{"id":"cb_practice_pdf:t4-math-m2-q17","source_id":"cb_practice_pdf","source_item_id":"t4-math-m2-q17","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-4","module_number":2,"position":17,"stem":"−3x+ 21px = 84 In the given equation, p is a constant. The equation has no solution. What is the value of p?","stimulus":"","stimulus_html":null,"stem_html":"<p>−3x+ 21px = 84 In the given equation, p is a constant. The equation has no solution. What is the value of p?</p>","rationale_html":"<p>Choice B is correct. A linear equation in one variable has no solution if and only if the equation is false; that is, when there is no value of x that produces a true - + = statement. It’s given that in the equation 3x 21px 84, p is a constant and the equation has no solution for x. Therefore, the value of the constant p is one - that results in a false equation. Factoring out the common factor of 3x on the - ( - )= left-hand side of the given equation yields 3x 1 7p 84. Dividing both sides - ( - )=- of this equation by 3 yields x 1 7p 28. Dividing both sides of this equation ( - ) = - 28 - = by 1 7p yields x - . This equation is false if and only if 1 7p 0. Adding 1 7p - = = 7p to both sides of 1 7p 0 yields 1 7p. Dividing both sides of this equation - 1= = 28 =1 by 7 yields p. It follows that the equation x - is false if and only if p . 7 1 7p 7 1 Therefore, the given equation has no solution if and only if the value of p is . 7 Choice A is incorrect and may result from conceptual or calculation errors. Choice C 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":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>0</p>","ord":0},{"label":"B","content_html":"<p>1/7</p>","ord":1},{"label":"C","content_html":"<p>4/3</p>","ord":2},{"label":"D","content_html":"<p>4</p>","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}}