Solve 1-2x/x>0

$$\frac { 1 - 2 x } { x } > 0$$

Solve for x

$$x\in \left(0,\frac{1}{2}\right)$$

Solution Steps

For the quotient to be positive, 1-2x and x have to be both negative or both positive. Consider the case when 1-2x and x are both negative.

$$1-2x<0 x<0$$

This is false for any x.

$$x\in \emptyset$$

Consider the case when 1-2x and x are both positive.

$$x>0 1-2x>0$$

The solution satisfying both inequalities is x\in \left(0,\frac{1}{2}\right).

$$x\in \left(0,\frac{1}{2}\right)$$

The final solution is the union of the obtained solutions.

$$x\in \left(0,\frac{1}{2}\right)$$