{"id":"cb_question_bank:c38b8af5-7270-4263-96a9-89fbb628a690","source_id":"cb_question_bank","source_item_id":"c38b8af5-7270-4263-96a9-89fbb628a690","external_id":"48cc6531-d8e0-4647-ac35-96cd60c2ea06","ibn":null,"question_id":"c7789423","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"E","score_band":2,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"StartAbsoluteValue x minus 2 EndAbsoluteValue equals 9 What is one possible solution to the given equation?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"StartAbsoluteValue x minus 2 EndAbsoluteValue equals 9\"><mrow>\n\t<mrow>\n\t\t<mfenced>\n\t\t\t<mrow>\n\t\t\t\t<mi>x</mi>\n\t\t\t\t<mo>-</mo>\n\t\t\t\t<mn>2</mn>\n\t\t\t</mrow>\n\t\t</mfenced>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>9</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: left;\">What is one possible solution to the given equation?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"11\"><mn>11</mn>\n</math> or <math alttext=\"negative 7\"><mo>-</mo><mn>7</mn>\n</math>. By the definition of absolute value, if <math alttext=\"StartAbsoluteValue x minus 2 EndAbsoluteValue equals 9\"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>9</mn></math>, then <math alttext=\"x minus 2 equals 9\"><mi>x</mi><mo>-</mo><mn>2</mn><mo>=</mo><mn>9</mn></math> or <math alttext=\"x minus 2 equals negative 9\"><mi>x</mi><mo>-</mo><mn>2</mn><mo>=</mo><mo>-</mo><mn>9</mn></math>. Adding <math alttext=\"2\"><mn>2</mn>\n</math> to both sides of the equation&nbsp;<math alttext=\"x minus 2 equals 9\"><mi>x</mi><mo>-</mo><mn>2</mn><mo>=</mo><mn>9</mn></math> yields <math alttext=\"x equals 11\"><mi>x</mi><mo>=</mo><mn>11</mn></math>. Adding <math alttext=\"2\"><mn>2</mn>\n</math> to both sides of the equation&nbsp;<math alttext=\"x minus 2 equals negative 9\"><mi>x</mi><mo>-</mo><mn>2</mn><mo>=</mo><mo>-</mo><mn>9</mn></math> yields <math alttext=\"x equals negative 7\"><mi>x</mi><mo>=</mo><mo>-</mo><mn>7</mn></math>. Thus, the given equation,&nbsp;<math alttext=\"StartAbsoluteValue x minus 2 EndAbsoluteValue equals 9\"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>9</mn></math>, has two possible solutions, <math alttext=\"11\"><mn>11</mn>\n</math> and <math alttext=\"negative 7\"><mo>-</mo><mn>7</mn>\n</math>. Note that 11 and -7 are examples of ways to enter a correct answer.</p>","correct_answer":["11","-7"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.823000+00:00","source_updated_at":"2023-08-02T20:25:59.823000+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}}