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welcome to my presentation on level three linear yeah level three linear equations okay so let me let's let's make up a problem let's say I had X plus 2 X plus 3 is equal to minus 7x minus 5 well in all of these linear equations the first things that we the first thing that we try to do is get all of our variables on one side of the equation and then get all of our constant terms on the other side of the equation and then it actually will become a level 1 linear equation so the first thing we can do is we could try to simplify each of the sides well we on this on this left side we have this X plus 2x well what is X plus 2x well that's like saying I have one Apple and now I have two apples so here I have One X and now I have two more X's and I'm adding together so that equals 3x 3x plus 3 is equal to minus 7x minus 5 now let's bring the 7x over on to the left hand side and we can do that by adding 7x to both sides 7x this is a review we we're adding the opposite so it's negative 7x so we add 7x so that's why and we do that because on the right side these two will cancel and the left side we get 10 X plus 3 equals and on the right side all we have left is the negative 5 almost there now we're at a level was it's a level two problem and now we just have to take this 3 and move to the other side we can do that by subtracting 3 from both sides that's a 3 minus 3 the left-hand side the threes cancel out that's why we subtract it three in the first place and you have 10x equals and then minus 5 minus 3 well that equals minus 8 now we just multiply both sides of this equation by 1 over 10 or the reciprocal of 10 which is the coefficient on X times one over ten you could also some people will say well we're just dividing both sides by 10 which is essentially what you're doing if you divide by 10 that's the same thing as multiplying by 1 over 10 well anyway the left hand side 1 over 10 times 10 well that equals 1 so we're just left with x equals negative 8 over 10 that can be reduced further they both share the common factor 2 so you divide by 2 so it's minus 4 over 5 I think that's right assuming that I didn't make any careless mistakes let's do another problem let's say I had 5 that's a 5x minus 3 minus 7x equals x plus 8 and in general if you want to work this out before I give you how I do it now's a good time to actually pause the video and you could you could try to work it out and then play it again and see what I have to say about it but assuming you want to hear it let me go and do it so let's do the same thing we first of all we can merge these two x's on the left hand side remember you can't add the 5 and the 3 because it's 3 is just a constant term while the 5 is 5 times X but the 5 times X and the negative 7 times X you can merge so 5 you just add the coefficient so it's 5 and negative 7 so that becomes negative 2x minus 3 is equal to X plus 8 now if we want to take this X that's on the right hand side and put over the left hand side we just subtract X from both sides the left-hand side becomes minus three X minus three is equal to these two x's cancel out it's equal to eight now we can just add three to both sides to get rid of that constant term three on the left-hand side these two threes will cancel out you get minus three X is equal to eleven now you just multiply both sides by negative one-third and once again this is just the same thing as dividing both sides by negative three and you get x equals negative 11 over three actually let's let's just for fun let's check this just to see and the cool thing about algebra is if you have enough time you can always make sure you got the right answer so we have 5x so we have five times negative 11 over three so that's I'm just I'm just going to take this and substitute it back into the original equation and you might want to try that out too so you have minus 55 over three that's just five times negative 11 over three that's a 3 minus 3 and what's 3 3 could also be written as minus 9 over 3 I'm skipping some steps but I think you know your fractions pretty good by this point so that's minus 9 over 3 and then minus 7x is the same thing as plus 77 over 3 because we have the minus 7 times minus 11 so it's plus 77 and and the equation is saying that should equal minus 11 over 3 that's what X is plus 1/8 is nothing but other than 24 over 3 let's add this up minus 55 minus 9 that's minus 64 if I'm right yeah that's minus 64 and then plus 77 minus 64 plus 77 is 13 so the left-hand side becomes 13 over three and then the right hand side minus 11 plus 24 well that's 13 and we still have over three so looks like we got the right solution it checks out so the correct answer was minus 11 over 3 hopefully you're ready by now to do some level 3 problems the only thing that makes us a little bit more complicated than level 2 is you just have to remember to merge the variables in the beginning and know that you could subtract variables or constants from both sides have fun