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Alright welcome everybody!
Today we are going to talk about two-step algebraic equation. We already done one-step. We did very well on those. I like to use a metaphor to talk about these. The metaphor I use is that a two-step algebraic notation is like a party. So let's all get ready and get to the party.
Alright so here we are. If you've ever been to a party outdoors, maybe a graduation party, that takes place under a tent. So I just like to draw the tent just like this and here is our equation 3x + 5 = 20. Alright and the first question I have for you is who is at the party and who isn't? And so if you look at this it's pretty easy to see that 3x + 5 is at the party. They're inside the tent. And 20, for some reason or another, is not.
Alright, my next question is who obviously came to the party together? And so we have 3x + 5 at the party. I think it's pretty obvious that 3 and x came to the party together because they are standing so close to each other. That?s what a coefficient and a variable do. They stand very close to each other.
And so of course a slow song comes on and the people who came to the party together want to slow dance. And my question is how can we give them some privacy? Alright so 3 and x want to dance so they had their friend +5. He?s like the third wheel, awkward friend. We want to get rid of him. So the way that we are going to get rid of the +5, is yep, by using inverse operations and subtracting 5. So what happens when we kick out minus five. Well, we have to make sure that we do it to both sides so those who two cancel out. I subtract five from here, and I am left with a new equation which is 3x = 15.
Okay, so we did step one of the two-step equation and we have a new equation of 3x = 15.
(Taylor Swift Bad Blood lyrics)
So if Taylor Swift has told us anything it?s that we should know how this party is going to end for 3 and x. Alright, so they had their slow song. Something went wrong. Who knows? But Taylor Swift has taught us that this is going to end in a break up. So my question to you is how are we going to break up this couple? Well, if you see a variable and a coefficient next to each other, there is a multiplication sign in between them, even if you can?t see it. So the way that we are going to break up this couple is by using division. So we are going to divide both sides by three. Alright! And I get a possible solution of x = 5. I think that is the answer but I am not going to encircle it yet until I do what I should always do in math which is check my answer. I am going to take my possible solution and I am going to put it in for my variable. And then I am going to use order of operations and evaluate these expressions. So I will get fifteen plus five, which gives me twenty. If that number matches the number that was outside of the tent, that wasn?t invited, then I have to be correct. And my solution has to be x equals five. And I could circle it and be confident that I?m correct.
Alright so let?s look at another one.
Ow you should come first to the realization, hopefully, that we use order of operations but in reverse. We added or subtracted first and then multiply or divide second. Alright so we get rid of the friend first and then break up the couple second.
So here is a new equation. A new party.
4x ? 12 = 8
Alright so let?s go through the story. 4x ? 12 is at the party. 8 is not. 4x clearly came together because they?re so close to each other. And -12 is the friend. Alright so we got to get rid of the friend -12 so we?re going to add twelve to both sides. If I do that, I?m left with 4x = 20. Alright that was step one. We are from a two-step equation now it?s just a one-step equation that we have done before. So we are going to divide both sides by four and left with x equals five. Alright then I have to check so I am going to put it back into my variable, and say okay, four times five is twenty and twenty minus twelve is indeed eight. So I have to be correct.
Alright I am going to leave you with one last problem that you are going to practice by yourself. The equation is y/6 + 7 = 11. Alright 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. Alright, good luck everybody!
This video is a tutorial on solving a two step algebraic equation. Each equation is like a party. This party involved slow dancing, third wheel friends, and a break up. Enjoy!