{"id":"cb_question_bank:51ac9902-64a1-498c-83b5-980692f40e0e","source_id":"cb_question_bank","source_item_id":"51ac9902-64a1-498c-83b5-980692f40e0e","external_id":null,"ibn":"027749-DC","question_id":"802549ac","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":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following is a solution to the given equation?","stimulus":"open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x plus 3, close parenthesis, equals, open parenthesis, x minus 2, close parenthesis, times, open parenthesis, x minus 3, close parenthesis, plus 10","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/107615e1d96e091274427fdb2b183546a082989ea28cb84ef2a4e66cde416f03\" alt=\"open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x plus 3, close parenthesis, equals, open parenthesis, x minus 2, close parenthesis, times, open parenthesis, x minus 3, close parenthesis, plus 10\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following is a solution to the given equation?</p>\n","rationale_html":"<p>Choice A is correct. Applying the distributive property on the left- and right-hand sides of the given equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/079124470501cf7548811bf79fb8dca8b8b589d3a1a228c103bde69fbd8ef3a7\" alt=\"x squared, plus 2 x, plus 3 x, plus 6, equals, x squared, minus 2 x, minus 3 x, plus 6, plus 10\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5cd6fdade9a0773ca3bfe09082e1473ca30a23b7fdd0721858402c0b4c6f6df6\" alt=\"x squared, plus 5 x, plus 6, equals, x squared, minus 5 x, plus 16\"></span>. Subtracting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3a186314172bc239fb025135d8722d39ee39bfefe4e212836956158aa0b9ff08\" alt=\"x squared \"></span> from and adding <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a9bbcfb6f28ff32dca971ab7c4faa8844625dea62443a649cbc984534e55c954\" alt=\"5 x\"></span> to both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/113fd17249202698f17c9c1224b0005e4d5a5874d2902dddac425ad2b8c517e2\" alt=\"10 x plus 6, equals 16\"></span>. Subtracting 6 from both sides of this equation and then dividing both sides by 10 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span>.</p><p>Choices B, C, and D are incorrect. Substituting 0, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a546b5be2c97283e2d1e93605f422844d5a87f3418a61a7d23019eb596b64f17\" alt=\"negative 2\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8d84f0934ecb7d96090b9c086b990db006ef3ed6d80c6aa9d1f4b6324479d5b8\" alt=\"negative 5\"></span> for <span class=\"italic\">x</span> in the given equation will result in a false statement. If <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37b98ea685bc6992d8e8e7df92ac8c58c1621b437bc601cc6767a21168bc15e0\" alt=\"x equals 0\"></span>, the given equation becomes <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f2e4dd0a9beb9034fa60841c8aac9a6154bae47a2eb31305b5b5532274ff08ca\" alt=\"6 equals 16\"></span>; if <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0edd49746d3055df6f32b5efedf4de1882d140a0d4f3698f8fb73b2b3693633b\" alt=\"x equals negative 2\"></span>, the given equation becomes <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7abb3b1ae3a4be5161039cfcc9b8b7fb5a7c7d57b93a050a6ee0e2c8dad78d52\" alt=\"0 equals 30\"></span>; and if <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e4dec3e5f618ee8d202e3a5a86a43dc0346ddc56760e3f46116daaf95773841d\" alt=\"x equals negative 5\"></span>, the given equation becomes <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/db7d30c7b6fe5ce0145f08de59fe014a109a9a182db8b1dff41589fabead1117\" alt=\"6 equals 66\"></span>. Therefore, the values 0, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a546b5be2c97283e2d1e93605f422844d5a87f3418a61a7d23019eb596b64f17\" alt=\"negative 2\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8d84f0934ecb7d96090b9c086b990db006ef3ed6d80c6aa9d1f4b6324479d5b8\" alt=\"negative 5\"></span> aren’t solutions to the given equation.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.622000+00:00","source_updated_at":"2023-08-02T20:25:59.622000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2f1494c799ca1decbcb94ac7e70aeb91da2c02dfba7cb54dae8e89aee537a8e1\" alt=\"1\"></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e646b570dc3598aa1fe55743f6c749ef456a13deb8575aca77a309272b8cbc26\" alt=\"0\"></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a546b5be2c97283e2d1e93605f422844d5a87f3418a61a7d23019eb596b64f17\" alt=\"negative 2\"></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8d84f0934ecb7d96090b9c086b990db006ef3ed6d80c6aa9d1f4b6324479d5b8\" alt=\"negative 5\"></span></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}}