For the first solution, the error is adding 1 to 3 to get 4 instead of subtracting 1 from 3 to get 2.
It should have been
I-4x + 1I > 3
- 4x + 1 > 3
- 4x > 3 - 1
- 4x > 2
x < - 2/4
x < - 1/2
For the second solution, the error was omitting the negative sign in the final answer. It should have been
-4x + 1 > - 3
- 4x > 2
x < -1/2