I guess, I know how to solve inequalities with absolute value, but I have problems with this one.
I tried to solve the inequation like this:
I started with case 1. than we have two possibilities $b<0$ and $b>0$
Firstly I took $b<0$ and I had another two possibilities
I take $|a+b|>0$ and in this case I had two possibilites according to to right side of the inequation
$|a-b|>0 ........... a+b\le a-b ......b\le-b$
$|a-b|<0..........a+b\le -a+b .......a\le -a$
I can do the same with other possibilites, but how do I know, if my solution (or even method) is right? there are so many conditions, that I am lost in them.
Thank you for your time.