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

[Gmat_mission]

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

[RaghavKhanna]

|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

[Scott@TargetTestPrep]

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