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Equations with Variables on Both Sides?!

Added Jan 25, 2017 •

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alright greetings today we are going to be covering how to solve equations but we're going to solve equations that have variables on both sides of the equal sign on the left there's going to be a variable on on the right there's going to be a variable so it's going to be something like this so we've solved equations that has 12 m + 17 equals 21 but what if its 12 m + 17 equals a 10 + 20 can you have ends on both sides will you know that the goal when you're trying to solve an equation is to get em by itself so that we know what an equals but in this case we have to ask the question which and are we going to try to get by itself are we going to try to get this one by itself or are we going to try to get this one by its so you can see that when there's variables on both sides of an equation equation so let's actually tackle one we're going to start with this equation right here Max - 10 equals 13 x + 40 + we're going to ask the question should I do 5x - 5x or should I do 13 x - 13x so how do we decide which one to do will the official way is to pick whichever one is smaller so in this case we would do 5x - 5x and we would subtract 5x from Bose but if you don't remember this fish away to do it it's okay to just pick one of the two ways to do it and then see what happens and then just make sure you check your shut the End by plugging in your solution to the original equation so  we're going to do the 5x - Beck's okay because if we subtracted 13 x from both sides we would get a negative number and we pawsitive numbers better so let's get rid of all this other stuff and let's just see what would happen I really did do - 13 x on both sides  if I did - 13 x on both sides this part cancel out which was nice I just have 40 over here but over here I would get negative 8 now that's not the end of the world we could solve this equation right but it's easier to solve equations when you don't have a negative number in front of the X now we can still do this and we get -8x equals 50 Nexus going to equal whatever 50 divided by -8 it's right so what I want you to see here is we shouldn't subtract 13x from both sides because it gave us a Negative X even though we can do it that way and it will still give us a good solution it's better okay  to not have a negative over there so the better choice would be to do 5 x - 5x + 13 men's 5x because if we did it that way we would cancel those X's out and we'd still have a positive over here so let's see what that looks like  let's cancel these out 5x - 5x cancels out I have -10 over here right and then  13 x - 5 x is going to come out to a positive 8x and then I'm just going to bring down my + 40  and now I can just solve the rest of this the way that I've always saw two step equations 40-40 cancels so I only have 8 x left over here and then -10 - 40 is -50 a notice on this problem or solution for X is going to be 50 / 8 again but it's negative  so we still got the same solution so I guess the moral of the story is we want this part right here  to come out positive but even if it doesn't everything still going to be cool  so play give you this equation what would be the easier first step we could subtract we could subtract 3x from both sides  red or we could subtract 17x from both sides which one would be better I think it would be better to subtract 3x from both sides because then  when you finish this problem these cancel out will have an easier more simple equation  the song with no negatives in their let make sense hopefully thank you probably know how to solve the rest of that equation right so what we're just dealing with here is the basic idea of making sure that you do the first step okay how about this one which one would you do first we could do - 5 x - 5 X or on this we could do + 6x + + 6x + notice that on this one that's actually the better move because this -6x + positive 6 x cancel out  because of that negative that was right here  cast it actually better to get rid of the -6x by doing a plus 6X so that now we have 11 x and it's a nice positive number  and we can stop the rest of our equation  just for fun let's go ahead and solve the rest of it - 3 - 3 these cancel out you have 11 X equals 50 - 3 which is 12 and so in this case I'm going to / 11 / 11 this will cancel out and I'll have X equals  12 / 11 you could do 12 / 11 on your calculator and give a decimal or could we just say that 11 goes into 12 what's with 111 leftover yeah. Is my solution all right so let's just do one more example problem and I think we'll be good to go  I'm going to do this one fast so see if you can follow along with me really fast what's bigger 12 in or a 1012 in is bigger so I'm going to get rid of the smaller when I'm going to do minus a 10-8 in this a 10 in this a 10 are going to cancel out at leaving only who won over here on the right side 12in - 8 in is a positive for in and then I'm going to bring the 17 down and then I'm going to get rid of the nope I'm going to get rid of this what team first cuz I get rid of the thing that's not attached to the variable and I'm going to do that for an equals to 194 and then I just have to divide both sides by 4 and I get in equals 4 divided by 4 what's 1 +  I just saw that equation except you know what I shouldn't have Circle that equation at the bottom and equals 1 why should I have circled that solution because I'm not a hundred percent sure that it actually is true does anyone I don't know I to see if  n equals 1 when I put that right in here so what's 12 * 112 what's 12 + 1729 okay well what's 8 * 1 8 + 21 does that come up to 29 does that work  I think at this point you're ready to try this yourself so here's one for you and then here's another can I see if you can solve both of those equations that both have variables on both sides and if you can then your house  thanks for watching thanks for listening if you have any questions ask me tomorrow

Uploaded by Jeff Marbut.

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Equations with Variables on Both Sides?!

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