If $3|3 – x| = 7,$ what is the product of all the possible values of $x?$ A. 1/9 B. 1/3 C. 2/3 D. 16/9 E. 32/9 [spoiler]OA=E[/spoiler] Source: Manhattan GMAT

|x-3| = 7/3 => x-3 = 7/3, when x-3>0 => x = 16/3 and, 3-x = 7/3, when x-3<0 x = 2/3 Product of possible values of x = 16/3 * 2/3 = 32/9

Gmat_mission wrote: ↑Sat Jun 06, 2020 5:16 am If $3|3 – x| = 7,$ what is the product of all the possible values of $x?$ A. 1/9 B. 1/3 C. 2/3 D. 16/9 E. 32/9 [spoiler]OA=E[/spoiler] Solution: Case 1. If 3 - x is positive, we have: 3(3 - x) = 7 9 - 3x = 7 -3x = -2 x = 2/3 Case 2. If (3 - x) is negative, we have: 3(-3 + x) = 7 3(x - 3) = 7 3x - 9 = 7 3x = 16 x = 16/3 Therefore, the product of all the possible values of x is 2/3 * 16/3 = 32/9. Answer: E

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If \(3|3 – x| = 7,\) what is the product of all the possible values of \(x?\)

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