Question

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

Explanation:

Step1: Find the critical points

Set \((x + 2)(x + 5)=0\).
Using the zero - product property \(x+2 = 0\) gives \(x=-2\), and \(x + 5=0\) gives \(x=-5\).

Step2: Test intervals

We have three intervals to test: \((-\infty,-5)\), \((-5,-2)\), and \((-2,\infty)\).

• For \(x=-6\) (in the interval \((-\infty,-5)\)): \((-6 + 2)(-6+5)=(-4)\times(-1)=4>0\).
• For \(x=-3\) (in the interval \((-5,-2)\)): \((-3 + 2)(-3+5)=(-1)\times2=-2<0\).
• For \(x=0\) (in the interval \((-2,\infty)\)): \((0 + 2)(0+5)=2\times5 = 10>0\).

Answer:

The solution of the inequality \((x + 2)(x + 5)<0\) is \(-5