# How do you solve and write the following in interval notation: -4<1/x<= 1 ?

Jul 17, 2018

We get $\left(- \infty , \frac{1}{4}\right)$ or $\left[1 , \setminus \infty\right)$

#### Explanation:

We are doing case work to solve this inequality:

a) $x > 0$
in this case we multiply the given inequality by $x$ and we get

$- 4 x < 1$ and $1 \le x$

so we have $x > - \frac{1}{4}$ and $x \ge 1$ so we get $x \ge 1$ in this case.

b)$x < 0$
we multiply by $x < 0$

so we get

$- 4 x > 1 \ge x$

solving this we get

$x < - \frac{1}{4}$ and $x \le 1$

so we get the solution

$x < - \frac{1}{4}$