Solve: 4-1/b<3/b
I assume you mean
4 - (1/b) < 3/b
Add 1/b to both sides and the < stays the same direction
4 < 4/b
1 < 1/b
Multiply both sides by b. Different rules apply about the < sign depending upon the sign of b.
If b is positive, b < 1. So 0<b<1 is one solution region.
If b is negative, b > 1 (which is a contradiction)
Therefore the only answer is 0<b<1