[Music] all right so this is a quick review on algebra um in physics this year they're going to be times when you will need to take a formula and rearrange it in order to solve for a particular unknown so we're just going to review a little bit how you go about rearranging an algebraic equation to solve for a particular uh variable okay so a few General hints to work from unfortunately there's no like one set algorithm to to follow but there are a few general rules of thumb that we can can use for us okay
first hint is to work backwards through pemos now pem do if you recall is the order of operations um and it stands for P stands for parentheses e stands for exponents m stands for multiplication and division and A and S stands for addition and subtraction right so um that's the order that we do things when we are trying to just straight out chug through some arithmetic but when we are solving an algebraic equation we have to undo all of those things so we have to work backwards we first work by um undoing any addition or
subtraction then we undo any multiplication or division then we undo any exponents and finally we undo uh anything within the parentheses okay and we'll go through a couple examples so you can kind of see what that looks like a little bit better another General hint is to combine like terms if you're solving for x and x appears on both sides of the equation you want to combine those two x's together get them on one side of the equation all right and then my last General hint is if the unknown that you're trying to solve for
is in the denominator of a fraction you want to get that thing out of the denominator that is the worst okay we never want the thing that we're solving for in the denominator so try to multiply to get it out of there all right now let's go through a couple of examples that kind show these different principles in practice okay so our first example says fals G Big M * Little M all / R 2 we are trying to solve for R okay now the first thing that I notice here is that the thing that
I'm solving for R is in the denominator of a fraction I do not like that I'm going to get it the heck out of there by multiplying both sides of the equation by R 2 okay I have to do the same thing to both sides of the equation that is key I can never do something just to one side and not to the other all right now if I multiply this right side by R 2qu now I've got it in the denominator and in the numerator so it cancels so now I've got f * R
2 is equal to Big G Big M * Little M okay so now my R is out of the denominator I'm feeling better now we just go and undo all the things that are happening to that R so I see two things happening to this R right now for one it's being multiplied by F and the other thing is it has an exponent of two now if we go back to that whole reverse order of operations I know I'm going to want to undo the multiplication before I undo the exponent so let's do that so
I'm going to un undo the multiplication so in order to undo multiplying by F I'm going to divide both sides by F since dividing is the opposite of multiplying these cancel out so that gives me R 2 is equal to G Big M little m / f and now all I need to do is undo the exponent okay now in order to undo do an exponent of two all I need to do is square root and I have to square root both sides all of both sides now the square root and the square cancel out
and that gives me R is equal to the square root of this whole thing G Big M Little M over f everything is in that square root right there right so there's our first example see what we had to do was we had to um get the r out of the denominator by multiplying and then we undid all the things that were happening to the r going in reverse order of operations let's try another example all right so another example is FAL V + a t and we want to solve for T okay now my
T is not in a denominator so that's good now I just need to figure out what are the things that are happening to this T I see two things happening to this t one is that it's being multiplied by a the other thing is that we are adding V to it now again we want to go in reverse order of operation so we're going to start by undoing any addition or subtraction okay so in order to undo this addition of V I'm going to subtract V from both sides that's going to cancel and so I
get Fus v = a t now all that's happening is I'm multiplying a Time T in order to undo that multiplication I'm going to divide so these A's cancel and so then I'm left with t = f - V all divided by a the whole thing right so that was just a quick little review of a few algebra problems if you have further questions you should of course feel free to talk to me thanks
