00:01
Okay, so we're asked to find the intervals of where our answer are.
00:06
And we have, for number six, it's the same expression.
00:10
We just have a different inequality sign.
00:12
Let's take a look at a and go through how we're going to solve that one.
00:17
So we have x times 7 minus 2x, and that needs to be greater than or equal to 3.
00:25
Now, if we start by distributing the x, we get 7x.
00:31
Minus 2x squared is greater than or equal to 3 now in this problem i have an x squared and when we have an x squared and we have an x and we have a constant we want to put our equation or inequality in the form of a x squared plus bx plus c meaning that this 3 needs to move over to the left -hand side so let's subtract three from both sides and that's going to leave us with negative 2x squared and we'll have a positive 7x and then minus 3 and that's going to be greater than or equal to zero.
01:14
So now i have a quadratic on the left hand side.
01:18
One method we could use to solve this is we could try factoring this and see if that works.
01:25
We could also try to use the quadratic formula and get our answer that way.
01:31
But more than the likely we're going to get two answers to this problem.
01:35
Let's see if we're able to factor this into a set of two parentheses.
01:43
And we'll make that greater than or equal to zero.
01:49
And if we can't factor, then we'll have to go and use the quadratic formula.
01:53
But let's check this out.
01:54
So to factor, one thing we can do is we can multiply our a value by our c value.
02:01
And i have an x on there.
02:03
That should not be an x.
02:04
That's a constant three.
02:06
And negative two times negative three is a positive six.
02:10
And then we're going to put our b value at the bottom of seven.
02:14
And so what i want is, what can i multiply to get six? that adds to get seven.
02:22
And if i do that, well, i get a six and a one.
02:27
So when i multiply six and one together, i get six.
02:32
And when i add those together, i get seven.
02:36
Now, we're not quite done with this yet.
02:40
Because we have an a value of negative 2, it has to be negative 2x plus 6, and then negative 2x plus 1.
02:52
And then if we can simplify, we can simplify.
02:56
So for our first one, i could divide both of these by negative 2.
03:00
And so that gives me x minus 3 times a negative 2.
03:06
2x plus 1.
03:08
And that's greater than or equal to 0.
03:12
So now what i want to do is i want to figure out, well, what are the values i can get? and these are going to be key points that i use.
03:20
So for example, x minus 3.
03:23
What keeps that greater than or equal to zero? actually, i just may get equal to zero.
03:29
And if i solve that one, i get x equals three.
03:32
So that's going to be a key point.
03:33
And then if i solve the other one, i got negative 2x plus 1 equals 0.
03:39
I'd subtract the 1, and then divide by negative 2, so i get x equals positive 1 1⁄2.
03:47
All right...