Explanation:
Here we have the following inequality:
[tex]\frac{(x-9)(x+1)}{(x-2)}\geq 0[/tex]
Remember that:
[tex](+)(+)=+ \\ \\ (-)(-)=+ \\ \\ (-)(+)=- \\ \\ (+)(-)=-[/tex]
Since we have a quotient from the inequality, the values that make it true are those such that:
- Numerator and denominator are both positive.
- Numerator and denominator are both negative.
An easy way to solve this inequality is by using graphing tools. In doing so we get the graph shown below whose solution is the shaded region in red. Therefore, the solution in interval notation is:
[tex]\boxed{[-1,2)\cup [9,\infty)}[/tex]
- Closed at -1 and 9 because those values makes the inequality to be zero.
- Open at 2 because the left side of the inequality is undefined at this value.
