Let's solve each inequality step by step:

1) 3x - 8 > x - 1
Subtract x from both sides:
2x - 8 > -1
Add 8 to both sides:
2x > 7
Divide by 2:
x > 3.5

2) x + 9 < 2x
Subtract x from both sides:
9 < x
So, x > 9.

3) 13x - 7 < 12x + 3
Subtract 12x from both sides:
x - 7 < 3
Add 7 to both sides:
x < 10

4) 20x + 11x < 18x - 2
Combine like terms:
31x < 18x - 2
Subtract 18x from both sides:
13x < -2
Divide by 13:
x < -2/13

5) 45 - 7x < 61 - 11x
Add 11x to both sides:
45 + 4x < 61
Subtract 45 from both sides:
4x < 16
Divide by 4:
x < 4

6) 32x + 10 < 6
Subtract 10 from both sides:
32x < -4
Divide by 32:
x < -1/8

7) 21x + 29 > 19x - 11
Subtract 19x from both sides:
2x + 29 > -11
Subtract 29 from both sides:
2x > -40
Divide by 2:
x > -20

Therefore, the solutions to these inequalities are:
1) x > 3.5
2) x > 9
3) x < 10
4) x < -2/13
5) x < 4
6) x < -1/8
7) x > -20