Question

solve for (x) and graph the solution.
((x + 2)(x+6)>0)
plot the endpoints. select an endpoint to change it from closed to open. select a segment, ray, or line to delete it.

Explanation:

Step1: Find the roots

Set $(x + 2)(x+6)=0$. Then $x+2 = 0$ gives $x=-2$ and $x + 6=0$ gives $x=-6$.

Step2: Analyze the sign

Consider the intervals $(-\infty,-6)$, $(-6,-2)$ and $(-2,\infty)$.
For $x<-6$, if $x=-7$, then $(-7 + 2)(-7 + 6)=(-5)\times(-1)=5>0$.
For $-6For $x>-2$, if $x=0$, then $(0 + 2)(0 + 6)=2\times6 = 12>0$.

Answer:

The solution of the inequality $(x + 2)(x + 6)>0$ is $x<-6$ or $x>-2$. On the number - line, we have open - circles at $x=-6$ and $x=-2$ and the shaded regions are to the left of $x = - 6$ and to the right of $x=-2$.