Question 578528
let:

......-x-2 < |3x-1| + |x-2| < x+2
........-x-2 < |4x-3| < x+2
..........-2+3 < 4x < 2+3
Solve each side
.-x-2 < |4x-3|.............|4x-3| < x+2
....-5x >-1.................... 3x  < 5
......x > 1/5....................x  < 5/3

1 is not an applicable answer. The answer is with in an interval of 1/5 < x < 5/3.