# How do you solve 1/x<4 using a sign chart?

Sep 24, 2017

Solution : $x < 0 \mathmr{and} x > \frac{1}{4} \mathmr{and} \left(- \infty , 0\right) \cup \left(\frac{1}{4} , \infty\right)$

#### Explanation:

$\frac{1}{x} < 4 \mathmr{and} \frac{1}{x} - 4 < 0 \mathmr{and} \frac{1 - 4 x}{x} < 0$ critical points are

$x = 0 , 1 - 4 x = 0 \mathmr{and} x = \frac{1}{4}$ . Function is undefined at $x = 0$

Sign chart :

When $x < 0$ sign of $\frac{1 - 4 x}{x}$ is (+/-) = - ; <0

When $0 < x < \frac{1}{4}$ sign of $\frac{1 - 4 x}{x}$ is (+/+) = + ; >0

When $x > \frac{1}{4}$ sign of $\frac{1 - 4 x}{x}$ is (-/+) = - ; <0

Solution : $x < 0 \mathmr{and} x > \frac{1}{4} \mathmr{and} \left(- \infty , 0\right) \cup \left(\frac{1}{4} , \infty\right)$ [Ans]