Alright, let's move on here. And right now we're gonna operation on both sides of the equations, and we're going to concentrate a little bit on division. Alright, so in this first example, I give you, three x equals six. And what do we want to do? We want to solve for x. So if you look, I divide the left side of the equation by three.

And what I have what I do on one side, I have to do to the other. So I divide six by three in my answer is x equals two. And again, if we want to do a check, three times two equals six. And there you go. So it checks. All right, so do Remember what you do with one side of the equation you need to do to the other.

Let's look at this one. This one's a little bit, we've expanded this one a little bit here for you. two x minus 12 equals 36. Well, we want to get x alone. Alrighty, so if you look, I add a plus 12 over here, and again, what I do on one side of the equation, I have to do on the other side, so I add that so now I've got two x equals 48. I need to get x alone.

So if I divide two x by two, I get x. And again, what I do from one side of the equation, I have to do to the other, so I multiply, divide 48 by two and get 24. So x equals 24. We can do a check here, we can say two times 24 minus 12 equals 36. Two times 24 is 48 minus 12 equals 36. So it checks.

Okay. Let's stop here and go to the next slide. And we have some problems for you to do. All right, here are the problems. So take a look at them. Here they are, I'm going to do them.

I'm going to do several of them on the next slide. So I want to want you to take a few minutes and do them and then we'll give you the answers and I'll do that Couple of them, maybe not all six, but at least two, maybe three. All right. So stop the slide do the problems, and the answers will be on the next. Next slide. All right, here are the answers.

And you can read them, I'm not gonna yell them out or call them out. But what I am going to do is I think we'll do this one for you. And we'll do these two here. All right. So what I'm going to do is I'm going to wipe the screen out and do them and then we'll move on. Okay, so on this problem here, we got four y equals 16.

What do I want to solve for I want to solve for y. All right, so what do I do? Well, maybe I should just divide this by four and divide this by four. And as we know previously, these cancel out or divide out so we have why 16 two divided by four equals four. So y equals four. All right, and I can do a check here for and I said y equals four, so four equals 16.

And that checks out right there. Four times four is 1616 equals 16. So we're good there. All right, on this one here, next one for x equals eight minus two. So let's, again we want to get x alone. So what I would do is say for x, and I simplify this, this side first six.

All right, now, again, I want to get x alone. So what I do on one side of the equation I do on the other so what do I do? I do divide by four, and I divide by four, right to get x alone. And four, six divided by four is 1.5. So that's my answer. x equals 1.5.

I can check. I can say four times 1.5 equals eight minus two. Four times 1.5 is six. Eight minus two is six. It checks. Alrighty, there we go.

Okay, on this one, we've got four x equals eight, plus four. So forex add, combine this side eight and forest 12. Now what I want to do, I want to divide by four again divided by four again, and we have x equals three is my answer. Now I can do a check, four times three because x equals three equals eight, plus four, four times three is 12. Eight and four is 12. It checks.

That's it. That's it. All right, Gauss. We're still doing methods of solving equations. So we're going to look at powers and roots now. And on this particular example, we give you x squared equals nine plus seven.

So I want to find what x is. Alright, so x squared e 16 I want to find x alone. So what do I do? I take the square root of x squared, and it's x. And then I take the square root of 16. And my main, my answer is plus four, r minus four, because four times four equals a plus 16.

And a minus four times a minus four equals plus 16. So in this, in this example, when I'm dealing, depending on when I'm dealing with square roots, alright, I can have the same number, meaning the same amplitude, but the sign may be different. In this case, in this example, the x equals four and x equals minus four Okay, well, as usual, we've got some problems for you to do. So, again, stop the presentation, do them. And I'm going to do a couple for you. When we come back, I'm probably going to do this one.

This one. This one, this one, actually I'll do. I'll do those five. We've kind of done this one already here. So I don't need to do that again. So I'll do those five.

So again, stop, stop the presentation, do the answers. Do the problems rather. And I'll, I'll do them for you the next slide along with the answers, okay. Okay, this one here y squared equals nine, we want to find y. So what do I do? Well, to get y alone, I take the square root of y squared what I do on one side of the equation I have to do to the other square root of y square A y squared is y square root of nine is three.

There's my answer y equals three. All right, if I want to check it, I'll do it down here. Check it, three squared equals nine. Three times three equals nine, it checks. Alright, this one here, x squared equals four b squared. So what do I need to do?

Well, I want to find x alone. So x squared, I'll find I'll find the square root here. But we can do this square root of four. And the square root of b squared. Remember that? All right, square root of x squared is x square root of four Is to square root of b squared is B.

So x equals to B. All right? Um, that's it. If I want to check it, I just since x equals to be, I just substitute and say, okay, x squared, so I say to be squared, I'm sorry to be, and I square that. Alright, it's for B squared. All right, so we're good.

On this one here, we've got x squared equals two plus three all squared. And again, I want to get x alone. So probably the first thing I want to do is kind of simplify this side. So I add two plus three is five squared. So x squared equals five squared. And again, let's simplify that one more time.

All right, five squared is 25. So x squared equals 25. Find the square root of x, the square root of 25. Square root of x squared is x. Square root of 25 is five, so x equals five. And again, I can check this I can say five squared equals two plus three squared.

Five squared equals five squared 25 equals 25. There's my answer on the checks. All righty. Okay, this one here, I squared equals 19 plus six kind of doing the same thing. over again. So I can say i squared equals 19 plus six.

So let's, let's simplify that side. 19 plus six is 25. Okay, I'm looking for I alone again. So the square root of i squared equals the square root of 25. What I do on this side after doing this side, square root device squared is i square root of 25 is five, so I equals five. I can check.

I can say five squared up here, because we said that i equals five. So five squared equals 19 plus six. All right, five squared is 2519 plus six is 25. So it checks. This one probably looks a little odd because there are no numbers in it, but Basically, what are we solving for a? Right?

So what I do to one side of the equation I do to the other, so a squared equals b squared. So what do I do? I take the square root of a squared, and that equals what what I do to one side of the equation I do to the other? Square root of A, A squared is a square root of b is b squared is B. So there's my answer. And I mean, we could plug it in, it's kind of redundant.

So we're good. They kind of threw a little bit of a little bit of an odd one in there. Okay, and here, here are the answers we did did like five of the six. So those are the answers. And we're good here where we're going to well wrap this lecture up, and we'll see you In the next section