Alright. So you'll notice in our equation, price is isolated by itself on the left-hand side of the equation, right? But sometimes we might want to rearrange the equation just so quantity is instead the isolated variable, right? So sometimes it could be the case that we want quantity to be just by itself on one side of the equation. So how do we do that? We're going to use just a little bit of algebra here to rearrange the equation. So let's go ahead and do that. I'm going to rewrite it.
P = 800 − 2 q dSo we want to get the quantity by itself, so the first thing we want to do is move the 800 to the other side.
P − 800 = − 2 Q DNow, to get the
Q Dall the way by itself, we need to get rid of the coefficient, the negative two in front of the
Q D, is right of that coefficient there for the quantity, but if we do that side by negative 2, we also have to do the other side by negative 2 as well. So this will cancel out these negatives, and we're going to be left with just quantity demanded on the right-hand side of the equation. But how do we do this P−800 over negative 2? Well, you might not remember exactly how to do that, so one thing I suggest is just take the denominator, the negative two, and just put it under each of them. So what we're going to have is
p ÷ − 2 − 800 ÷ − 2and that's exactly what is happening here right?
P ÷ − 2 − 800 ÷ − 2and 800 divided by negative 2 is going to give us negative 400, right? And
P ÷ − 2, well that's the same thing as saying negative half p, right?
− P 2 − − 400Right? So one more thing, do you guys remember from algebra is when we have two negatives, negative and a negative makes a positive, and we're going to end up with this formula right here.
− P 2 + 400 = Q DThat is how we got the quantity demanded by itself. We could also rewrite this.
400 − P 2 = Q Dright? I just rearranged the terms so that the negative term wasn't first. I think it's just easier to read like that.
Q D = 400 − P 2right? So I just took the right hand side and I flipped it. I just put the QD on the left and the little equation stuff on the right. So that is how we switch which variable is isolated with just a little bit of algebra. There's more than one way to do this, so if you have another way you're more comfortable with, to switch the variables around, go ahead and do it your way. This is just the way I would have done it.
Alright, we're going to do the same thing now with supply and we'll have another example of isolating variables there as well. Alright. Let's move on to supply.