Question

graph the solution to the following inequality on the number line.

$x^{2}<4x$

note that you can use the aleks graphing calculator to help get your answer.

Explanation:

Step1: Rearrange the inequality

Subtract \(4x\) from both sides: \(x^{2}-4x < 0\). Factor out \(x\): \(x(x - 4)<0\).

Step2: Find the critical points

Set \(x=0\) and \(x - 4=0\) (i.e., \(x = 4\)). These are the points where the expression \(x(x - 4)\) equals zero.

Step3: Test intervals

• For \(x<0\) (e.g., \(x=-1\)), \((-1)\times(-1 - 4)=(-1)\times(-5)=5>0\).
• For \(0
• For \(x>4\) (e.g., \(x=5\)), \(5\times(5 - 4)=5\times1 = 5>0\).

Answer:

The solution of the inequality \(x^{2}<4x\) is \(0