Question

X-5For the function g(x) =solve the following inequality.7X+7g(x) > 0

Answer 1

$g(x)=\frac{x-5}{x+7}$

We need to find the points x where

$\frac{x-5}{x+7}>0$

This can only happens if both, the numerator and the denominator have the same sign, that is

$\begin{gathered} x-5>0 \\ x>5 \\ \text{and} \\ x+7>0 \\ x>-7 \end{gathered}$

or

$\begin{gathered} x-5$

The first pair of inequalities leads to the set

$(5,\infty)\cap(-7,\infty)=(5,\infty)$

and the second

$(-\infty,5)\cap(-\infty,-7)=(-\infty,7)$

Then, the answer is

$(-\infty,-7)\cup(5,\infty)$