{"id":"cb_question_bank:ea3f7dd0-4961-4bb2-a04b-81311220add2","source_id":"cb_question_bank","source_item_id":"ea3f7dd0-4961-4bb2-a04b-81311220add2","external_id":"63a0e21a-3df7-463a-b0b7-6bf2eeefbcb4","ibn":null,"question_id":"eafdbbbd","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":"one fourth left parenthesis x plus 5 right parenthesis minus one third left parenthesis x plus 5 right parenthesis equals negative 7 What value of x is the solution to the given equation?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"one fourth left parenthesis x plus 5 right parenthesis minus one third left parenthesis x plus 5 right parenthesis equals negative 7\"><mfrac><mn>1</mn><mrow><mn>4</mn></mrow></mfrac><mfenced><mrow><mi>x</mi><mo>+</mo><mrow><mn>5</mn></mrow></mrow></mfenced><mo>-</mo><mfrac><mn>1</mn><mrow><mn>3</mn></mrow></mfrac><mfenced><mrow><mi>x</mi><mo>+</mo><mrow><mn>5</mn></mrow></mrow></mfenced><mo>=</mo><mo>-</mo><mrow><mn>7</mn></mrow></math></p>\n<p style=\"text-align: left;\">What value of <math alttext=\"x\"><mi>x</mi>\n</math>&nbsp;is the solution to the given equation?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. For the given equation,&nbsp;<math alttext=\"left parenthesis x plus 5 right parenthesis\"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math> is a factor of both terms on the left-hand side. Therefore, the given equation can be rewritten as <math alttext=\"left parenthesis one fourth minus one third right parenthesis left parenthesis x plus 5 right parenthesis equals negative 7\"><mfenced><mrow><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mo>-</mo><mn>7</mn></math>, or <math alttext=\"left parenthesis three twelfths minus four twelfths right parenthesis left parenthesis x plus 5 right parenthesis equals negative 7\"><mfenced><mrow><mfrac><mn>3</mn><mn>12</mn></mfrac><mo>-</mo><mfrac><mn>4</mn><mn>12</mn></mfrac></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mo>-</mo><mn>7</mn></math>, which is equivalent to&nbsp;<math alttext=\"minus one twelfth left parenthesis x plus 5 right parenthesis equals negative 7\"><mo>-</mo><mfrac><mn>1</mn><mn>12</mn></mfrac><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mo>-</mo><mn>7</mn></math>. Multiplying both sides of this equation by <math alttext=\"negative 12\"><mo>-</mo><mn>12</mn>\n</math> yields <math alttext=\"x plus 5 equals 84\"><mi>x</mi><mo>+</mo><mn>5</mn><mo>=</mo><mn>84</mn></math>. Subtracting <math alttext=\"5\"><mn>5</mn>\n</math> from both sides of this equation yields <math alttext=\"x equals 79\"><mi>x</mi><mo>=</mo><mn>79</mn></math>.&nbsp;</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This is the value of <math alttext=\"x\"><mi>x</mi>\n</math> for which the left-hand side of the given equation equals <math alttext=\"seven twelfths\"><mfrac>\n\t<mn>7</mn>\n\t<mn>12</mn>\n</mfrac>\n</math>, not <math alttext=\"negative 7\"><mo>-</mo><mn>7</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is the value of <math alttext=\"x\"><mi>x</mi>\n</math> for which the left-hand side of the given equation equals <math alttext=\"0\"><mn>0</mn>\n</math>, not <math alttext=\"negative 7\"><mo>-</mo><mn>7</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is the value of <math alttext=\"x\"><mi>x</mi>\n</math> for which the left-hand side of the given equation equals <math alttext=\"negative StartFraction 209 Over 12 EndFraction\"><mrow>\n\t<mo>-</mo>\n\t<mfrac>\n\t\t<mn>209</mn>\n\t\t<mn>12</mn>\n\t</mfrac>\n</mrow>\n</math>, not <math alttext=\"negative 7\"><mo>-</mo><mn>7</mn>\n</math>.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.810000+00:00","source_updated_at":"2023-08-02T20:25:59.810000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"negative 12\"><mo>-</mo><mn>12</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"negative 5\"><mo>-</mo><mn>5</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"79\"><mn>79</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"204\"><mn>204</mn>\n</math></p>","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}}