Question

solve for x and graph the solution.
-3(x + 3)(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: Divide both sides by -3

When dividing an inequality by a negative number, the inequality sign flips. So we get \((x + 3)(x + 4)>0\).

Step2: Find the critical points

Set \((x + 3)(x + 4)=0\). Using the zero - product property \(x+3 = 0\) gives \(x=-3\), and \(x + 4=0\) gives \(x=-4\).

Step3: Test intervals

• For \(x<-4\) (let \(x=-5\)), \((-5 + 3)(-5 + 4)=(-2)\times(-1)=2>0\).
• For \(-4
• For \(x>-3\) (let \(x=0\)), \((0 + 3)(0 + 4)=12>0\).

Answer:

The solution of the inequality \(-3(x + 3)(x + 4)<0\) is \(x<-4\) or \(x>-3\). On the number - line, we have open circles at \(x=-4\) and \(x=-3\), and the graph consists of two rays: one to the left of \(x = -4\) (towards \(-\infty\)) and one to the right of \(x=-3\) (towards \(\infty\)).