# How do you solve (x-2)/(2x+5)<0 using a sign chart?

Dec 27, 2016

The answer is x in ] -5/2, 2[

#### Explanation:

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

The domain of $f \left(x\right)$ is ${D}_{f} \left(x\right) = \mathbb{R} - \left\{- \frac{5}{2}\right\}$

Now, we can 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}$$- \frac{5}{2}$$\textcolor{w h i t e}{a a a a a}$$2$$\textcolor{w h i t e}{a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$2 x + 5$$\textcolor{w h i t e}{a a a a}$$-$$\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}$$+$

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

$\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}$$+$$\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}$$+$

Therefore,

$f \left(x\right) < 0$, when x in ] -5/2, 2[