{"id":"cb_question_bank:3884e6ef-9feb-4172-a182-a388bc3c2a5b","source_id":"cb_question_bank","source_item_id":"3884e6ef-9feb-4172-a182-a388bc3c2a5b","external_id":null,"ibn":"027743-DC","question_id":"12ee1edc","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the given equation, b is a constant. If the equation has no solution, what is the value of b ?","stimulus":"open parenthesis, b minus 2, close parenthesis, times x, equals 8","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/53581ecdfaf85bd7b7eb92bea68dae5d17b2c13a775c3a6f0ede1c015306a135\" alt=\"open parenthesis, b minus 2, close parenthesis, times x, equals 8\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">In the given equation, <span class=\"italic\">b</span> is a constant. If the equation has no solution, what is the value of <span class=\"italic\">b</span> ?</p>\n","rationale_html":"<p>Choice A is correct. This equation has no solution when there is no value of <span class=\"italic\">x</span> that produces a true statement. Solving the given equation for <span class=\"italic\">x</span> by dividing both sides by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6faa385519d221c504036d3069e914c05aa660ca83cf0b96890443996f8211ea\" alt=\"open parenthesis, b minus 2, close parenthesis\"></span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/59a0243082ff212038045183d8d36cd0a10e5ecbd35f92e25dca2175a4374f8f\" alt=\"x equals, the fraction with numerator 8, and denominator, open parenthesis, b minus 2, close parenthesis\"></span>. When <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/797dca7180231512af6a76eb04bfcd4038f6ce057551dd954b8765b311f9e3ba\" alt=\"open parenthesis, b minus 2, close parenthesis, equals 0\"></span>, the right-hand side of this equation will be undefined, and the equation will have no solution. Therefore, when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9575f4491dd1ea691fb892d943a6559484f8c037cb47b520371c8479da185906\" alt=\"b equals 2\"></span>, there is no value of <span class=\"italic\">x</span> that satisfies the given equation.</p><p>Choices B, C, and D are incorrect. Substituting 4, 6, and 10 for <span class=\"italic\">b</span> in the given equation yields exactly one solution, rather than no solution, for <span class=\"italic\">x</span>. For example, substituting 4 for <span class=\"italic\">b</span> in the given equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4ecd2ea4259b665270c3e12f3de6eb57193ac533d260c7a445eee494897b40bf\" alt=\"open parenthesis, 4 minus 2, close parenthesis, times x, equals 8\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b7c82acbf4c468ec58b37b64f51d444895db1a9c8f03e15f563bcee7e3eb2880\" alt=\"2 x equals 8\"></span>. Dividing both sides of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b7c82acbf4c468ec58b37b64f51d444895db1a9c8f03e15f563bcee7e3eb2880\" alt=\"2 x equals 8\"></span> by 2 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7d90bc5cab99d91a4fc94163803642158e44f5a08bde8400e28498891da16def\" alt=\"x equals 4\"></span>. Similarly, if <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4b04b642b9e39e58667e0a0bf8e16d7eeda8cca2d3dfdbdc737044046f4514af\" alt=\"b equals 6 \"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b766972f5d80cf0d7519b0d67af9a82fe8582c6f2fe2520db54e5807a8a0bba3\" alt=\"b equals 10\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/401169281090f4f1d9aafeeb928524e672d737cdce814b4e9256c5e06a42d325\" alt=\"x equals 2 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span>, respectively.</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 \">2</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">4</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">6</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">10</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}}