Question

solve for x and graph the solution.
4(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.
submit

Explanation:

Step1: Analyze the inequality

Since \(4>0\), the inequality \(4(x - 4)(x - 5)<0\) is equivalent to \((x - 4)(x - 5)<0\).

Step2: Find the critical points

Set \((x - 4)(x - 5)=0\). Using the zero - product property \(a\times b = 0\) implies \(a = 0\) or \(b = 0\). So \(x-4=0\) gives \(x = 4\) and \(x - 5=0\) gives \(x=5\).

Step3: Test intervals

• For \(x<4\), let \(x = 3\). Then \((3 - 4)(3 - 5)=(-1)\times(-2)=2>0\).
• For \(4
• For \(x>5\), let \(x = 6\). Then \((6 - 4)(6 - 5)=2\times1 = 2>0\).

Answer:

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