# How do you solve (w-6)/w<=0 using a sign chart?

Jan 23, 2017

The answer is x in ]0,6]

#### Explanation:

Let $f \left(w\right) = \frac{w - 6}{w}$

The domain of $f \left(w\right)$ is ${D}_{f} \left(w\right) = \mathbb{R} - \left\{0\right\}$

Let's build the sign chart

$\textcolor{w h i t e}{a a a a}$$w$$\textcolor{w h i t e}{a a a a}$$- \infty$$\textcolor{w h i t e}{a a a a a}$$0$$\textcolor{w h i t e}{a a a a a}$$6$$\textcolor{w h i t e}{a a a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$w$$\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 a}$$w - 6$$\textcolor{w h i t e}{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 a}$$f \left(w\right)$$\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}$$+$

Therefore,

$f \left(w\right) \le 0$ when x in ]0,6]