Question

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

Answer 1

`g(x)=(x-5)/(x+7)`

We need to find the points x where

`(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<0 \\ x<5 \\ \text{and} \\ x+7<0 \\ x<-7 \end{gathered}`

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)`