Okay, in this lecture here, we're going to start talking about transposing terms and ways that we can solve for a literal number. Most of the time, it's x, y, z, but it can be any variable. All right. So I mean this, we've looked at this one before x plus four equals 10. Well, what do we want to do? We want to get x alone.

All right, so I've subtracted a four from the left side of the equation. And again, what I do on one side, I have to do on the other. So I subtracted A minus four on the right side, we needed to get x alone. So my answer is x equals six. Okay, that's it. It should be some whatever review we're going to build Upon this as we go on in this section, okay, what I'd like you to do now is to hit the pause button on this, this part of the presentation and do these eight problems.

And I'm going to do several of them for you. I'm going to tell you the ones I'm going to do for you in about 30 seconds, but take the time do them. All right, that's, again, that's how you're going to learn. And I am going to be doing this one for you. This one for you. This one for you.

And this one, so we'll do those four. And so again, hit the pause button, do them and I'll wipe the screen out and start with y squared minus four equals five. Okay, thanks. Okay, we have y squared minus four equals five. So what's the first thing I want to do? I want to get y alone.

So I'm going to simplify this to get y squared. So what I have to do, I'm going to add a plus four here. And when I do on one side of the equation, I've got to do to the other solid a plus four over here. So y squared equals nine. Now what? Take the square root of y squared, square root of nine, square root of y squared is y, square root of nine is three, so y equals three.

Okay, on this one here, we have three x plus seven equals two x plus eight, and we want to solve for x. So what I can do here is I can put my literal numbers on my variables on one side and my whole numbers on the other. So I'm going to say minus seven over here, which will leave me with three x equal to x. And then if what I do on one side of the equation I have to do to the other. Okay? So I'm left with what?

Minus one? I'm sorry, a plus one. All right, so now I have three x equals two x plus one. I want to solve for x. So So why don't I subtract a minus two X on this side. And again, when I do on one side, I have to do on the other.

So I've left on this side here. I'm left with a one or a plus one. All right, and over here, three x minus two x equals x. So x equals minus one. Okay? I'm sorry, x equals plus one.

Now I can check this and I think we'll check this on this one here. All right, so let me let me erase some of these. We're saying x equals one. All right, I've cleaned this slide off. So x equals one. So now I'm going to substitute One correct so we've got three times one plus seven equals two times one plus eight.

Okay, we got three plus seven equals two plus eight. seven plus three or three plus seven is 10. Two plus eight is 10. So it checks out. Okay, well, let's look at this one here, two, a minus five equals b plus three. So let's try to we're solving for a. Alright, so let's start off by trying to get a loan.

So what I'm going to do is I'm going to add a plus five over here, and again, what I do on one side of the equation I need to do on the other. So I have to a minus five plus five b equals zero equal b. Three plus five is what? Eight. And again, I want to get a alone. So why don't I just divide by two here?

That divides out a cancels out. I have a equals b plus eight divided by two. That's it. That's it, guys. Okay, let's do the last one. Okay, and this problem here we have x plus y squared equals y squared plus seven, and we're solving for x.

So what do I want to do? I want to get x alone. So why don't I just subtract the Y squared work? from each side All right, if I do that x plus y squared minus y squared equals x and y plus y squared plus one minus y squared equals seven. So x equals seven. That's it.

Okay. Talk to you on the next section. All right, I thought I'd just go over one like this. Again, I'm not sure if I hit it, but it could be a review. So we've got six x minus eight equals four x plus two. What I want to do is I want to get the unknowns on the left side of the equal sign and the numbers on the right.

So I just subtract the minus four x over here. Again, what I do on one side of the equation I have to do to the other, and then I add a plus eight over here. And again, what I do to one side of the equation, I have to do the other. So I get this here, six x minus four x equals two plus eight. I just simplify the term, six minus four x is two X. Two plus eight is 10.

I want to get x alone, I want to solve for x. So I divide by two to get one x. And again, what I do on one side of the equation, I've got to do to the other. So 10 divided by two is five. So x equals five. That's my answer.

All right. I just wanted to hit that make sure I covered it. I think we did a problem previously, and I felt as though I didn't really specify that so I wanted to put it here. So we're good. So let's go on. Okay, so Here we go.

Okay, so I do I want to find a. So what do I do? Well, let's do with this say for a and I got a minus 32. So what happens if I add 32? Okay, so I got for a plus 32 minus 32 is zero, I don't have to show that what I do on one side of the equation I have to do to the other. So I get to a plus 32.

All right, I want to get a loan. So why don't I subtract the two a from both sides. So a plus to a minus two A is going to be Zero, I don't have to show it. But I've got 32 for a minus two A is to a right for a minus two, a is to a left. All right, so now what do I do? I gotta get a alone I divided by two divided by two, I get a 16.

There's my answer a equals 16. Okay, let's go on to the next one. Okay, let's check this one in Previously, we said that x equals two. So let's plug in a two for x and see if it works out. So I've got eight times two minus six equals 12 times two minus 14. Well, two times eight is 16 minus six equals two times 12 was 24. minus 1416 minus six is 1024 minus 14 is 10.

So we check, so we did it right x and d is two. Okay, and this example here we have five parenthesis x minus two, close parentheses, equal 30. And we want to find x. So let we should probably multiply this out. So I have five x minus 10 equals 30. Did I change anything?

No, all I did was multiply this part of the equation I didn't change the value anyway. Okay, so now what do we want to do? We want to get x alone. So five x Minus 10. So let's add a 10. Right?

Equals 30 plus 10. So now I have five x minus 10 plus 10 is zero, I don't have to show it. What I do to the right left side of the equation I do to the right. 30 plus 10 is 40. All right, now I divide by five. And I have x equals what?

Eight. That's my answer, eight. Okay, now if we do a check, all right, and so Now I got to do what's in the parentheses first. Because five times six is 30 and 30 equals 30. So it checks. Okay, in this example, we have five minus parenthesis, x minus two equals 30.

And we want to find x. So if I look at this one, this one here a little bit different, but it's not too bad. We can actually put a one there. All right, so I was saying, even though we don't show it, we're multiplying that by one. All right, x minus two equals 30. All right, so now five, I've got a minus one minus one times x. is a minus x minus one times a minus two is a plus two equals 30.

Now I combine my terms, five plus two is seven minus x equals 30. I want to get x alone, okay? x alone. So I subtract a seven. All right, and I have I have a minus x minus seven minus 30 is 23. So minus x equals 23.

I want to find a positive x, so I multiply this by minus one doesn't change the value. So minus one times x is a plus x 23 times a minus one is a minus 23. So x equals minus 23. Okay, so let's let's check this one. And we said X was 23. I forgot to put it up there x is 23, actually a minus 23.

And let's just do it. So was saying, five minus, minus 23 minus two equal 30. Well, if you remember, this is actually a minus one isn't there. So minus one times a minus 23. is a plus 23 minus one plus a minus one times a minus two is a plus two. All right, minus times a minus that changes this to plus. So what do we have?

5678 910. So 30 equals 30 because five plus 23 plus two equals 3030 equals 30. It checks. Okay. Okay on this last example where we're going to solve for x, and we have two x plus four, times two x minus four, and we want that equal to four x squared plus two x right here. So I'm going to simplify, I think we simplified to the left first, what's on the left of the equation for us.

So we're going to multiply two x times two x, right and we got four x squared. And then we're going to multiply the outer and the inner terms. So I've got two x times a minus four, that's a minus eight x. And then the enter two terms, plus four times two x is a plus eight x. And then I multiply here plus four times a minus four, and that is what minus 16 and that's quite equal four x squared plus two x. Okay, so now I'm going to still simplify over here to the left.

So I've got four x squared minus x minus eight x plus eight x is zero. I don't have to show that. So it's actually let me erase that it's a minus 16, not a plus. So I have a minus 16. And that's going to equal four x squared plus two x. Okay, so let's looking at this now.

I've got a four x squared over here and a four x squared over there. Well, what I do to one side of the equation I can do to the other and I don't alter the value or the solution. So a five minus a four x squared over here and minus a four x squared. Over here, I'm left with because I have a plus four x squared and a minus four x squared. That's a zero. I don't have to show that but I'm putting it down anyways.

So I've got a minus 16 equals plus four x squared minus four x is still a zero. I don't have to show it, but I'm putting it down just to clarify it to x. So now I have minus 16 equal to x. Divide to divide two. And what do I have? I have x equals a month. minus eight.

That's my answer. X is a minus eight. All right, let's clear the slide, we're going to do a check on this. Okay, we're going to check, check this one. And remember, we saw that x equals A minus eight. So all I'm going to do is I'm going to plug in minus eight here.

So let's do this one. So I get to x times a minus eight, plus four times two times a minus eight, minus four. And that's going to be for minus eight squared plus two times a minus eight. So let's simplify over here. So two times minus eight is minus 16. plus four. Two times a minus eight over here is still a minus 16 minus four.

All right, I gotta put the, I forgot to put the equal sign in there. So equals. Okay, so now we got four times. Right? eight squared, eight times eight is 64 plus two times minus eight, which is a minus 16. All right, just remember, are we here I have four times a minus h squared.

A minus eight times a minus eight is a positive number, in this case, four times 64. So let's go back over here. To the left and simplify it, okay, minus 16 plus four is what? Minus 12. Okay, minus 16 plus a minus four is a minus 20. Okay, four times 64.

Well, I'm going to have to kind of stop it and use the calculator. Okay, so four times 64 is 256 plus a minus 16. So I'm just going to say minus 16. All right, so let's go over here, a minus 12 times a minus 20. It is a plus 240 to 56 minus 16 is 240. So it checks.

So we're right, x equals A minus eight. All right. Okay, well, that pretty much ends this section. This was a long one. You may have to play these solutions, one or two or three times, but do them, follow them. Make sure you understand the more of these problems you'll do, the easier it will be for you.