# Stupid Math Question: Absolute Values

First, what is the solution to: | a-b | = | (a-b)| = a-b, correct?
So, then what’s the solution to:
|-a-b| = |(-a-b)| = | -1*(a+b)| = |-(a+b)| = a+b, correct? or no?

Just a little rusty…thanks!

• Jinx

Both depend on the values of a and b.

The first could be a-b or b-a, whichever is nonnegative.

The second could be -a-b or a+b, again, whichever is nonnegative.

Both depend on the values of a and b.

The first could be a-b or b-a, whichever is nonnegative.

The second could be -a-b or a+b, again, whichever is nonnegative.

Hmm, so Cabbage, would you say that we cannot even say that | -X | = X ? - Jinx

That’s correct. For example, if x = -1, then we have |x| = -x = -(-1) = 1. In the past, this has caused some of my calculus students no end of frustration–they get confused when they see that sometimes |x| = -x; they don’t expect a negative sign there.

In general, |x| is defined to be:

1. |x| = x, if x >= 0

2. |x| = -x, if x < 0.

No, |-X| = X always. But in the case |a-b| it depends on whether a > b or not. For example, |3-5] = |-2| = 2 = b-a, but |5-3| = |2| = 2 = a-b.

|a-b| does not equal a-b for any value of b greater than a.
You are differentiating between |a-b| and |(a-b)| when they are literally the same thing. Same for |-a-b| and |(-a-b)|.
If b less than -a then the second one does not hold true.

As was said above, it all depends on the values in that you use.

what would be the point of absolute value if you could just get rid of it whenever you wanted ?

you can’t get rid of it until you know the sign of the stuff you’re looking at.

Oops…I retract that |X| = X part. It’s either X or -X, whichever is positive.

Not true. IF X=-1 then |-X| != X.