Solve x-4/x<0

$$\frac { x - 4 } { x } < 0$$

Solve for x

$$x\in \left(0,4\right)$$

Solution Steps

For the quotient to be negative, x-4 and x have to be of the opposite signs. Consider the case when x-4 is positive and x is negative.

$$x-4>0 x<0$$

This is false for any x.

$$x\in \emptyset$$

Consider the case when x is positive and x-4 is negative.

$$x>0 x-4<0$$

The solution satisfying both inequalities is x\in \left(0,4\right).

$$x\in \left(0,4\right)$$

The final solution is the union of the obtained solutions.

$$x\in \left(0,4\right)$$