1 Answer

Bvanvugt · Answer 1 · 2023-04-20T23:53:08+0000

Given inequality:

$x^2\text{ - 6x > 0}$

The steps for solving the problem are outlined below:

Step1 : solve the inequality by factorizing:

$\begin{gathered} x^2\text{ -6x > 0} \\ x(x\text{ - 6\rparen > 0} \end{gathered}$

Step 2: Identify the intervals:

The possible intervals of solution are:

$\begin{gathered} x\text{ < 0} \\ 0\text{ < x < 6} \\ x\text{ > 6} \end{gathered}$

Using the given inequality we can confirm if the solution range satisfies the given inequality

The valid intervals of solutions are:

$x\text{ <}0\text{ , x > 6}$

Hence, the solution set in interval notation is:

$(-\infty\text{, 0\rparen U \lparen6, }\infty)$

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