Hi Patrick!
You must be more rigurous in such problems.
First of all we need a condition: , else the inequality has no solution.
Now:
If (1) the inequality becomes
(2)
From (1) and (2) we have (3)
If (4) the inequality becomes
(5)
From (4) and (5) we have (6)
Now, from (3) and (6) yields
I usually just split it into two inequalities, which is kind of similar to what Patrick did:
We have two cases (one where what is in the absolute values is positive, and one where it's negative):
case 1:
.............. 1st condition
case 2:
................. I think Patrick knows why I made the left side negative, so i won't explain
................. 2nd condidtion
Putting both conditions into one, we get:
..................this is the form the question asked the answer to be put in
or equivalently, as red_dog said,