Question

solve for x and graph the solution.
(x + 5)(x + 6) < 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 \((x + 5)(x + 6)=0\).
Using the zero - product property \(x+5 = 0\) gives \(x=-5\), and \(x + 6=0\) gives \(x=-6\).

Step2: Test intervals

We have three intervals: \((-\infty,-6)\), \((-6,-5)\), and \((-5,\infty)\).

• For \(x=-7\) (in the interval \((-\infty,-6)\)): \((-7 + 5)(-7+6)=(-2)\times(-1)=2>0\).
• For \(x=-5.5\) (in the interval \((-6,-5)\)): \((-5.5 + 5)(-5.5+6)=(-0.5)\times(0.5)=-0.25<0\).
• For \(x=0\) (in the interval \((-5,\infty)\)): \((0 + 5)(0+6)=30>0\).

Answer:

The solution of the inequality \((x + 5)(x + 6)<0\) is \(-6