Given: ||x - 2| + 7| = 6AAPL wrote:e-GMAT
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
OA A
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
