Question

Hello! I need some help with this homework question posted below. Q21

Answer 1

Given the inequality:

`(x-7)^2(x+5)>0`

This is:

`\begin{gathered} (x-7)^2>0 \\ \text{and } \\ x+5>0 \end{gathered}`

Then solve for x in each one:

`\begin{gathered} (x-7)^2>0 \\ \sqrt[]{(x-7)^2}>\sqrt[]{0} \\ x-7>0 \\ x-7+7>0+7 \\ x>7 \end{gathered}`

And

`\begin{gathered} x+5>0 \\ x+5-5>0-5 \\ x>-5 \end{gathered}`

So, identify the intervals:

`-57}`

In interval notation, the answer is:

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