Solving absolute value equation

[Mr Davis 97]

I have the following equation: $\left | r-5 \right | = \left | r+2 \right |$.

What is a general, analytical way that I can solve equations like these? I always get stumped when trying to solve them...

 

[Mark44]

I have the following equation: $\left | r-5 \right | = \left | r+2 \right |$.

What is a general, analytical way that I can solve equations like these? I always get stumped when trying to solve them...

Look at two cases:
1. Both expressions are the same sign; i.e., both are positive or both are negative.
2. The two expressions are opposite in sign.

The solution to the original equation is the union of the solution sets for the two cases.