$$ x^{2}

Question

$$ x^{2}<6 x $$ Note that you can use the ALEKS graphing calculator to help get your answer.

UpStudy AI · Accepted Answer

Solve the equation $$ x^{2}<6x $$.
Solve the inequality by following steps:
- step0: Solve the inequality by testing the values in the interval:
  $$x^{2}\lt 6x$$
- step1: Move the expression to the left side:
  $$x^{2}-6x\lt 0$$
- step2: Rewrite the expression:
  $$x^{2}-6x=0$$
- step3: Factor the expression:
  $$x\left(x-6ight)=0$$
- step4: Separate into possible cases:
  $$\begin{align}&x=0\&x-6=0\end{align}$$
- step5: Solve the equation:
  $$\begin{align}&x=0\&x=6\end{align}$$
- step6: Determine the test intervals:
  $$\begin{align}&x<0\&06\end{align}$$
- step7: Choose a value:
  $$\begin{align}&x_{1}=-1\&x_{2}=3\&x_{3}=7\end{align}$$
- step8: Test the chosen value:
  $$\begin{align}&x<0	extrm{ }	extrm{is not a solution}\&06	extrm{ }	extrm{is not a solution}\end{align}$$
- step9: The final solution is $$0The solution is $$0 < x < 6$$.

Note that you can use the ALEKS graphing calculator to help get your answer.

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