BTGModeratorVI wrote: ↑Thu Aug 27, 2020 12:09 pm
If x is an integer, then how many values of x will satisfy the equation ||x - 2| + 7| = 6?
A) 0
B) 1
C) 2
D) 3
E) 4
Answer:
A
Source: e-GMAT
Given: |
|x - 2| + 7| = 6
This means EITHER
|x - 2| + 7 = 6 OR
|x - 2| + 7 = -6
Let's examine each possibility....
Take:
|x - 2| + 7 = 6
Subtract 7 from both sides to get: |x - 2| = -1
Since the absolute value of any expression will ALWAYS be greater than or equal to 0, we can see that the equation |x - 2| = -1 has no solution.
Take:
|x - 2| + 7 = -6
Subtract 7 from both sides to get: |x - 2| = -13
Since the absolute value of any expression will ALWAYS be greater than or equal to 0, we can see that the equation |x - 2| = -13 has no solution.
Since there are no values of X that will satisfy the original equation, correct answer is A
Cheers,
Brent
