{"id":"cb_practice_pdf:t7-math-m2-q23","source_id":"cb_practice_pdf","source_item_id":"t7-math-m2-q23","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-7","module_number":2,"position":23,"stem":"- - - - - - -_=_b−15x - - The linear function g is defined by g(x), g(c+7) = where b is a constant. If c/4, where c is a constant, which of the following expressions represents the value of b?","stimulus":"","stimulus_html":null,"stem_html":"<p>- - - - - - -_=_b−15x - - The linear function g is defined by g(x), g(c+7) = where b is a constant. If c/4, where c is a constant, which of the following expressions represents the value of b?</p>","rationale_html":"<p>Choice C is correct. It’s given that g^c +7 h = 4c . Therefore, for the given linear = + =c + c function g, when x c 7, g^xh . Substituting c 7 for x and for g^xh in 4 4 g^xh = b -15 x yields 4c= b -15 ^c +7 h. Applying the distributive property to the right-hand side of this equation yields 4c= b -15 c -105 . Adding 15 c to both sides of this equation yields 4c+15 c = b -105 . Adding 105 to both sides of this equation yields 4c+15 c +105= b, or 6 4 1 c+105= b. Therefore, the expression that represents the value of b is 6 4 1 c+105 . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>15c/4 +7</p>","ord":0},{"label":"B","content_html":"<p>19c/4 +105</p>","ord":1},{"label":"C","content_html":"<p>61c/4 15c+105</p>","ord":2},{"label":"D","content_html":"","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}