I'm confused. Apparently -|x| is different from -x. Could somebody explain??? (I used x for a substitute for numbers.)

Answer 1

|x| is always positive
|x| = x if x >= 0
|x| = -x if x < 0

So, -|x| is always negative
|3| = 3
|-3| = 3
-(|-3|) = -(3) which is x if x = -3, not -x