To solve for x, we will first simplify the equation by distributing on the right side:

2x + 3abs(x) - 2 = 4 + 2(2x - 1) - x
2x + 3abs(x) - 2 = 4 + 4x - 2 - x

Now combine like terms:

2x + 3*abs(x) - 2 = 2x + 2

Since the absolute value of x can be either x or -x, we need to consider both cases:

Case 1: x >= 0
2x + 3x - 2 = 2x + 2
5x - 2 = 2x + 2
3x = 4
x = 4/3

Case 2: x < 0
2x - 3x - 2 = 2x + 2
-x - 2 = 2x + 2
-3x = 4
x = -4/3

Therefore, the solutions for x are x = 4/3 or x = -4/3.