{"id":"cb_question_bank:77004eb2-52b1-431b-8d22-9fe73211d2af","source_id":"cb_question_bank","source_item_id":"77004eb2-52b1-431b-8d22-9fe73211d2af","external_id":null,"ibn":"020349-DC","question_id":"550b352c","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"E","score_band":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"How many solutions exist to the equation shown above?","stimulus":"10 equals, 2 x plus 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/e2afbec829a7a7be34f6a444eeff5ec9d33cdf03373a278fcdaee172c0f96ee0\" alt=\"10 equals, 2 x plus 4\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">How many solutions exist to the equation shown above?</p>\n","rationale_html":"<p>Choice B is correct. Subtracting 4 from each side of the given equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e8a1325ab0c40b865a38caf535802264c0abad5f6a7f8053ab8edb4e3c4de265\" alt=\"6 equals 2 x\"></span>, or <span class=\"italic\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ceba1165e53a8baa1cf03f75cde85da34750b8ab2728ef25385d77f80f8276c5\" alt=\"x equals 3\"></span></span>, so the equation has a unique solution of <span class=\"italic\"></span><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. Since 3 is a value of <span class=\"italic\">x</span> that satisfies the given equation, the equation has at least 1 solution. Choice C is incorrect. Linear equations can have 0, 1, or infinitely many solutions; no linear equation has exactly 3 solutions. Choice D is incorrect. If a linear equation has infinitely many solutions, it can be reduced to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4916ff43d6476b41ff006070114c9bf37a8dd2fa857adf0288c2f5f5c1da1037\" alt=\"0 equals 0\"></span>. This equation reduces to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ceba1165e53a8baa1cf03f75cde85da34750b8ab2728ef25385d77f80f8276c5\" alt=\"x equals 3\"></span>, so there is only 1 solution.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.616000+00:00","source_updated_at":"2023-08-02T20:25:59.616000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">None</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">Exactly 1</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">Exactly 3</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">Infinitely many</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}}