Chapter 4.6, Problem 19AYU

In Problems 19-48, solve each inequality algebraically.

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

To determine

To find: The inequality algebraically.

Answer to Problem 19AYU

$\left\{x|-\infty <x\le -2\right\}$

Explanation of Solution

Given:

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

Since ${\left(x-5\right)}^2$ never less than zero, therefore the only possibility is $x+2<0$.

$x<-2$

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