# How do you solve 1/x+1>=0 using a sign chart?

Sep 9, 2017

Solution is $x \le - 1$ or $x \ge 0$ and in interval form it is $\left\{x \in \left(- \infty , - 1\right] \cup \left[0 , \infty\right)\right\}$

#### Explanation:

We can write $\frac{1}{x} + 1 \ge 0$ as $\frac{1 + x}{x} \ge 0$

Hence, for inequality ti satisfy,

we should have sign of both $1 + x$ and $x$ same i.e.

$1 + x \ge 0$ and $x \ge 0$ i.e. $x \ge - 1$ and $x \ge 0$ i.e. $x \ge 0$

or $1 + x \le 0$ and $x \le 0$ i.e. $x \le - 1$ and $x \le 0$ i.e. $x \le - 1$

Hence solution is $x \le - 1$ or $x \ge 0$ and in interval form it is $\left\{x \in \left(- \infty , - 1\right] \cup \left[0 , \infty\right)\right\}$