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

Step 1: Solve the first inequality: (2x - 3)/5 - (x + 1)/2 <= 0. Multiply by 10: 2(2x - 3) - 5(x + 1) <= 0 => 4x - 6 - 5x - 5 <= 0 => -x - 11 <= 0 => -x <= 11 => x >= -11.

Step 2: Solve the second inequality: -3x + 4 >= -2x - 6. Add 3x to both sides and add 6 to both sides: 4 + 6 >= -2x + 3x => 10 >= x => x <= 10.

Step 3: Find the intersection of the solutions. Since x >= -11 and x <= 10, the common solution is -11 <= x <= 10.

Answer: -11 <= x <= 10.