1+3x > 10

Subtract 1 from both sides:
3x > 9

Divide by 3:
x > 3

3x + 8 < 0

Subtract 8 from both sides:
3x < -8

Divide by 3:
x < -8/3

6 - x < 2

Subtract 6 from both sides:
-x < -4

Multiply by -1 (reverse inequality):
x > 4

9 - x > 0

Subtract 9 from both sides:
-x > -9

Multiply by -1 (reverse inequality):
x < 9

Therefore, the solution to the system of inequalities is -3 < x < 4.