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![If [4-x]/[x-2]=-3/x, then x could equal which of the following?](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If [4-x]/[x-2]=-3/x, then x could equal which of the following?"){kind=icon}
Updated on: 25 Aug 2025, 11:26
Originally posted by Sajjad1994 on 25 Aug 2025, 11:22.
Last edited by Sajjad1994 on 25 Aug 2025, 11:26, edited 1 time in total.
Last edited by Sajjad1994 on 25 Aug 2025, 11:26, edited 1 time in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
88% (00:54) correct
11% (00:35) wrong based on 17 sessions
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Date
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If \(\frac{4-x}{x-2} \) = \( \frac{-3}{x},\) then x could equal which of the following?
A. 10
B. 9
C. 8
D. 7
E. 6
A. 10
B. 9
C. 8
D. 7
E. 6
30 Aug 2025, 06:49
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Official Explanation
Cross-multiply to obtain \(x(4 - x) = -3(x - 2).\) Distribute on both sides to obtain \(4x - x^2 = -3x + 6.\) Now subtract 4x from each side, and add \(x^2\) to each side, in order to combine like terms and to get one side equal to zero. Then \(0 = x^2 - 7x + 6.\) Factor the right side by noting that \((x - 6)(x- 1) = x^2 - 1x - 6x + 6 = x^2 - 7x + 6.\) So \((x - 6)( x - 1) = 0\) and \(x\) could equal 6 or 1, the values that make either expression in parentheses equal to 0. Both values check in the original equation, but only x = 6, (E) is listed as an answer choice.
Answer: E
Cross-multiply to obtain \(x(4 - x) = -3(x - 2).\) Distribute on both sides to obtain \(4x - x^2 = -3x + 6.\) Now subtract 4x from each side, and add \(x^2\) to each side, in order to combine like terms and to get one side equal to zero. Then \(0 = x^2 - 7x + 6.\) Factor the right side by noting that \((x - 6)(x- 1) = x^2 - 1x - 6x + 6 = x^2 - 7x + 6.\) So \((x - 6)( x - 1) = 0\) and \(x\) could equal 6 or 1, the values that make either expression in parentheses equal to 0. Both values check in the original equation, but only x = 6, (E) is listed as an answer choice.
Answer: E
