(x-2)/3 - (x+1)/2 >= 1 4x - 3(2x-1) > 5

1. Simplify the first inequality: 2(x-2) - 3(x+1) >= 6 => 2x - 4 - 3x - 3 >= 6 => -x - 7 >= 6 => -x >= 13 => x <= -13.

2. Simplify the second inequality: 4x - 6x + 3 > 5 => -2x > 2 => x < -1.

3. Find the intersection of the solutions: x <= -13 and x < -1. The intersection is x <= -13.