why is it that some absolute values are negative?

Question

you have said that absolute value is never negative but when you are told to simplify -|-4| the answer is negative.why is that so?thanks

Answer 1

Sammy,

 

If I read your question correctly, then here's the scoop.

 

The absolute value of either a positive or a negative number is indeed always positive: |+4| = |-4| = 4.

 

But then you have a negative sign in front of the absolute value: -|-4|= -(|-4|) = -(+4) = -4.

In effect you have two sequential operations: first taking the absolute value, then flipping its sign.