Hello,

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 :

1/x<4

Multiplying by x, we get : 1<4x, since x>0.

--> x>1/4

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.

1/x<4

Multiplying by x, we get 1>4x, because x is negative !

--> x<1/4

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)