Question

graph the solution to the following inequ
$x^{2}-6x<-8$
note that you can use the aleks graphin

Explanation:

Step1: Rewrite the inequality

First, rewrite \(x^{2}-6x < - 8\) as \(x^{2}-6x + 8<0\).

Step2: Factor the quadratic expression

Factor \(x^{2}-6x + 8\) as \((x - 2)(x - 4)<0\).

Step3: Find the critical points

Set \((x - 2)(x - 4)=0\). The critical points are \(x = 2\) and \(x = 4\).

Step4: Test intervals

• For \(x<2\) (e.g., \(x = 1\)): \((1 - 2)(1 - 4)=(-1)\times(-3)=3>0\).
• For \(2
• For \(x>4\) (e.g., \(x = 5\)): \((5 - 2)(5 - 4)=(3)\times(1)=3>0\).

Answer:

The solution of the inequality \(x^{2}-6x < - 8\) is \(2