Given inequality:
[tex]x^2\text{ - 6x > 0}[/tex]
The steps for solving the problem are outlined below:
Step1 : solve the inequality by factorizing:
[tex]\begin{gathered} x^2\text{ -6x > 0} \\ x(x\text{ - 6\rparen > 0} \end{gathered}[/tex]
Step 2: Identify the intervals:
The possible intervals of solution are:
[tex]\begin{gathered} x\text{ < 0} \\ 0\text{ < x < 6} \\ x\text{ > 6} \end{gathered}[/tex]
Using the given inequality we can confirm if the solution range satisfies the given inequality
The valid intervals of solutions are:
[tex]x\text{ <}0\text{ , x > 6}[/tex]
Hence, the solution set in interval notation is:
[tex](-\infty\text{, 0\rparen U \lparen6, }\infty)[/tex]
