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Absolute value [Pending...]

My question

If x = -|w|, which of the following MUST be true

A. x=-w
B. x=w
C. x^2=w
D. x^2=w^2
E. x^3=w^3

Why option (a) is not the correct answer? the question clearly says x=-|w|
which means
|w|=-x

and by definition, w=-x

regards

Relevant page

If x = -|w|, which of the following must be true : GMAT Problem Solving (PS)

What I've done so far

x=-|w|
=> |w|=-x
=> w=-x

or

w^2=x^2

i am stuck between A or D

X

If x = -|w|, which of the following MUST be true

A. x=-w
B. x=w
C. x^2=w
D. x^2=w^2
E. x^3=w^3

Why option (a) is not the correct answer? the question clearly says x=-|w|
which means
|w|=-x

and by definition, w=-x

regards
Relevant page

<a href="https://gmatclub.com/forum/if-x-w-which-of-the-following-must-be-true-218960.html">If x = -|w|, which of the following must be true : GMAT Problem Solving (PS)					</a>

What I've done so far

x=-|w|
=> |w|=-x
=> w=-x

or

w^2=x^2

i am stuck between A or D

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