1, close parenthesis, equals x plus 4\"></span>. Applying the distributive property of multiplication to the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/13eef8d85b129490df7a147c259275e9544423dd31e470fe5f10b4a1b12d7d9b\" alt=\"2 times, open parenthesis, x plus 1, close parenthesis \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5965063abff8a5b12af466fb0e7d29af6d39866f874e6681fd0656846ec67e14\" alt=\"2 times x, plus, 2 times 1\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bac9c39c91424d74bde90a5119178f9979302f602b5a39555d10b6bb7b851e5b\" alt=\"2 x plus 2\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bdf4277c16698b25e2f73943aaf8ee8754ec54c70c814356c8cee028cf9e13aa\" alt=\"2 x plus 2, equals, x plus 4\"></span>. Subtracting <span class=\"italic\">x</span> and 2 from both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/401169281090f4f1d9aafeeb928524e672d737cdce814b4e9256c5e06a42d325\" alt=\"x equals 2\"></span>.</p><p>Choices A, C, and D are incorrect. If <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37b98ea685bc6992d8e8e7df92ac8c58c1621b437bc601cc6767a21168bc15e0\" alt=\"x equals 0\"></span>, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e2532d7d9e0fa22f7905d4e3eb559a07cbc9218115b3e1893c4adbf92e087a72\" alt=\"the fraction with numerator 2 times, open parenthesis, 0 plus 1, close parenthesis, and denominator 0 plus 5, end fraction, equals 1 minus, the fraction with numerator 1, and denominator 0 plus 5, end fraction\"></span>. This can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3f87af4c2de0a187665c630cc25938bff543c7b37312220753ca7d41bcf59ad9\" alt=\"2 over 5, equals 4 over 5\"></span>, which is a false statement. Therefore, 0 isn’t a solution to the given equation. Substituting 3 and 5 into the given equation yields similarly false statements.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.619000+00:00","source_updated_at":"2023-08-02T20:25:59.619000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">0</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">2</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">3</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">5</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}}