{"id":"cb_question_bank:0c7bf634-cf0a-4c21-8589-65fd3dad2906","source_id":"cb_question_bank","source_item_id":"0c7bf634-cf0a-4c21-8589-65fd3dad2906","external_id":"c9ba957d-0aef-4fba-942a-16b7f4d4d31b","ibn":null,"question_id":"3a9d60b2","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":"H","score_band":6,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"2 StartAbsoluteValue 4 minus x EndAbsoluteValue plus 3 StartAbsoluteValue 4 minus x EndAbsoluteValue equals 25 What is the positive solution to the given equation?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"2 StartAbsoluteValue 4 minus x EndAbsoluteValue plus 3 StartAbsoluteValue 4 minus x EndAbsoluteValue equals 25\"><mrow><mn>2</mn></mrow><mfenced><mrow><mrow><mn>4</mn></mrow><mo>-</mo><mi>x</mi></mrow></mfenced><mo>+</mo><mrow><mn>3</mn></mrow><mfenced><mrow><mrow><mn>4</mn></mrow><mo>-</mo><mi>x</mi></mrow></mfenced><mo>=</mo><mrow><mn>25</mn></mrow></math></p>\n<p style=\"text-align: left;\">What is the positive solution to the given equation?</p>","rationale_html":"<p>The correct answer is <math alttext=\"9\"><mn>9</mn>\n</math>. The given equation can be rewritten as&nbsp;<math alttext=\"5 StartAbsoluteValue 4 minus x EndAbsoluteValue equals 25\"><mn>5</mn><mfenced><mrow><mn>4</mn><mo>-</mo><mi>x</mi></mrow></mfenced><mo>=</mo><mn>25</mn></math>. Dividing each side of this equation by <math alttext=\"5\"><mn>5</mn>\n</math> yields&nbsp;<math alttext=\"StartAbsoluteValue 4 minus x EndAbsoluteValue equals 5\"><mfenced><mrow><mn>4</mn><mo>-</mo><mi>x</mi></mrow></mfenced><mo>=</mo><mn>5</mn></math>. By the definition of absolute value, if <math alttext=\"StartAbsoluteValue 4 minus x EndAbsoluteValue equals 5\"><mfenced><mrow><mn>4</mn><mo>-</mo><mi>x</mi></mrow></mfenced><mo>=</mo><mn>5</mn></math>, then <math alttext=\"4 minus x equals 5\"><mn>4</mn><mo>-</mo><mi>x</mi><mo>=</mo><mn>5</mn></math> or <math alttext=\"4 minus x equals negative 5\"><mn>4</mn><mo>-</mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>5</mn></math>. Subtracting <math alttext=\"4\"><mn>4</mn>\n</math> from each side of the equation&nbsp;<math alttext=\"4 minus x equals 5\"><mn>4</mn><mo>-</mo><mi>x</mi><mo>=</mo><mn>5</mn></math> yields&nbsp;<math alttext=\"negative x equals 1\"><mo>-</mo><mi>x</mi><mo>=</mo><mn>1</mn></math>. Dividing each side of this equation by <math alttext=\"negative 1\"><mo>-</mo><mn>1</mn>\n</math> yields&nbsp;<math alttext=\"x equals negative 1\"><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn></math>. Similarly, subtracting <math alttext=\"4\"><mn>4</mn>\n</math> from each side of the equation <math alttext=\"4 minus x equals negative 5\"><mn>4</mn><mo>-</mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>5</mn></math> yields&nbsp;<math alttext=\"negative x equals negative 9\"><mo>-</mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>9</mn></math>. Dividing each side of this equation by <math alttext=\"negative 1\"><mo>-</mo><mn>1</mn>\n</math> yields&nbsp;<math alttext=\"x equals 9\"><mi>x</mi><mo>=</mo><mn>9</mn></math>. Therefore, since the two solutions to the given equation are <math alttext=\"negative 1\"><mo>-</mo><mn>1</mn>\n</math> and <math alttext=\"9\"><mn>9</mn>\n</math>, the positive solution to the given equation is <math alttext=\"9\"><mn>9</mn>\n</math>.</p>","correct_answer":["9"],"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}}