Originally Posted by

**Aluminium** I'm comparing two sums here and can't see the logic why I need to use less than/more than signs or less than-equal to/more than-equal to.

Sum 1 -

(8-x)/(9-x) <= 0

Sum 2 -

(8-x)(x-2) >= 0

For both of these I need to find the roots of the inequality, illustrate them on a number line, then pick a number within the interval and check whether it fits with being less than or equal to zero - or more than or equal to zero.

Now, where I'm picking my intervals is where my problem begins.

Take Sum 1, my intervals are:

x<=8 , 8<x<=9 and x>9

The signs here are correct, my answer is [8;9)

What is the logic for putting <= instead of < in such a sum during my intervals? Because I'm not seeing it.

In my Sum 2, my intervals are:

x<=2, 2<x<=8 and x>8 -- And the answer tells me that this is wrong! The answer should be [2;8], which means that the intervals should be: x<2, 2<=x<=8 and x>8

Is there some set of rules I'm not aware of?