Question

graph the solution to the following inequality on the number line. -x^2 - 2x > -15. note that you can use the aleks graphing calculator to help get your answer.

Explanation:

Step1: Rewrite the inequality

First, rewrite $-x^{2}-2x > - 15$ as $-x^{2}-2x + 15>0$, or equivalently $x^{2}+2x - 15<0$.

Step2: Factor the quadratic

Factor $x^{2}+2x - 15$ to get $(x + 5)(x - 3)<0$.

Step3: Find the roots

Set $(x + 5)(x - 3)=0$. The roots are $x=-5$ and $x = 3$.

Step4: Test intervals

Test the intervals $(-\infty,-5)$, $(-5,3)$ and $(3,\infty)$.
For $x<-5$, let $x=-6$. Then $(-6 + 5)(-6 - 3)=(-1)\times(-9)=9>0$.
For $-5For $x>3$, let $x = 4$. Then $(4 + 5)(4 - 3)=(9)\times(1)=9>0$.

Answer:

The solution of the inequality $x^{2}+2x - 15<0$ is $-5