00:01
Okay, so in solving this inequality, i want to find some key points that are going to be helpful here.
00:07
One of the key points is going to be when does this equal zero? okay, so that's going to be x plus seven equals zero.
00:13
That happens when x is a negative seven.
00:16
I also want to take an account when does my denom equal zero.
00:19
So that's two values that it cannot be.
00:22
Okay.
00:23
So if i factor that x plus two and x minus two, and i want to make sure that's not equal zero.
00:28
So x cannot equal a put negative 2 and x cannot equal a positive 2.
00:34
So i like to look at these on a number line now.
00:38
So i've got some key points.
00:40
I've got 2, negative 2, and negative 7.
00:43
So remember, since this is greater than or equal to 0, negative 7 does equal 0 when i plug it in.
00:50
So negative 7 plus 7 is 0, divided by all this is 0.
00:53
So i know that negative 7 is part of my number line.
00:56
So let's put 0 here.
00:57
One, two, three, four, five, six, seven, eight.
01:02
Okay, so that's a part of it.
01:04
One, two, three, four, five, that's fine.
01:07
Here's negative two and here's positive two.
01:10
I'll put open circles on both of those because they cannot be plugged in since they cause zero in my denominator.
01:17
What i have now is three sections of values.
01:21
Okay.
01:22
I want to figure out which sets of numbers are going to give me a true inequality here.
01:27
Okay.
01:29
So i'm going to just give, give myself a very rough estimate in some of these.
01:34
So for example, if i choose a test value like zero, and i plug that in, that's zero plus seven and that's zero squared minus four, well, that becomes seven over a negative four.
01:45
Is a negative number greater than equal to zero? no.
01:50
This is not part of my solution, which means everything in between is also not going to be part of my solution.
01:56
I know seven is a part of my solution, so i feel confident.
01:59
That's going to be everything here, just in case i could plug in something like three here.
02:04
So if i did that, that would give me three plus seven is a positive number, and then three squared minus four is also a positive number.
02:12
That would equal to 10 over nine minus five is that...