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Missouri State University

Campbell University

University of Michigan - Ann Arbor

07:29

James C.

Using Models Use the model given to answer the questions about the object or process being modeled. An ocean diver models the pressure $P$ ( in $\mathrm{lb} / \mathrm{in}^{2} )$ ) at depth $d$ (in ft) by $$P=14.7+0.45 d$$ (a) Make a table that gives the pressure for each 10 -ft change in depth, from a depth of 0 ft to 60 $\mathrm{ft}$ . (b) If the pressure is $30 \mathrm{lb} / \mathrm{in}^{2},$ what is the depth?

01:13

Amy J.

The model $L=4 S$ gives the total number of legs that $S$ sheep have. Using this model, we find that 12 sheep have $L=$ __________ legs.

00:57

06:25

Daniel P.

Using Models Use the model given to answer the questions about the object or process being modeled. The portion of a floating iceberg that is below the water sur- face is much larger than the portion above the surface. The total volume $V$ of an iceberg is modeled by $$V=9.5 S$$ where $S$ is the volume showing above the surface. (a) Find the total volume of an iceberg if the volume show- ing above the surface is 4 $\mathrm{km}^{3}$ . (b) Find the volume showing above the surface for an ice- berg with total volume 19 $\mathrm{km}^{3}$ .

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So in this section we're going to talk about what equations and inequalities are as they are very important piece of algae. So the first thing is what an equation is. Well, we've been discussing expressions over the last couple of sections. So what in equation is it's a statement in which two expressions are set equal to each other. So if we want to come up with a formal definition of an equation, it's a mathematical statement that states that two expressions are equal to each other. Just gonna line this up are equal to each other. So that's essentially what an equation is. It's a mathematical statement that states that two expressions are equal to each other. So, for example, I could have, um, the mathematical expression to X plus five. So this would be our example. Two. X. Well, let's make that a little legible for us. So let's go with two X plus five. And let's say that was equal to eight X minus three. So essentially, what we're saying is this expression to X plus five is equal or the same as eight X minus three, and in the next couple of examples, will show you how to determine if certain values of X are solutions to an equation and the process to start being able to solve some equations using mental map. But the biggest thing for an equation? Just note that it states that two expressions are equal to each other. Well, then, what's an inequality? Well, and inequality kind of is along the same lines, except we're not always going to be finding values of X that are gonna make it equal to it. It's going to have some type of inequality nous to it, which will explain in a second. So if we needed to come up with a definition for inequality. What we would say is that it's a mathematical statement that uses Oops. Let's get that back here. Oh, we'll just start typing again. So it's a mathematical format. This in the second. So inequality is a mathematical statement that uses an inequality sign to compare two expressions or to mathematical expressions. Oh, right, a little bit bigger for us. So, like I said, Inequality is a mathematical statement that uses an inequality sign to compare to mathematical expressions. So a lot of times we're comparing whether they're greater than each other less than each other. Maybe they could be less than or equal to each other at the same time. But that's why we're using the word compare. So now what are these inequality symbols we're talking about? Well, there's going to be four of them, and it's very important that you know each of them. So the first one is the symbol right here, okay. And what this symbol means is less than so. This symbol indicates less than so. It means that the number to the left or the expression to the left is going to be less than the one to the right. So, for example, let's say I had one plus three is less than five. Well, this would be true because one plus three is four and four is less than five. OK, so that's our first inequality Simple. Next, we could have what's gonna look like a lesson sign. But then there's going to be a little line underneath. Well, what this means is that it's less than or equal thio, so less than or equal to. So what that means is the expression on the left could be less then, or it could be equal to it. So, for example, let's say I gave you that eight minus three is less than or equal to five. Well, this would be true because eight minus three is five and five is less than or equal to five because it's equal to it. So that would be one way to represent it. So we could have actually have that same value. Or I could say that seven plus 10 is less than or equal to or sorry seven plus two is less than equal the 10. This would also be true because seven plus two is nine and two is less than or equal to 10. Because it's less than so. It doesn't actually have to be equal. It could be either case, all right, so our next inequality simple. It's going to kind of look like the opposite of less them. And in fact, it means the opposite. It means greater than so. This is a greater than symbol, meaning the expression to the left is greater than the expression to the right. So, for example, I could have two times five is greater than seven, and this would be to true because two times five is 10 and 10 is greater than seven and lastly are last in the quality symbol. Again, it's gonna look like are greater than sign, but it's gonna have that little line underneath. So what this is going to mean is greater than or equal to. So it means just the same as it did before. It could be greater than it, or it could actually be equal. So, for example, I could say that one plus two is greater than or equal to zero, because one plus two is three and three is greater than or equal to zero because it's greater than it. Or, for example, we could say that uh, eight plus five is greater than or equal to 13 because eight plus five is 13, which is greater than or equal to 13 because it is, in fact, equal to it. So these are the four inequality signs that you'll see throughout, um, algebra. Um, they're very important to know. Um, my hint for less, then, is if you were to take your two hands and turn them to make your to inequality signs, your left hand makes your less than sign That's the trick. I always tell my kids, and in the next couple examples, we'll see some basic ways to determine if inequalities or true or false.

Linear Functions

Solve Linear Inequalities

Functions

Systems of Equations and Inequalities

Graph Linear Functions

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