MHB Is the Definition of Absolute Value Always True?

[mathdad]

The definition of absolute value states the following:

| x | = x when x is > or = 0

| x | = -x when x < 0

I can use the above definition to rewrite expressions that do not contain absolute values.

| x - 3 |, where x < 3

If x < 3, then we can say that (x - 3) is less than 0.

So, -(x - 3) = -x + 3 = (3 - x).

Correct?

 

[HallsofIvy]

Yes, for x< 3, |x- 3|= 3- x. For example, if x= 2, |2- 3|= |-1|= 1= 3- 2.

And, of course, if [math]x\ge 3[/math], |x- 3|= x- 3.