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: Simplify the inequality

Multiply both sides by - 1 (and reverse the inequality sign). We get \((x + 4)(x - 5)<0\).

Step2: Find the roots

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

Step3: Test intervals

We have three intervals: \(x<-4\), \(-45\).

• For \(x<-4\) (e.g., \(x=-5\)): \((-5 + 4)(-5 - 5)=(-1)\times(-10)=10>0\).
• For \(-4
• For \(x>5\) (e.g., \(x=6\)): \((6 + 4)(6 - 5)=(10)\times(1)=10>0\).

Answer:

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