{"id":"cb_question_bank:a7617033-7abc-44a4-9ee8-225a9f3a077a","source_id":"cb_question_bank","source_item_id":"a7617033-7abc-44a4-9ee8-225a9f3a077a","external_id":"830cf5a2-7b06-43e1-bf6c-fb7814a69db0","ibn":null,"question_id":"aee9fd2d","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If StartFraction x plus 6 Over 3 EndFraction equals StartFraction x plus 6 Over 13 EndFraction , the value of x plus 6 is between which of the following pairs of values?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">If <math alttext=\"StartFraction x plus 6 Over 3 EndFraction equals StartFraction x plus 6 Over 13 EndFraction\"><mfrac><mrow><mi>x</mi><mo>+</mo><mrow><mn>6</mn></mrow></mrow><mrow><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mrow><mn>6</mn></mrow></mrow><mrow><mn>13</mn></mrow></mfrac></math>, the value of <math alttext=\"x plus 6\"><mi>x</mi><mo>+</mo><mrow><mn>6</mn></mrow></math> is between which of the following pairs of values?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. Multiplying both sides of the given equation by <math alttext=\"left parenthesis 3 right parenthesis left parenthesis 13 right parenthesis\"><mfenced><mn>3</mn></mfenced><mfenced><mn>13</mn></mfenced></math>, or <math alttext=\"39\"><mn>39</mn>\n</math>, yields <math alttext=\"left parenthesis 39 right parenthesis left parenthesis StartFraction x plus 6 Over 3 EndFraction right parenthesis equals left parenthesis 39 right parenthesis left parenthesis StartFraction x plus 6 Over 13 EndFraction right parenthesis\"><mfenced><mn>39</mn></mfenced><mfenced><mfrac><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mn>3</mn></mfrac></mfenced><mo>=</mo><mfenced><mn>39</mn></mfenced><mfenced><mfrac><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mn>13</mn></mfrac></mfenced></math>, or&nbsp;<math alttext=\"13 left parenthesis x plus 6 right parenthesis equals 3 left parenthesis x plus 6 right parenthesis\"><mn>13</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced><mo>=</mo><mn>3</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced></math>. Subtracting&nbsp;<math alttext=\"3 left parenthesis x plus 6 right parenthesis\"><mn>3</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced></math> from both sides of this equation yields&nbsp;<math alttext=\"10 left parenthesis x plus 6 right parenthesis equals 0\"><mn>10</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math>. Dividing both sides of this equation by <math alttext=\"10\"><mn>10</mn>\n</math> yields <math alttext=\"x plus 6 equals 0\"><mi>x</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>0</mn></math>. Therefore, if&nbsp;<math alttext=\"StartFraction x plus 6 Over 3 EndFraction equals StartFraction x plus 6 Over 13 EndFraction\"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mn>3</mn></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mn>13</mn></mfrac></math>, then the value of <math alttext=\"x plus 6\"><mi>x</mi><mo>+</mo><mn>6</mn></math> is <math alttext=\"0\"><mn>0</mn>\n</math>. It follows that of the given choices, the value of <math alttext=\"x plus 6\"><mi>x</mi><mo>+</mo><mn>6</mn></math> is between <math alttext=\"negative 2\"><mo>-</mo><mn>2</mn>\n</math> and <math alttext=\"2\"><mn>2</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.809000+00:00","source_updated_at":"2023-08-02T20:25:59.809000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"negative 7\"><mo>-</mo><mn>7</mn>\n</math> and <math alttext=\"negative 3\"><mo>-</mo><mn>3</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"negative 2\"><mo>-</mo><mn>2</mn>\n</math> and <math alttext=\"2\"><mn>2</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"2\"><mn>2</mn>\n</math> and <math alttext=\"7\"><mn>7</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"8\"><mn>8</mn>\n</math> and <math alttext=\"13\"><mn>13</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}}