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 $-x^{2}+2x\leq - 15$ as $x^{2}-2x - 15\geq0$.

Step2: Factor the quadratic

Factor $x^{2}-2x - 15$ to get $(x - 5)(x+3)\geq0$.

Step3: Find the roots

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

Step4: Test intervals

Test the intervals $x<-3$, $-35$.
For $x<-3$, let $x=-4$. Then $(-4 - 5)(-4 + 3)=(-9)\times(-1)=9\geq0$, so $x<-3$ is part of the solution.
For $-3For $x>5$, let $x=6$. Then $(6 - 5)(6 + 3)=1\times9 = 9\geq0$, so $x>5$ is part of the solution.

Answer:

The solution is $x\leq - 3$ or $x\geq5$. On the number - line, we have a closed circle at $x=-3$ and shade to the left, and a closed circle at $x = 5$ and shade to the right.