|3x+1|-|2-x|<3

|3x+1|-|2-x|<3

Formal Way:

Case 1
|3x+1| < 3 + |2-x|

3x+1 < 3 + |2-x| AND -3x-1 < 3 + |2-x|
|2-x| > 3x-2 AND |2-x| > -3x-4

which leads to
a) 2-x > 3x-2 OR -2+x > 3x-2
-4x > -4 OR -2x > 0
x < 1 OR x < 0 ----> x < 1

b) 2-x > -3x - 4 OR -2 + x > -3x - 4
2x > -6 OR 4x > -6
X > -3 OR x > -3 ----> x > -3

so x < 1 AND x > -3

for

-3 > x > 1

verification:
http://www.wolframalpha.com/input/?i=%7C3x%2B1%7C-%7C2-x%7C%3C3+for+x+from+-5+to+4