The problem is a system of two linear inequalities:
1) 2(x-1) - 3(x-2) < x
2) 6x - 3 < 17 - (x-5)
Solving the first inequality:
2x - 2 - 3x + 6 < x
-x + 4 < x
4 < 2x
2 < x
Solving the second inequality:
6x - 3 < 17 - x + 5
6x - 3 < 22 - x
7x < 25
x < 25/7
Combining the solutions:
Since x > 2 and x < 25/7, the solution is 2 < x < 25/7.