Question

solve for x and graph the solution.
3x(x + 3) < 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.
submit

Explanation:

Step1: Find the critical points

Set \(3x(x + 3)=0\). Using the zero - product property \(ab = 0\) implies \(a=0\) or \(b = 0\).
For \(3x=0\), we get \(x = 0\). For \(x + 3=0\), we get \(x=-3\).

Step2: Test intervals

We have three intervals to test: \((-\infty,-3)\), \((-3,0)\), and \((0,\infty)\).

• For the interval \((-\infty,-3)\), let \(x=-4\). Then \(3(-4)(-4 + 3)=3(-4)(-1)=12>0\).
• For the interval \((-3,0)\), let \(x=-1\). Then \(3(-1)(-1 + 3)=3(-1)(2)=-6<0\).
• For the interval \((0,\infty)\), let \(x = 1\). Then \(3(1)(1 + 3)=3\times1\times4 = 12>0\).

Answer:

The solution of the inequality \(3x(x + 3)<0\) is \(-3