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Current time:0:00Total duration:5:35

Video transcript

so we have an equation it says ax plus 3x is equal to BX plus 5 and what I want to do together is to solve for X and if we solve for X is going to be in terms of a B and other numbers so pause the video and see if you can do that alright now let's do this together and what I'm going to do is I'm going to try to group all of the X terms let's group all the X terms on the left-hand side so I already have a X and 3x on the left-hand side let's get BX onto the left-hand side as well and I can do that by subtracting B X from both sides and if I subtract B X from both sides I'm going to get I'm going to get on the right-hand side I'm going to have a on the left-hand side on a X plus 3 X minus BX so that I could do that in that color for fun minus BX and that's going to be equal to well BX minus BX is just 0 and I have 5 it is equal to 5 and now what I can do is I can factor an X out of this left-hand side of this equation out of all of the terms so I can rewrite this as x times well ax divided by X is a 3x divided by X is 3 and then negative B X divided by X is just going to be negative B I can keep writing it in that pink color and that's all going to be equal to 5 and now to solve for X I can just divide both sides by what the thing that's mult being that X is being multiplied by by a plus 3 minus B so I can divide both sides by a plus 3 minus B a plus 3 minus B on this side they cancel out and I have X is equal to 5 over a plus 3 minus B and we are done let's do one more of these so another equation here we have a here we have a times the quantity 5 minus X is equal to BX minus 8 so once again pause the video and see if you can solve for X well the way I like to approach these is let's just expand everything all out so let me just distribute this a and then I'm going to collect all the X terms on one side and all of the non X terms on the other side and essentially do what I just did in the in the last example so let's first distribute this a so the left-hand side becomes 5a I could say 8 times 5 or 5 a minus ax ax that is going to be equal to BX minus 8 now we can subtract B X from both sides so we're going to subtract B X from the left hand side BX from the right hand side and once again the whole reason I'm doing that I want all the X terms on the left and all the not X terms on the right and actually since I want I want all the not X terms on the right I can actually subtract 5a from both sides as well so I'm kind of doing two steps at once here but hopefully it makes sense I'm trying to get rid of the BX here I'm trying to get rid of the 5a here so I subtract 5a there and I'll subtract 5a there and then let's see what this gives us so the 5a is canceled out and on the left hand side I have negative a X negative ax minus BX - move in that same green color minus BX and on the right hand side I have this is going to be equal to the BX is canceled out and I have negative 8 minus 5 a negative 8 - same magenta color minus 5a and let's see both I've now step I have all my X's on one side all my non X's on the other side and here I can factor out an X and if i factor out an X what do I have actually one thing that might be nice let me just multiply both sides by negative one if I multiply both sides by negative 1 I get ax plus BX plus VX is equal to 8 plus 5a that just gets rid of all of those negative signs and now I can factor out an X here so let me factor out an X and I get X times a plus B a plus B is going to be equal to 8 plus 5 a 8 plus 5 a and we're in the homestretch now we can just divide both sides by a plus B so we could divide both sides by a plus B a plus B and we're going to be left with X is equal to 8 plus 5 a plus 5a over over actually I'll write 8 and B in our original colors a plus so this was that a that a plus B so this is the B that's the same B a plus B and we're done we have now solved for X in terms of some in terms of A's and B's and other things and we are all done