How do I find the critical values to solve the following inequality

I really don't understand the method to getting the critical values.
Could I have a step to step explanation for these
Here is two that I need explaining and when I have had it explained, I will do the other 8 all by myself (at least try)

1. (x-2)(x-8)>0

2. (x-2)(x+5)≤0

In the first one the critical values are 2, 8 which make each bracket 0. Then you need to examine the intervals (-inf, 2), (2, 8), (8, inf). You can use any value in the interval to check so I would use x = 1, 3, 10 and find that the first and last work.

For this sort of inequality there is another way to do it. For the product to be positive you need both positive or both negative which happens with x > 8 and x < 2.

For you second one with the inequality less than, you need the brackets to have opposite signs.

Change the inequality to an equality, and solve for x. The critical values will be at those values.

For example, (x-2) (x -8) = 0. That has solutions x = 2, and x = 8. So we can divide the whole number line into three parts.

Part 1. -infinity to x = 2
Part 2. x = 2 to x = 8
Part 3. x = 8 to +infinity.

Now you just have to check each part, using any number in that part (but not the end points). You also need to check the end points (x = 2 and x = 8)

Check part 1. Lets use x = 0. Then (x -2) (x-8) = (0-2) (0-8) = +16. So the original inequality is TRUE.

If you check part 2, you should find that the inequality is FALSE, and then for part 3 it is TRUE.

You also need to check when x = 2. The inequality is FALSE. And when x = 8, the inequality is FALSE.

So the final answer is x < 2 and 8 < x.

idk try typeing it into google or open study