# How do you solve x/(x+2)>=2?

Jan 1, 2017

The answer is x in [-4, 2[

#### Explanation:

You cannot do crossing over

$\frac{x}{x + 2} \ge 2$

$\frac{x}{x + 2} - 2 \ge 0$

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

$\frac{x - 2 x - 4}{x + 2} \ge 0$

$\frac{- x - 4}{x + 2} \ge 0$

Let $f \left(x\right) = \frac{- x - 4}{x + 2}$

We can do a sign chart

$\textcolor{w h i t e}{a a a a}$$x$$\textcolor{w h i t e}{a a a a a a}$$- \infty$$\textcolor{w h i t e}{a a a a a}$$- 4$$\textcolor{w h i t e}{a a a a a a a}$$- 2$$\textcolor{w h i t e}{a a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$- x - 4$$\textcolor{w h i t e}{a a a a a}$$+$$\textcolor{w h i t e}{a a a a}$$0$$\textcolor{w h i t e}{a a a}$$-$$\textcolor{w h i t e}{a a}$∥$\textcolor{w h i t e}{a a}$$-$

$\textcolor{w h i t e}{a a a a}$$x + 2$$\textcolor{w h i t e}{a a a a a a a}$$-$$\textcolor{w h i t e}{a a a a}$color(white)(aaa)-$\textcolor{w h i t e}{a a a}$∥$\textcolor{w h i t e}{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 a a a}$$-$$\textcolor{w h i t e}{a a a a}$color(white)(aaa)+$\textcolor{w h i t e}{a a a}$∥$\textcolor{w h i t e}{a a}$$-$

Therefore,

$f \left(x\right) \ge 0$, when x in [-4, 2[