{"id":"cb_question_bank:fefd0641-1549-4867-b848-7eaf6422e3c6","source_id":"cb_question_bank","source_item_id":"fefd0641-1549-4867-b848-7eaf6422e3c6","external_id":"295f9556-4a27-49ca-b269-fb8917b7e050","ibn":null,"question_id":"d4d513ff","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"E","score_band":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which expression is equivalent to 12 x plus 27 ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Which expression is equivalent to <math alttext=\"12 x plus 27\"><mrow>\n\t<mrow>\n\t\t<mn>12</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>27</mn>\n</mrow>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. Each term in the given expression, <math alttext=\"12 x plus 27\"><mrow>\n\t<mrow>\n\t\t<mn>12</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>27</mn>\n</mrow>\n</math>, has a common factor of <math alttext=\"3\"><mn>3</mn>\n</math>. Therefore, the expression can be rewritten as&nbsp;<math alttext=\"3 left parenthesis 4 x right parenthesis plus 3 left parenthesis 9 right parenthesis\"><mn>3</mn><mfenced><mrow><mn>4</mn><mi>x</mi></mrow></mfenced><mo>+</mo><mn>3</mn><mfenced><mn>9</mn></mfenced></math>, or&nbsp;<math alttext=\"3 left parenthesis 4 x plus 9 right parenthesis\"><mn>3</mn><mfenced><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced></math>. Thus, the expression&nbsp;<math alttext=\"3 left parenthesis 4 x plus 9 right parenthesis\"><mn>3</mn><mfenced><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfenced></math> is equivalent to the given expression.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This expression is equivalent to <math alttext=\"108 x plus 12\"><mrow>\n\t<mrow>\n\t\t<mn>108</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>12</mn>\n</mrow>\n</math>, not <math alttext=\"12 x plus 27\"><mrow>\n\t<mrow>\n\t\t<mn>12</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>27</mn>\n</mrow>\n</math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This expression is equivalent to <math alttext=\"324 x plus 27\"><mrow>\n\t<mrow>\n\t\t<mn>324</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>27</mn>\n</mrow>\n</math>, not <math alttext=\"12 x plus 27\"><mrow>\n\t<mrow>\n\t\t<mn>12</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>27</mn>\n</mrow>\n</math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This expression is equivalent to <math alttext=\"27 x plus 72\"><mrow>\n\t<mrow>\n\t\t<mn>27</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>72</mn>\n</mrow>\n</math>, not <math alttext=\"12 x plus 27\"><mrow>\n\t<mrow>\n\t\t<mn>12</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>27</mn>\n</mrow>\n</math>.</p>","correct_answer":["C"],"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=\"12 left parenthesis 9 x plus 1 right parenthesis\"><mrow><mn>12</mn></mrow><mfenced><mrow><mrow><mn>9</mn></mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"27 left parenthesis 12 x plus 1 right parenthesis\"><mrow><mn>27</mn></mrow><mfenced><mrow><mrow><mn>12</mn></mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"3 left parenthesis 4 x plus 9 right parenthesis\"><mrow><mn>3</mn></mrow><mfenced><mrow><mrow><mn>4</mn></mrow><mi>x</mi><mo>+</mo><mrow><mn>9</mn></mrow></mrow></mfenced></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"3 left parenthesis 9 x plus 24 right parenthesis\"><mrow><mn>3</mn></mrow><mfenced><mrow><mrow><mn>9</mn></mrow><mi>x</mi><mo>+</mo><mrow><mn>24</mn></mrow></mrow></mfenced></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}}