Intro to combining like terms

let's say that I've got to Chuck Norris's or maybe it's Chuck nor I and to that I am going to add another three Chuck Norris's so I'm gonna add another three Chuck Norris's and this might seem a little bit obvious but how many Chuck Norrises do I now have well two Chuck Norris's we can represent this is literally a Chuck Norris plus a Chuck Norris so let me do that a Chuck Norris plus another Chuck Norris - Chuck Norris's you could also use it as two times Chuck Norris and this is just another way of representing it and three Chuck Norris is three is Chuck Norris is you could do that as a Chuck Norris plus a Chuck Norris plus another Chuck Norris and so we would have a grand total and this might be very simple for you but you would have a grand total of one two three four five Chuck Norrises so this would be equal to this would be equal to five Chuck Norrises now let's get a little bit more abstract here Chuck Norris is a very tangible thing so let's go to a little bit more of traditional algebraic notation if I have 2 X's 2 X's and rember 2x this is what we could do this as 2 X's or 2 times X and to that I were to add 3 X's and to that I would add 3 X's how many X's do I have well once again 2 X's that's 2 times X you could view that as an X plus an X we don't know what the value of x is but whatever that value is we can add it to itself and then 3 X's are going to be that value let me do the neck same green color 3 X's are going to be that value plus that value plus whatever that value is and so how many X's do I now have well I'm going to have 1 2 3 4 5 X's so 2x plus 3x is equal to is equal to 5x and if you think about it all we really did and hopefully you conceptualize added the two numbers that we're multiplying the X and these numbers the 2 or the 3 they're called coefficients very fancy word but it's just this constant number this regular number that's multiplied by the variable you just add the two and the three to get your 5x now let's think about this a little bit more let's go back to this original expression the two Chuck Norrises plus three Chuck Norris's let's say two that we were to add let's say we were to add some type of a let's say we were to add seven plums over here so this is my drawing of a plum so we have seven plums plus two Chuck Norris's plus three Chuck Norrises and let's say that I add another two plums I add another two plums here so what would this whole thing be well I wouldn't add the 7 to the 2 to the 3 plus the to the we're adding different things here you have two Chuck Norris's and three Chuck Norris's so they're still going to simplify to five Chuck Norrises and then we would separately think about the plums we have seven plums and we're adding another two plums we're going to have nine plums plus nine plums so this simplifies to five Chuck Norrises and nine plums similarly over here if I had instead of just 2x plus 3x if I had seven y 7y plus 2x plus 3x plus 2y what do i now have well I can't add the XS and the Y's they could very well represent a different number so all I can do is really add the X's and then I get the 5x and then I'd separately add the Y if I have seven wise and to that I add two y's I'm going to have nine wise if I have seven of something and I had two of something I now have nine of that something so I'm going to have nine wise so you add that we've done a different color you add this and this you get that you add the x's you add the x's you get that right over there so hopefully that makes a little sense actually I'll throw out one more idea so given this what would happen if I were to have two x plus one plus seven X plus 5 well once again you might be tempted to add the two plus the one but they're adding different things these are two x's this is just the number one so you really just have to add the x's together so you're going to say well I got two x's and I'm going to add seven X's to that well that means I had now have 9x is and then separately you would say well I've got just the abstract number one and then I got another five one plus five is going to be equal to six