If |x|=−x, which of the following must be true?

[VJesus12]

If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x^2>x
D. x^3<0
E. 2x<x

The OA is B.

Experts, I have a doubt with the option D. Is not true the option D? May you give me some help here? Please.

[GMATGuruNY]

If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x^2>x
D. x^3<0
E. 2x < x

Case 1: x=0, with the result that |x|=0 and -x=0
Eliminate C, D, and E, which are not true for x=0.

Case 2: x=-1, with the result that |x|=1 and -x=1
Eliminate A, which is not true for x=-1.

The correct answer is B.

[Brent@GMATPrepNow]

If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x^2>x
D. x^3<0
E. 2x<x

We know that |x| is always greater than or equal to zero
So, if |x| = -x, then we can be certain that -x is greater than or equal to zero
In other words, -x ≥0
To solve for x, multiply both sides of the inequality by -1 to get: x ≤0
Answer: B

Cheers,
Brent

[Scott@TargetTestPrep]

If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x^2>x
D. x^3<0
E. 2x<x

Since |x| is always greater than or equal to zero, in order for -x to be greater than or equal to zero, x must be less than or equal to zero.

Answer: B