# How do you graph and solve |1/x| > 2 ?

Mar 29, 2018

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

#### Explanation:

graph{(y-|1/x|)(y-2)=0 [-10, 10, -5, 5]}

$x \ne 0$

For absolute values, there are $2$ solutions.

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

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

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

BY a sign chart the solution is ${S}_{1} = x \in \left(0 , \frac{1}{2}\right)$

and

$- \frac{1}{x} < 2$

$\implies$, $\frac{1}{x} + 2 > 0$

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

BY a sign chart the solution is ${S}_{2} = x \in \left(- \frac{1}{2} , 0\right)$

The solution is

$S = {S}_{1} \cup {S}_{2}$