{"id":"cb_question_bank:307e1c7f-87c2-4c82-9c5e-2db49eb15c11","source_id":"cb_question_bank","source_item_id":"307e1c7f-87c2-4c82-9c5e-2db49eb15c11","external_id":"214d64ec-0e1a-4a3f-8fcb-73b3eecf4a6b","ibn":null,"question_id":"5c94e6fa","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"E","score_band":3,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"3 x plus 21 equals 3 x plus k In the given equation, k is a constant. The equation has infinitely many solutions. What is the value of k ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"3 x plus 21 equals 3 x plus k\"><mrow><mn>3</mn></mrow><mi>x</mi><mo>+</mo><mrow><mn>21</mn></mrow><mo>=</mo><mrow><mn>3</mn></mrow><mi>x</mi><mo>+</mo><mi>k</mi></math></p>\n<p style=\"text-align: left;\">In the given equation, <math alttext=\"k\"><mi>k</mi>\n</math> is a constant. The equation has infinitely many solutions. What is the value of <math alttext=\"k\"><mi>k</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"21\"><mn>21</mn>\n</math>. It's given that the equation <math alttext=\"3 x plus 21 equals 3 x plus k\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>3</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>21</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>3</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mi>k</mi>\n\t</mrow>\n</mrow>\n</math> has infinitely many solutions. If an equation in one variable has infinitely many solutions, then the equation is true for any value of the variable. Subtracting <math alttext=\"3 x\"><mrow>\n\t<mn>3</mn>\n\t<mi>x</mi>\n</mrow>\n</math> from both sides of the given equation yields <math alttext=\"k equals 21\"><mrow>\n\t<mi>k</mi>\n\t<mo>=</mo>\n\t<mn>21</mn>\n</mrow>\n</math>. Since this equation must be true for any value of <math alttext=\"x\"><mi>x</mi>\n</math>, the value of <math alttext=\"k\"><mi>k</mi>\n</math> is <math alttext=\"21\"><mn>21</mn>\n</math>.</p>","correct_answer":["21"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.809000+00:00","source_updated_at":"2023-08-02T20:25:59.809000+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}}