hello welcome back to the physics one course in this lesson we're going to cover a review of essential algebra this is part one of two so what we're gonna do now is review the absolute most essential things that you have to know in algebra or in pre-algebra too in order to do well in physics so what we're gonna do is review it here and solve a couple of problems and you should be feel very comfortable at the end of this with how to do these basic concepts now I will say that if at the end of this lesson if you're have your eyes crossed and have no idea what I'm talking about at all then you need to go back to my algebra class and watch the first few lessons of that because I blow all of this stuff up in too many hours of examples so if you're fuzzy at all go back and get some more practice before proceeding I'm trying to set the groundwork for you so that physics is very easy enough and not hard so we're gonna do this basic review in order to get that done so there's this thing called a number line I know that you all know what a number line is but we're gonna review it here so here's 0 we call that the the origin or the middle point of the number line and we have numbers going this direction I'm not gonna go for on and on forever but you might guess this is one two three four five six and it goes on and on and on that direction and then come in the other net way we have negative one negative two negative three and negative four is negative five negative six let's just keep it symmetric so negative one negative two negative three negative four negative five negative six so obviously the negative numbers go on to negative infinity and the positive numbers go on to positive infinity so these are called positive integers negative integers now of course there are numbers in between the integers so you can have one point five or three point six four two or over on this side you might have negative four point nine nine nine or negative one point two three four so we have negative and positive numbers what we drawing on the number line is just the integer values of the kind of the positive and negative whole numbers right now we need to know how to use this but specifically we need to know how to add things together I know that you know how to add numbers but when I say adding I'm talking about adding negative numbers to positive numbers it's crucial because if you can't do that then if I teach you to solve an equation and you can't add two negative numbers together you're going to everything wrong so we're gonna do a quick review of that to refresh your memory on how it's done first let's start off with something everybody knows three plus four everybody know what that is three plus four so we have this number line for reference but what really happens here can we go one more space out here you'll see why in just a second so this is seven this is negative seven so the way to add numbers is you take the first number you find where it is on the number line which is right here at three right so put a little dot right here and then we're gonna increase by four so when you're adding something it means you're going to the right you're getting bigger by four more units so one two three four we've increased and we land it on seven so the answer here is seven now you all know this because it's you know first grade math three plus four is seven but the general rule that we get from this is that when we add a positive number and add to it another positive number always always always we always get what we call a positive number that's something you all know from first grade but I'm just writing it down to be complete because the next thing we're going to talk about is we're gonna mix it up a little bit what if I have negative one which is here on this number line I'm going to add to it I'm gonna put it in parenthesis to keep the signs away from each other but I'm adding a negative number to this negative number that I already started with what's that going to be equal to and for some students this is where the the wheels come off of the Train because it gets confusing like well what do I do with this well you start with this number and you're increasing but the deal is is you're starting from negative one so to start over again let me kind of erase these dots we're starting from negative one now but here's what you have to think we're adding which usually means we're going to the right getting bigger