This is for Nonlinear inequalities in one variable, via solving the quadratic inequalities. I also have to put the solution set in interval notation.

For example.

X-5/X-7>(or equal to) 0.

First I have to find the denominator that makes the value to 0. So this will be X=7. But also the numerator gets changed to x=5. What my question is, is the test point really needed? Because can't you just look at the solution and see if the number is greater than(or equal to)0?. 5>0 or 7>0. Neither of these are true so the notation set would look like (5,7), right? But also, about the test points, the numbers that get plugged into the variables, are they just random numbers I can pick and choose from?