{"id":"cb_question_bank:1dbf3ca7-43e1-4758-859b-a4383833730e","source_id":"cb_question_bank","source_item_id":"1dbf3ca7-43e1-4758-859b-a4383833730e","external_id":null,"ibn":"11064-DC","question_id":"f65288e8","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":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If x is a solution to the given equation, which of the following is a possible value of x plus 5 ?","stimulus":"the fraction with numerator 1, and denominator x squared, plus 10 x, plus 25, end fraction, equals 4","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/793ba5087be8e2e4caf58537c0df62f38c8e89548bbe566c8cf1d3518f0d37c5\" alt=\"the fraction with numerator 1, and denominator x squared, plus 10 x, plus 25, end fraction, equals 4\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">If <span class=\"italic \">x</span> is a solution to the given equation, which of the following is a possible value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f774c766794ca6883d8aa2c0e5603f5668852b808fcfb2f4940cd18d6758cb03\" alt=\"x plus 5\"></span> ?</p>\n","rationale_html":"<p>Choice A is correct. The given equation can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/263ca9a6d2a99b32978dfe1e82df093626ac256c6f97e2b834a74b2b4e2ea760\" alt=\"the fraction 1 over, open parenthesis, x plus 5, close parenthesis, squared, end fraction, equals 4\"></span>. Multiplying both sides of this equation by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce35c2006c3047da13b556fa0f50c64bf3808ae29b6da17edabbe973ae0249ce\" alt=\"open parenthesis, x plus 5, close parenthesis, squared \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/508ebb9addb631a59b6fe36ce090b4a81747f48ff3d6964126281b815784d701\" alt=\"1 equals, 4 times, open parenthesis, x plus 5, close parenthesis, squared\"></span>. Dividing both sides of this equation by 4 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7563587462b9aec69329a171040cda3031e478bc557aa2984fd91ffb2f8f2a93\" alt=\"one fourth equals, open parenthesis, x plus 5, close parenthesis, squared\"></span>. Taking the square root of both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/80026dedb91855bf615a528ee73b1a54a3739c66a1e92bc556ea46deefa7fccd\" alt=\"one half equals, x plus 5 \"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/59c52a13adf579efaddb12d9c10693474fc6449cc8f8cc98072cf63a5652f480\" alt=\"negative one half equals, x plus 5\"></span>. Therefore, a possible value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f774c766794ca6883d8aa2c0e5603f5668852b808fcfb2f4940cd18d6758cb03\" alt=\"x plus 5 \"></span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/acd304db4db3ee4a427462753769f86b9941b320104a3856da731c39db5d894c\" alt=\"one half\"></span>.<br>\nChoices B, C, and D are incorrect and may result from computational or conceptual errors.</p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.638000+00:00","source_updated_at":"2023-08-02T20:25:59.638000+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/acd304db4db3ee4a427462753769f86b9941b320104a3856da731c39db5d894c\" alt=\"one half\"></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/c07dd1b3634a62972e13523df568fe0411662f40a588412490b6b3c77df4e541\" alt=\"five halves\"></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/37a2f4f1fc31ac525401c6495d04b09ede20153a22a52b0992f41ae9a4b8501a\" alt=\"nine halves\"></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/da105c49f141078ad3026c419259b1f6e4b627a3427a84475c4e138dfcb56ecc\" alt=\"eleven halves\"></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}}