{"id":"cb_practice_pdf:t10-math-m1-q27","source_id":"cb_practice_pdf","source_item_id":"t10-math-m1-q27","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":"spr","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-10","module_number":1,"position":27,"stem":"x(x+1)−56 = 4x(x−7) What is the sum of the solutions to the given equation? OP","stimulus":"","stimulus_html":null,"stem_html":"

x(x+1)−56 = 4x(x−7) What is the sum of the solutions to the given equation? OP

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29 The correct answer is 3. Applying the distributive property to the left-hand side +1 -56 2+ -56 of the given equation, x^x h , yields x x . Applying the distributive 4 -7 4 2-28 property to the right-hand side of the given equation, x^x h, yields x x. 2+ -56=4 2-28 Thus, the equation becomes x x x x. Combining like terms on the 0= 4 2- 2 + -28 - +56 left- and right-hand sides of this equation yields ^ x x h ^ x xh , 3 2-29 +56=0 2+ + =0 or x x . For a quadratic equation in the form ax bx c , where a, b, and c are constants, the quadratic formula gives the solutions to the =_ - b ! b 2-4 aci -29 56 equation in the form x 2 . Substituting 3 for a, for b, and for a 3 2-29 +56=0 c from the equation x x into the quadratic formula yields x =_ 29! ^ -2 2 9 h3 2-4 ^ 3 h^ 56 hi , or x = 2 6 9!1 6 3 . It follows that the solutions to the given ^ h 29 13 29 13 + - equation are 6 6 and 6 6. Adding these two solutions gives the sum of the 29 13 29 13 29 29 29 + + - + solutions: 6 6 6 6, which is equivalent to 6 6, or 3. Note that 29/3, 9.666, and 9.667 are examples of ways to enter a correct answer. 39 SAT PRACTICE TEST #10 ANSWER EXPLANATIONS

","correct_answer":["3"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"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}}