On this equation right here, I've got -25 and a plus 1/5. It's very similar to the previous equation, but we're going to have to instead of multiplying by -1/3, we're going to have to multiply by 5. And we're going to have to add a 25 to both sides. So if have price equals -25 + 1/5 quantity. So I add a 25 to both sides here. Add a 25 to both sides. So now you're left with P + 25 and this 25 cancels out so I'm left with a 1/5 quantity. In order to get rid of this 1/5 I have to multiply this by 5. But anything I do to the left hand side needs to be done to the right hand side, I'm going to multiply this times 5 as well. So I am left with 5 price here plus 125 is equal to quantity, this is the quantity of supplies so I'll include that little s there. So now, I gotta flip my sides and I'm left with a quantity supply over here, here's my Qs = 5P + 125. So I mean once you get in the habit of what you need to do and you'd be consistent, it's that difficult, again, using the word trick. Let's try this one, this one is maybe a little more tricky than the other ones here. If I'm going to solve for price, it means I'm going to get price all by his or her lonesome and then I have to solve for this. So let's run the P let see we have to do, 1/- epsilon = P- mc/P, this a thing that's a caught the Learner Index from economics. The epsilon refers to an elasticity where P is pricing. MC equals marginal cost. But if I'm trying to get something that's in the numerator and the denominator by it's lonesome, I'm going to find it to be a little bit challenging to do this. Now, I could essentially do some operations to begin with and then simplify. So remember how when I had, in these previous equations, like price minus 30 divided by 2. I have to divide the price by 2, and I have to divide the 30 by 2 or the price by -2 or the 30 by -2. I'll have to multiply price by -3 and multiply the -120 by -3, all right? So here's what I could do, okay? I could say this is really equal to 1 over -epsilon. I've got price over price, Minus a Marginal Cost over price. Well, this thing turns into a 1. And this is MC/P, now, however, I go 1 price here. So I could try to simplify this a little bit more. So here is what I could do. I could let say I can subtract this 1 from both sides, right? because we're trying to get price by himself or herself. So I say, okay, I've got 1 over -epsilon and I'm going to subtract the 1 from this side, which means I have to subtract a 1 from this side. So I've got 1 over -epsilon minus 1, equals -MC/P, right? Now, what I can do is, to get price out from over here, I'm going to multiply this by price, but I'm also going to multiply this by price, right here. When I multiply this say by price my prices cancel. Now, I'm left with the P times 1 over -epsilon minus 1 equals -MC. So I can then divide both sides by this entire beast, 1 over negative epsilon minus 1. And I have to divide this MC by 1 over -epsilon minus 1. All of this cancels out and I'm left with price by his or her lonesome. So if I take this up to here I'm left with this, P = -MC over 1 over -epsilon minus 1. So now, I’ve got price by itself. So just solve this equation for price. It's not difficult but you do have to go through each step and engage in a very methodical process. So if you multiply something on the left, you have to multiply it by the right. You divide something on the right you have to divide on the left. The last equation is really straight forward, one of the reason I write it down there is because it's a very variable equation in micro economics. So if we have this right here, P x MPL = W, and we want to get P by itself, we say P = W / MPL. What if we want to get MPL by itself? Well, that will be MPL = W / P. This is very valuable equation, we use this a lot in different classes in MBA studies. And so the truth is that even with a very, very simple equation, you can modify it one way, modify it the second way. You just have to be very consistent about how you're doing it. I would recommend practicing more of these problems and getting yourself very comfortable with inverting algebraic equations. You're going to end up using it quite a bit.
