Question

solve for x and graph the solution.
-x(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.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Explanation:

Step1: Find the critical points

Set \(-x(x + 3)=0\). Then \(x = 0\) or \(x=-3\) (by the zero - product property \(ab = 0\) implies \(a = 0\) or \(b = 0\)).

Step2: Test intervals

• Interval 1: \(x<-3\)

Let \(x=-4\). Then \(-x(x + 3)=-(-4)(-4 + 3)=4\times(-1)=-4<0\).

• Interval 2: \(-3

Let \(x=-1\). Then \(-x(x + 3)=-(-1)(-1 + 3)=1\times2 = 2>0\).

• Interval 3: \(x>0\)

Let \(x = 1\). Then \(-x(x + 3)=-(1)(1 + 3)=-4<0\).

Answer:

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