# How do you solve (2x-1)/(x+5)>=0 using a sign chart?

Dec 19, 2016

The answer is x in ] -oo,-5 [ uu [1/2, +oo[

#### Explanation:

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

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}$$\textcolor{w h i t e}{a a a a}$$- 5$$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a}$$\frac{1}{2}$$\textcolor{w h i t e}{a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$x + 5$$\textcolor{w h i t e}{a a a a a a}$$-$$\textcolor{w h i t e}{a a}$$\textcolor{w h i t e}{a a a}$∥$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a}$color(white)(aa)+

$\textcolor{w h i t e}{a a a a}$$2 x - 1$$\textcolor{w h i t e}{a a a a a a}$$-$$\textcolor{w h i t e}{a a}$$\textcolor{w h i t e}{a a}$∥$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a}$color(white)(aa)+

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

Therefore,

$f \left(x\right) \ge 0$, when x in ] -oo,-5 [ uu [1/2, +oo[

graph{y-(2x-1)/(x+5)=0 [-52, 52.07, -26, 26]}