00:01
In this one, we were given x times quantity x minus 3 times quantity x plus 2, and we're told that it's greater than 0, and we're asked to find the solution set.
00:08
First of, let's find the zeros.
00:10
The zeros occur at x equals 0, 3, and minus 2.
00:16
Now, if we plug this on a number line, so we have our minus 2 here, we have our 0 here, and we have our 3 here.
00:25
So we're going to take a value from this from region 1, region 2, region 3, and region 4, and see which one of these satisfies this inequality.
00:37
Well, if we take a number, let's say to the left of negative 2, let's say negative 3, we are in region 1 of negative 3, we are going to get negative 3 times negative 6 times negative 1.
00:55
And this gives us negative 18, so region 1 does not work.
01:02
Now let's take a look at region 2, and let's do negative 1, which gives us negative 1 times negative 4 times 1, which gives us 4 is greater than 0, so this works.
01:18
That's a checkmark.
01:19
Now let's take a look at region 3.
01:21
Region 3, we are going to do, let's do 1 in region, the value 1 in region 3...