00:01
We need to solve the following.
00:02
So the first one says quadratic inequality.
00:05
So it has to have an inequality in the expression.
00:11
So a doesn't.
00:13
C doesn't even have equal or inequality.
00:17
And then for it to be a quadratic, it has to have an x squared.
00:21
So d doesn't.
00:22
So letter b is our only choice.
00:24
So we need to pick which of the following numbers is less than or equal to negative 2.
00:30
Well, negative 2 is equal to negative 2.
00:32
Negative 1 is bigger.
00:33
0 is bigger and 1 is bigger.
00:36
And so then we have to write the following and set notation.
00:40
So we have x is greater than negative 2.
00:42
So greater than negative 2, but less than 6.
00:51
So that matches answer choice b.
00:54
Then we have 4.
00:56
There's no equal signs.
00:57
There's only going to be parentheses in our interval notation.
01:00
So so that throws out a, b, and d, so we're only left with c.
01:05
So then we have to factor x squared minus 5x plus.
01:16
I'm factoring.
01:19
So we have x minus 5, x plus 3 is greater than 0.
01:28
So we get x minus 5.
01:30
Well, we're going to first think of it as an equation.
01:32
So we can get our solution.
01:34
So it equals 0.
01:35
So we get zero and then x plus three is equal to zero.
01:39
So x is equal to negative five and x is equal to negative three.
01:43
So we have to have a negative five and a negative five, a positive five and a negative three.
01:53
So if it doesn't have a positive five and a negative three, it's wrong.
01:57
So c is gone and b is gone.
02:02
So now we've got to check.
02:03
So we have our little number line here.
02:06
So we have negative three and then we have positive.
02:10
Positive 5.
02:11
So if we plug in negative 3, it makes this equal to 0.
02:15
It has to be greater than 0, so negative 3 is not included.
02:20
And the same thing if we plug in 5, it's not included.
02:24
So now we're going to plug in a number that's in the middle to see if we shade less than or greater than.
02:31
So we're going to try 0 itself.
02:33
So we plug in 0.
02:36
We get 0 minus 5, 0 ,000.
02:40
Plus three.
02:41
So that's negative five and three.
02:45
That's negative 15.
02:47
Negative 15 is not greater than zero.
02:52
That's not true.
02:56
So we can't shade any numbers between negative three and five.
03:00
So it has to be numbers that are smaller than negative three.
03:04
We got to shade in this direction and we got to shade in this direction.
03:08
So that means that a is the answer to choice, not d...