A). |x| = |-x| This is always true. The definition of 'absolute' value is 'size of the number without its sign'. That's what this expression says.
b). |x| = -|x| This is never true, because an absolute value is never negative. This one would true if x=0 . So maybe some people might say it's sometimes true, but that doesn't feel right to me. I say never.
c). |-x| = -|x| This looks to me like exactly the same situation as (b), and I would say all the same things about it.
