Okay, welcome to math for electronics, section eight methods for solving solving equations. I'm Al, and this is Al's electronic classroom. What we're going to look at here are operations on both sides of the equation. transposing terms, solution of numerical equations and inverting factors in literal equations. So let's go to the next slide and start this off. All right, so here we're going to start off start off with the methods of solving equations.

And we're going to throw up I'll put some some equations up as some examples up and show you how we do it. Okay, so when this is so in this first equation, we've got x plus three equal five, and we and we Want to find the value of x here? All right, so on the bullet, all right there must do the same operation on both sides of the equation. So I start off with x plus three equals five. What do I want to do? I want to solve for x.

So I want to get x alone on one side of the equation. So what I can do here is in this step here, I can subtract R, or better still, I'm going to say it this way, add a minus three, which I'm showing you right here. And right there. So if I add, if I say x plus three plus a minus three, that's going to leave me with x. And again, what I do on my one side of the equation I need to do on the other side of the equation. So I say five minus three equals two.

So in this example, my answer is x equals two. Now I can check that by plugging it in. And I can say since x equals two, I can say two plus three equals five. Whoops, that's my three right there. Two plus three equals five. That's right, two plus three is five.

So I know that I've solved this equation properly, and x equals two. Okay, I've cleaned off the slide and let's go to this example right here. x minus 12 equals 36. And again, I'm solving for x. So what Do I want to get x alone? So I add right there I add a plus 12.

All right, what I do on one side of the equation I must do on the other. So I add a plus 12 on this side. So 36 plus 12 x equals 48 is my answer. Okay, so now I can I can check it, I can say, by using this equation here, let me let me clean this glide off. So by using this equation here, I just substitute 48 for x, I say 48 minus 12 equals 36. And that is correct because when I submit tract 12 from 48.

I get 36. So I know I've done it right. Okay. So you may if this seems a little tricky for you, why don't you just look at it again. And I'm sure if you do it one more time, and maybe total three, you'll get what I mean. Alright, so I'm going to stop now and we're going to go to the next slide.

All right, so on this slide here, I've given you some problems. So again, take the time, do them. All right, the ones that may be a bit different here, than what I've gone through those two examples on the previous slide is this one, and this one, the other ones are pretty straightforward to what I've done pretty Previously. All right, take a look at them. Take the time, do them. The answers are on the next slide.

Okay, I will do. I will do this one and this one on the next slide. But again, I want you to take the time to do them. All right, we're going to stop here, you're going to stop, you're going to do them. We'll see you on the next slide. All right, I'm assuming that you've tried to do them, and now you're looking for the answers.

The answers are right here. All right, x on the first one x plus two x is three y plus two equals nine y is seven. x squared plus two equals 18. x is four. A is seven. I plus two is for C plus two equals six. C is for now.

Said previously that I am going to do this one and this one for you in which I'm going to do that now. So I'm gonna white out the screen and doing alright, so here we have it x squared plus two equals 18. All right, so what's my next step? Well, what are we trying to do? We're trying to get x alone, right there. Alright, so second, I can say x squared plus two plus a minus two equals 818 minus two.

Okay, so what I've done is I've subtracted a two from both sides of the equation. All right, and what am I left with? I'm left with if I simplify that I'm left with x squared equals 16. But what I want to do is I want to get x alone. So if I've got an x squared and I want x, what do I do? Well, I take the square root of x squared and the square root of 16.

What's the square root of x squared is x, what's the square root of 16? You may have to use the calculator. But the square root of 16 is four. That's my answer, x equals four. Now I can check. And I can say, and what I can do is I can go back to my original equation, and substitute four in there for x.

So I can say force four squared plus two equals 18. squared. That means four times 416 plus two equals 18. It works. There's my answer. Okay, on this next one, two A plus seven equals 21. Again, we want to try to get a loan.

So what's the first thing I'll do? I'll say two A plus seven plus a minus seven equals 21 minus seven, or plus or minus seven, I should say. All right. So now, what am I simplify this to a plus seven plus a minus seven is zero. I don't have to put the zero in there. Equals 21 minus seven is 14.

What do I want to do? I want to get a loan. So how do I do that? Well, if I divide two on each side, the two cancels out. Two goes into 14, seven times. So a equals seven.

All right, now if I want to check that, I say two times seven plus seven equals 21. Two times seven is 14, plus seven equals 21. It checks all right?