Question

Hello, I need some assistance with this homework question please for precalculusHW Q18

Answer 1

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)`