Let's solve the equation step by step:

First, simplify both sides of the equation:

2|x-1| - 3x - 5 = 2 - 2(3x-1) - 2x
2|x-1| - 3x - 5 = 2 - 6x + 2 - 2x
2|x-1| - 3x - 5 = -4x + 4

Next, distribute the absolute value on the left side:

2(x-1) - 3x - 5 = -4x + 4 (when x ≥ 1)
2(-x+1) - 3x - 5 = -4x + 4 (when x < 1)

Simplify each possibility:

2x - 2 - 3x - 5 = -4x + 4 => -x - 7 = -4x + 4
-x + 3x +7 = 4x - 4 => 2x + 7 = 4x - 4

Now, solve each equation separately:

1st case:
-x - 7 = -4x + 4
3x = 11
x = 11/3

2nd case:
2x + 7 = 4x - 4
2x + 4x = 11
6x = 11
x = 11/6

Therefore, the solutions for the equation are x = 11/3 and x = 11/6.