{"id":"cb_question_bank:e3ab0e0b-9dc0-4eb8-ae61-5552c39b8189","source_id":"cb_question_bank","source_item_id":"e3ab0e0b-9dc0-4eb8-ae61-5552c39b8189","external_id":null,"ibn":"027085-DC","question_id":"e53870b6","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":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the given equation, k is a constant. If the equation has infinitely many solutions, what is the value of k ?","stimulus":"6 x plus k, equals, 6 x plus 5","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/ad0c4f6fc76b5b903ab05868581feb8969d6bfa10c6c75a8c70758705851ab65\" alt=\"6 x plus k, equals, 6 x plus 5\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">In the given equation, <span class=\"italic\">k</span> is a constant. If the equation has infinitely many solutions, what is the value of <span class=\"italic\">k</span> ?</p>\n","rationale_html":"<p>The correct answer is 5. Subtracting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1cc34fe7838fa24cd243dff62448a1211316e727f3ef01060a526d2d44f47a2b\" alt=\"6 x\"></span> from both sides of the given equation gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f9ad746316c95d97c528c729003117b0de250d840e78abf6dcdd9eb315dcdad1\" alt=\"k equals 5\"></span>, so for any value of <span class=\"italic\">x</span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ad0c4f6fc76b5b903ab05868581feb8969d6bfa10c6c75a8c70758705851ab65\" alt=\"6 x plus k, equals, 6 x plus 5 \"></span> if and only if <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f9ad746316c95d97c528c729003117b0de250d840e78abf6dcdd9eb315dcdad1\" alt=\"k equals 5\"></span>. Therefore, if the given equation has infinitely many solutions, the value of <span class=\"italic\">k</span> is 5.</p>\n","correct_answer":["5"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.621000+00:00","source_updated_at":"2023-08-02T20:25:59.621000+00:00","options":[],"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}}