# How do you solve \frac { 3x + 7} { 14- 7x } \geq 0?

Dec 1, 2016

The answer is =x in [-7/3, 2[

#### Explanation:

Let $f \left(x\right) = \frac{3 x + 7}{14 - 7 x}$

The domain of $f \left(x\right)$ is D_f(x)=RR-{2}

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}$$- \frac{7}{3}$$\textcolor{w h i t e}{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}$$\left(3 x + 7\right)$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a a}$$+$

$\textcolor{w h i t e}{a a a a}$$\left(14 - 7 x\right)$$\textcolor{w h i t e}{a a a}$$+$$\textcolor{w h i t e}{a a a a}$$+$∥$\textcolor{w h i t e}{a a}$$-$

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

Therefore,$f \left(x\right) \ge 0$, when x in [-7/3, 2[ #

graph{(3x+7)/(14-7x) [-11.34, 11.17, -5.03, 6.22]}