Solve 2x-1/2x>0

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

Solve for x

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

Solution Steps

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

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

The solution satisfying both inequalities is x<0.

$$x<0$$

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

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

The solution satisfying both inequalities is x>\frac{1}{2}.

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

The final solution is the union of the obtained solutions.

$$x<0\text{; }x>\frac{1}{2}$$