Question

solve for x and graph the solution.
-4(x + 1)(x - 5) > 0
plot the endpoints. select an endpoint to change it from a segment, ray, or line to delete it.

Explanation:

Step1: Divide both sides by -4

When dividing an inequality by a negative number, the direction of the inequality sign changes. So we get \((x + 1)(x - 5)<0\).

Step2: Find the roots

Set \((x + 1)(x - 5)=0\). By the zero - product property, \(x+1 = 0\) gives \(x=-1\) and \(x - 5=0\) gives \(x = 5\). These are the critical points.

Step3: Test intervals

We have three intervals to test: \((-\infty,-1)\), \((-1,5)\) and \((5,\infty)\).
For \(x<-1\), let \(x=-2\). Then \((-2 + 1)(-2 - 5)=(-1)\times(-7)=7>0\).
For \(-1For \(x>5\), let \(x=6\). Then \((6 + 1)(6 - 5)=(7)\times(1)=7>0\).

Answer:

The solution of the inequality \(-4(x + 1)(x - 5)>0\) is \(-1