Chapter 4.6, Problem 20AYU

In Problems 19-48, solve each inequality algebraically.

$\left(x\text{ - 5}\right){\left(x\text{ + 2}\right)}^2\text{ > 0}$

To determine

To find: The inequality algebraically.

Answer to Problem 20AYU

$\left\{x|x>5\right\}$

Explanation of Solution

Given:

$\left(x-5\right){\left(x+2\right)}^2>0$

Since ${\left(x+2\right)}^2>0$ therefore the only possibility is $x-5>0$.

$x>5$

So $\left(x-5\right){\left(x+2\right)}^2>0$ for $x>5$. The solution set is $\left\{x|x>5\right\}$ or, using interval notation $\left(5,\infty \right)$.