Let's solve this inequality step by step:

2(x-3) - 1 > 3(x-2) - 4(x+1)

Distribute on both sides:
2x - 6 - 1 > 3x - 6 - 4x - 4

Combine like terms:
2x - 7 > 3x - 6 - 4x - 4
2x - 7 > -x - 10

Rearrange the terms:
2x + x > -7 - 10
3x > -17

Divide by 3 to solve for x:
x > -17/3

Therefore, the solution to the inequality is x > -17/3.