Question

solve for x and graph the solution.
(x + 4)(x + 5) < 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 critical points

Set \((x + 4)(x + 5)=0\).
Using the zero - product property \(x+4 = 0\) gives \(x=-4\), and \(x + 5=0\) gives \(x=-5\).

Step2: Test intervals

We have three intervals: \((-\infty,-5)\), \((-5,-4)\), and \((-4,\infty)\).

• For \(x=-6\) (in the interval \((-\infty,-5)\)): \((-6 + 4)(-6+5)=(-2)\times(-1)=2>0\).
• For \(x = -4.5\) (in the interval \((-5,-4)\)): \((-4.5 + 4)(-4.5+5)=(-0.5)\times(0.5)=-0.25<0\).
• For \(x=0\) (in the interval \((-4,\infty)\)): \((0 + 4)(0+5)=20>0\).

Answer:

The solution of the inequality \((x + 4)(x + 5)<0\) is \(-5