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If \(x\) is an integer, then how many values of \(x\) will

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by Brent@GMATPrepNow » Wed Nov 20, 2019 10:06 am
AAPL 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
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
Brent Hanneson - Creator of GMATPrepNow.com
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