Solve 2-1/x>0

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

Solve for x

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

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x}{x}.

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

Since \frac{2x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

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

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

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

The solution satisfying both inequalities is x<0.

$$x<0$$

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

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

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

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

The final solution is the union of the obtained solutions.

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