Quick math question

Doing this work and for the lesson it never mentioned it anywhere in the notes, basically

"if x is an element of R (real numbers?) and |x| (absolute value) - x does not equal zero, what do you know about x?

A) x < 0

B) x > 0

C) x (is less than or equal to) 0

D) x (is greater than or equal to) 0

I'm asking this because I'm one of those guys where if I can't find the answer for one question, even if there's 50 questions ahead I just can't go on without finding the answer first, so how would I go about figuring this out?

 

X is less than zero.

For the absolute value of x to be different than x itself (And therefore not equal zero when one is subtracted from the other), x must be negative. However, if it is zero, 0-0 is still zero.

 

X < 0