Ok, there is one thing you should know. When multiplying by a negative number, the direction of the inequality changes.
For example : 2<3
When multiplying by -1, you get -2>-3
So here, intuitively, you should separate the situations :
1) firstly, if x is positive
2) secondly, if x is negative
1) If x is positive :
Multiplying by x, we get : 1<4x, since x>0.
Solution to this is (1/4, pos infinity)
2) If x is negative :
Here, it's immediate because 1/x is negative, hence always inferior to 4.
But let's apply the method.
Multiplying by x, we get 1>4x, because x is negative !
Because x is negative, you gotta find all the negative numbers which verify x<1/4.
This is true for all x negative.
Thus the solution to this is (neg infinity, 0)