Two Step Equation Party

All right, welcome, everybody. Today, I'm going to talk to you about two step algebraic equations. We've already done one step. We did it very well on those. I like to use a metaphor to talk about these. The metaphor I use is at a two step algebraic equation is like a party. So let's all get ready and go to the party. All right, so here we are. If you've ever been to a party outdoors, maybe a graduation party takes place under a tent, so I just like to draw the tent, just like this. And here's our equation three X plus 5 equals 20. And the first question I have for you is who is at the party and who isn't. So if you look at this, I think it's pretty easy to see that three X plus 5 is at the party there inside the tent and 20 for some reason or another is not. All right, my next question is, who obviously came to the party together? And so we have three X plus 5 at the party. And I think it's pretty obvious that three and X came to the party together. Because they're standing so close to each other. That's what a coefficient and a variable do, they are right next to each other. All right, so of course, no song comes on. The people who came to the party together want to be slow dance. How can we give them some privacy? All right, so three next one to dance and they have their friend plus 5. He's like the third wheel awkward friend and we want to get rid of him so the way that we're going to get rid of a plus 5 is by yep using inverse operations and subtracting 5. So what happens when we kick out -5? Well, we have to make sure we do it to both sides, so those who cancel out. And I subtract 5 from here. And I'm left with a new equation of three X equals 15, all right, so we did step one of a two step equation and we have a new equation of three X equals 15. 'cause baby now we got bad blood you know it used to be mad love so take a look what you've done 'cause baby now we got bad blood hey now we got Taylor Swift just told us anything. It's that we should know how this party's gonna end for three and X all right, they had that slow song. Something went wrong, who knows? But Taylor Swift has sort of said, this is gonna end in a breakup. So my question to you is, how are we going to break up this couple? Well, if you see a coefficient of variable next to each other, there is a multiplication sign in between them, even if you can't see it. So the way that we're going to break up this couple is by using division. So I'm going to divide both sides by three. All right, and I get a possible solution of X equals 5. I think that's the answer, but I'm not going to circle it yet until I do what I should always do in math, which is check my answer. When I take my possible solution, and I'm going to put it in for my variable, and then I'm going to use order of operations and evaluate this expression. I get 15 plus 5, excuse me, 20. And if that number matches the number that was outside of the tent, that wasn't invited. Then I have to be correct in my solution has to be X equals 5, and I could circle it and be confident that I'm correct. All right, so let's look at another one. Oh, first you should come to the realization, hopefully, that. We use order of operations but in reverse. We added or subtracted first and then multiplied or divide second. So we get rid of the friend first, then break up the couple second. So here's a new equation new party. Four X -12 equals 8. So let's go through the story. Four X -12 is at the party, 8 is not four X clearly came together because they're so close to each other and -12 is the friend. All right, so we've got to get rid of the friend -12. So we're going to add 12 to both sides. If I do that, I'm left with four X equals 20. All right, that was step one. We are from a two step equation now, just one step equation, which we've done before. So we're going to divide both sides by four. And left with X equals 5. All right, then I have to check, so I'm going to put it back in for my variable and say, okay, four times 5 is 20. And 20 -12 is indeed 8. So I have to be correct. All right, I'm going to leave you with one last problem for you to practice by yourself. The equation is four. I'm sorry, excuse me. Y over 6 plus 7 equals 11. All right, so try this problem on your own. Go through the story, get rid of the friend first, break up the couple second, get a solution, and then check that solution to make sure you're correct. All right, good luck, everybody.