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What is the value of |x+4|+x?

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What is the value of |x+4|+x?

by Vincen » Mon Jan 29, 2018 3:17 am
What is the value of |x+4|+x?

(1) x ≤ −4

(2) |x+4| = 0

The OA is the option D.

I don't know how to prove that the statement (1) is sufficient. Experts, can you help me? I am confused.
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Source: — Data Sufficiency |
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by GMATGuruNY » Mon Jan 29, 2018 3:44 am
Vincen wrote:What is the value of |x+4|+x?

(1) x ≤ −4

(2) |x+4| = 0
If x≤0, then |x| = -x.

Statement 1: x≤-4
Thus:
x+4≤0, with the result that |x+4| = -(x+4).
Substituting |x+4| = -(x+4) into |x+4|+x, we get:
-(x+4) + x = -x - 4 + x = -4.
SUFFICIENT.

Statement 2: |x+4| = 0
Thus:
x=-4, with the result that |x+4|+x = |-4+4| + (-4) = 0 - 4 = -4.
SUFFICIENT.

The correct answer is D.

Statement 1 can also be evaluated by testing cases.
If x=-4, then |x+4|+x = |-4+4| + (-4) = 0 - 4 = -4.
If x=-5, then |x+4|+x = |-5+4| + (-5) = 1 - 5 = -4.
If x=-4.5, then |x+4|+x = |-4.5+4| + (-4.5) = 0.5 - 4.5 = -4.
If x=-10, then |x+4|+x = |-10+4| + (-10) = 6 - 10 = -4.
In every case, |x+4|+x = -4.
SUFFICIENT.
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