In this video, I'd like to talk to you about absolute value inequalities. There are two kinds of inequalities that we talk about here. One is where you've got an example like absolute value of x is less than 5. And the other one, so I can go ahead and contrast, is like the absolute value of x is greater than 5. Now, first let me say it doesn't matter if I put the equal to on there. I just didn't for the example. But notice one is absolute value less than, and the other one is absolute value greater than.
Absolute value, when you start to look at its many facets, one part of it is that it reflects distance. So this says the distance is no more than five units. Here, this one says the distance. is more than 5 units on either side of something. In this case, the 5. So when you look back over here, how do you get rid of the absolute value is our algebra question.
So you say, well, x has to be somewhere between a negative 5 and a positive 5. See, and check that real quick in your mind. Pick a number like negative 3. Put a negative 3 in there. Absolute value 3 is less than 5. Pick something like positive 4. 4 is less than 5. Yeah, so it works. So anytime you see absolute value less than or less than or equal to, it's between. It's a between scenario.
That's how you get rid of the absolute value. The other one says, and watch closely here. Absolute value greater than, it means that x can be greater than 5 or x can be less than negative 5. Okay, so it's going to be either sides of negative 5 that direction, positive 5 other side of it. So it's a split. That's how I remember these things.
I look at this is between and this is split because let me draw the picture and it'll make more sense especially if you're graphical like I am. You come over here and you say well we're between a negative five and a five. Again these aren't playing any piece to it so we're between negative five and five.
And there's my interval notation. This one says we have to split it. Now, this is where the infinities are going to come in handy. The first one over here on the left, I'll just pick on him. X is less than the negative 5, or X is greater than the 5. So how you write the interval, it takes two of them.
It says negative infinity to negative five union with, which is the same as OR, you can pick over in this set from five to infinity. So that's the concept behind the lesson. If you can practice that, Just know that there's two cases, absolute value less than, absolute value greater than, one's a between, one's a split. Get that punched in your head really good.
Just get it poked in there. Then you can do all these problems. Okay?
So next video, I'm just going to do some examples.