{"id":"cb_question_bank:44e032e4-a809-46c6-857e-a101e0a7b888","source_id":"cb_question_bank","source_item_id":"44e032e4-a809-46c6-857e-a101e0a7b888","external_id":"e9630635-49ff-4317-9dc7-81fb2b4d2e19","ibn":null,"question_id":"e6cb2402","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"3 left parenthesis k x plus 13 right parenthesis equals StartFraction 48 Over 17 EndFraction x plus 36 In the given equation, k is a constant. The equation has no solution. What is the value of k ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"3 left parenthesis k x plus 13 right parenthesis equals StartFraction 48 Over 17 EndFraction x plus 36\"><mn>3</mn><mo>(</mo><mi>k</mi><mi>x</mi><mo>+</mo><mrow><mn>13</mn></mrow><mo>)</mo><mo>=</mo><mfrac>\n\t<mn>48</mn>\n\t<mn>17</mn>\n</mfrac>\n<mrow>\n\t<mi>x</mi>\n\t<mo>+</mo>\n\t<mn>36</mn>\n</mrow>\n</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 no solution. 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=\"StartFraction 16 Over 17 EndFraction\"><mfrac><mn>16</mn><mn>17</mn></mfrac></math>. It's given that the equation <math alttext=\"3 left parenthesis k x plus 13 right parenthesis equals StartFraction 48 Over 17 EndFraction x plus 36\"><mn>3</mn><mfenced><mrow><mi>k</mi><mi>x</mi><mo>+</mo><mn>13</mn></mrow></mfenced><mo>=</mo><mfrac><mn>48</mn><mn>17</mn></mfrac><mi>x</mi><mo>+</mo><mn>36</mn></math> has no solution. A linear equation in the form&nbsp;<math alttext=\"a x plus b equals c x plus d\"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mo>=</mo><mi>c</mi><mi>x</mi><mo>+</mo><mi>d</mi></math>, where <math alttext=\"a\"><mi>a</mi>\n</math>, <math alttext=\"b\"><mi>b</mi>\n</math>, <math alttext=\"c\"><mi>c</mi>\n</math>, and <math alttext=\"d\"><mi>d</mi>\n</math> are constants, has no solution only when the coefficients of <math alttext=\"x\"><mi>x</mi>\n</math> on each side of the equation are equal and the constant terms aren't equal. Dividing both sides of the given equation by <math alttext=\"3\"><mn>3</mn>\n</math> yields <math alttext=\"k x plus 13 equals StartFraction 48 Over 51 EndFraction x plus StartFraction 36 Over 3 EndFraction\"><mi>k</mi><mi>x</mi><mo>+</mo><mn>13</mn><mo>=</mo><mfrac><mn>48</mn><mn>51</mn></mfrac><mi>x</mi><mo>+</mo><mfrac><mn>36</mn><mn>3</mn></mfrac></math>, or&nbsp;<math alttext=\"k x plus 13 equals StartFraction 16 Over 17 EndFraction x plus 12\"><mi>k</mi><mi>x</mi><mo>+</mo><mn>13</mn><mo>=</mo><mfrac><mn>16</mn><mn>17</mn></mfrac><mi>x</mi><mo>+</mo><mn>12</mn></math>. Since the coefficients of <math alttext=\"x\"><mi>x</mi>\n</math> on each side of the equation must be equal, it follows that the value of <math alttext=\"k\"><mi>k</mi>\n</math> is <math alttext=\"StartFraction 16 Over 17 EndFraction\"><mfrac>\n\t<mn>16</mn>\n\t<mn>17</mn>\n</mfrac>\n</math>. Note that 16/17, .9411, .9412, and 0.941 are examples of ways to enter a correct answer.</p>","correct_answer":[".9411",".9412","16/17"],"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}}