{"id":"cb_question_bank:0a047024-b70d-43ac-8d8f-fade14c45deb","source_id":"cb_question_bank","source_item_id":"0a047024-b70d-43ac-8d8f-fade14c45deb","external_id":"d228702c-741e-49d7-ad2d-527046f58b94","ibn":null,"question_id":"52931bfa","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which expression is equivalent to StartFraction 8 x left parenthesis x minus 7 right parenthesis minus 3 left parenthesis x minus 7 right parenthesis Over 2 x minus 14 EndFraction , where x greater than 7 ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Which expression is equivalent to <math alttext=\"StartFraction 8 x left parenthesis x minus 7 right parenthesis minus 3 left parenthesis x minus 7 right parenthesis Over 2 x minus 14 EndFraction\"><mfrac><mrow><mrow><mn>8</mn></mrow><mi>x</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mrow><mn>7</mn></mrow></mrow></mfenced><mo>-</mo><mrow><mn>3</mn></mrow><mfenced><mrow><mi>x</mi><mo>-</mo><mrow><mn>7</mn></mrow></mrow></mfenced></mrow><mrow><mrow><mn>2</mn></mrow><mi>x</mi><mo>-</mo><mrow><mn>14</mn></mrow></mrow></mfrac></math>, where <math alttext=\"x greater than 7\"><mi>x</mi><mo>&gt;</mo><mrow><mn>7</mn></mrow></math>?</p>","rationale_html":"<p>Choice B is correct. The given expression has a common factor of <math alttext=\"2\"><mn>2</mn>\n</math> in the denominator, so the expression can be rewritten as <math alttext=\"StartFraction 8 x left parenthesis x minus 7 right parenthesis minus 3 left parenthesis x minus 7 right parenthesis Over 2 left parenthesis x minus 7 right parenthesis EndFraction\"><mfrac><mrow><mn>8</mn><mi>x</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced><mo>-</mo><mn>3</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced></mrow></mfrac></math>. The three terms in this expression have a common factor of <math alttext=\"left parenthesis x minus 7 right parenthesis\"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced></math>. Since it's given that&nbsp;<math alttext=\"x greater than 7\"><mi>x</mi><mo>&gt;</mo><mn>7</mn></math>, <math alttext=\"x\"><mi>x</mi>\n</math> can't be equal to <math alttext=\"7\"><mn>7</mn>\n</math>, which means <math alttext=\"left parenthesis x minus 7 right parenthesis\"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced></math> can't be equal to <math alttext=\"0\"><mn>0</mn>\n</math>. Therefore, each term in the expression, <math alttext=\"StartFraction 8 x left parenthesis x minus 7 right parenthesis minus 3 left parenthesis x minus 7 right parenthesis Over 2 left parenthesis x minus 7 right parenthesis EndFraction\"><mfrac><mrow><mn>8</mn><mi>x</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced><mo>-</mo><mn>3</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced></mrow></mfrac></math>, can be divided by <math alttext=\"left parenthesis x minus 7 right parenthesis\"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced></math>, which gives&nbsp;<math alttext=\"StartFraction 8 x minus 3 Over 2 EndFraction\"><mfrac><mrow><mn>8</mn><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mn>2</mn></mfrac></math>.</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect&nbsp;and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect&nbsp;and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.821000+00:00","source_updated_at":"2023-08-02T20:25:59.821000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"StartFraction x minus 7 Over 5 EndFraction\"><mfrac><mrow><mi>x</mi><mo>-</mo><mrow><mn>7</mn></mrow></mrow><mrow><mn>5</mn></mrow></mfrac></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"StartFraction 8 x minus 3 Over 2 EndFraction\"><mfrac><mrow><mrow><mn>8</mn></mrow><mi>x</mi><mo>-</mo><mrow><mn>3</mn></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"StartFraction 8 x squared minus 3 x minus 14 Over 2 x minus 14 EndFraction\"><mfrac><mrow><mrow><mn>8</mn></mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mrow><mn>3</mn></mrow><mi>x</mi><mo>-</mo><mrow><mn>14</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow><mi>x</mi><mo>-</mo><mrow><mn>14</mn></mrow></mrow></mfrac></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"StartFraction 8 x squared minus 3 x minus 77 Over 2 x minus 14 EndFraction\"><mfrac><mrow><mrow><mn>8</mn></mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mrow><mn>3</mn></mrow><mi>x</mi><mo>-</mo><mrow><mn>77</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow><mi>x</mi><mo>-</mo><mrow><mn>14</mn></mrow></mrow></mfrac></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. 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