Question

solve for x and graph the solution.
3(x + 2)(x + 4) < 0
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Find the roots

Set $3(x + 2)(x + 4)=0$. Then $x+2 = 0$ gives $x=-2$ and $x + 4=0$ gives $x=-4$.

Step2: Test intervals

We have three intervals: $x<-4$, $-4-2$.
For $x<-4$, let $x=-5$, then $3(-5 + 2)(-5 + 4)=3\times(-3)\times(-1)=9>0$.
For $-4For $x>-2$, let $x=0$, then $3(0 + 2)(0 + 4)=3\times2\times4 = 24>0$.

Answer:

The solution of the inequality is $-4