{"id":"cb_question_bank:7c32d5dc-d4db-4253-821a-7b994756fc6d","source_id":"cb_question_bank","source_item_id":"7c32d5dc-d4db-4253-821a-7b994756fc6d","external_id":"d406296c-cba6-440d-94d6-5bf2accfba2a","ibn":null,"question_id":"771bd0ca","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"5 left parenthesis t plus 3 right parenthesis minus 7 left parenthesis t plus 3 right parenthesis equals 38 What value of t is the solution to the given equation?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"5 left parenthesis t plus 3 right parenthesis minus 7 left parenthesis t plus 3 right parenthesis equals 38\"><mrow><mn>5</mn></mrow><mo>(</mo><mi>t</mi><mo>+</mo><mrow><mn>3</mn></mrow><mo>)</mo><mo>-</mo><mrow><mn>7</mn></mrow><mo>(</mo><mi>t</mi><mo>+</mo><mrow><mn>3</mn></mrow><mo>)</mo><mo>=</mo><mrow><mn>38</mn></mrow></math></p>\n<p style=\"text-align: left;\">What value of <math alttext=\"t\"><mi>t</mi>\n</math> is the solution to the given equation?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"negative 22\"><mo>-</mo><mn>22</mn>\n</math>. The given equation can be rewritten as <math alttext=\"minus 2 left parenthesis t plus 3 right parenthesis equals 38\"><mo>-</mo><mn>2</mn><mfenced><mrow><mi>t</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>=</mo><mn>38</mn></math>. Dividing both sides of this equation by <math alttext=\"negative 2\"><mo>-</mo><mn>2</mn>\n</math> yields <math alttext=\"t plus 3 equals negative 19\"><mi>t</mi><mo>+</mo><mn>3</mn><mo>=</mo><mo>-</mo><mn>19</mn></math>. Subtracting <math alttext=\"3\"><mn>3</mn>\n</math> from both sides of this equation yields <math alttext=\"t equals negative 22\"><mrow>\n\t<mi>t</mi>\n\t<mo>=</mo>\n\t<mo>-</mo><mn>22</mn>\n</mrow>\n</math>. Therefore, <math alttext=\"negative 22\"><mo>-</mo><mn>22</mn>\n</math> is the value of <math alttext=\"t\"><mi>t</mi>\n</math> that is the solution to the given equation.</p>","correct_answer":["-22"],"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}}