# How do you solve (x+2)/(x+5)>=1 using a sign chart?

##### 1 Answer
Nov 28, 2016

The answer is x in ] -oo,-5 [

#### Explanation:

Let's rewrite the equation as

$f \left(x\right) = \frac{x + 2}{x + 5} - 1 \ge 0$

$f \left(x\right) = \frac{\left(x + 2\right) - \left(x + 5\right)}{x + 5} \ge 0$

$f \left(x\right) = \frac{x + 2 - x - 5}{x + 5} = - \frac{3}{x + 5} \ge 0$

The domain of $f \left(x\right)$ is ${D}_{f} \left(x\right) = \mathbb{R} - \left\{- 5\right\}$

Let's do the sign chart

$\textcolor{w h i t e}{a a a a}$$x$$\textcolor{w h i t e}{a a a a}$$- \infty$$\textcolor{w h i t e}{a a a a}$$- 5$$\textcolor{w h i t e}{a a a a}$$+ \infty$

$\textcolor{w h i t e}{a}$$- \left(x + 5\right)$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a a a}$$-$

$\textcolor{w h i t e}{a a a a}$$f \left(x\right)$$\textcolor{w h i t e}{a a a a a}$$+$$\textcolor{w h i t e}{a a a a a}$$-$

Therefore,

$f \left(x \ge 0\right)$ when x in ] -oo,-5 [

graph{-3/(x+5) [-18.99, 6.32, -6.33, 6.33]}