(2x-3)/5 - (x+1)/2 <= 0 -3x+4 >= -2x-6

1. Simplify the first inequality: 2(2x-3) - 5(x+1) <= 0 => 4x - 6 - 5x - 5 <= 0 => -x - 11 <= 0 => -x <= 11 => x >= -11.

2. Simplify the second inequality: -3x + 4 >= -2x - 6 => 4 + 6 >= -2x + 3x => 10 >= x => x <= 10.

3. Find the intersection of the solutions: x >= -11 and x <= 10. The intersection is -11 <= x <= 10.