okay in this part of the lesson I'd like to talk to you about solving linear equations just got a few examples again we're kind of in review mode again so let's talk about how to handle these kinds of exercises so with the equation I work the left side and the right side you'll notice on the left we can take this 3 and distribute it take this 3 and we can distribute it through and same over here on the right side we can distribute the 2 now I can't forget some of those pieces of that plus 7 so let's go through this we've got 3 times X 3 times the negative 2 and then the seven term so if I stay on this left side for another step you can see where we can put those together that's basically 7 minus 6 which is 1 over here on the right side I'm go ahead and distribute the 2 so distribute in mathworld just means multiply okay so 2x in the 10 there's no combining like I did on the left so I'm just going to rewrite that again keep it organized now the goal is since I have the left side simplifying the right side simplified get the X's on one side what you do to one side you do to the other so I'm just going to basically subtract 2x to remove it from this side but I also need to subtract it from that other side what you do to one you have to do to the end so these will combine to give me 3 minus 2 or just 1x and then one more step of moving that one over so you always do the opposite sign of zero it out and so we end up with 1 X is equal to in this case those combine to be none and that would be my solution all that means is if X is 9 this sentence this math sentence also known as an equation that's true ok number 2 so we're just reviewing some techniques here notice I've got fractions like in the previous video we were reviewing fractions the first thing I would recommend is to come over here and if you've got a whole value put it over one and then go and get your common denominator that's very key right here common denominator in this case 8 so you would need to multiply this one by four top and bottom to make it an eight so let me pause right there and say this would be 4x over 8 you mean that 8 down here to get that common denominator so that would take multiplying by 2 so that one would look like 6x over 8 this last fraction you're again you're going after that common denominator which is an 8 so 8 times 1 would give you that 8 so you know we've got a common denominator that's the key up in the top that now turns to a 40 so this is very key to getting that common denominator once you've got that common denominator and you're playing with this equation you don't need it anymore you just say look for X would have to be equivalent to the 6x and of course yeah you heard me right once you get a common denominator you don't have to worry about those bottoms anymore it's the tops that are gonna have to be equal so now I can subtract the X is to bring them in this case I'm going to bring them over to this side or minus 6 that's negative 2 now you've got to get the X by itself so we can report out the answer so you'd say well I needed to buy it off that negative 2 so those will divide right off of there leaving me with 1x and that should be a negative 40 divided by 2 now I've got two more quick examples here I want to show you so I'm going to erase the board and come right back feel free to pause the video what you need to okay we're back with two more examples to finish off this review part if you want to pause the video and just write those down you can or you can just follow along with me so in this first one you'll see on what two terms over here on the left two terms on the right there fractional terms so I need to go after common denominator now just to save a little space since this is considered a whole term it's not fractional because the denominator is just one so what I can do now is I could once I write that over one then I can go and say hey what's a common denominator to this whole equation the whole thing not just to one side because I want it all the way across consistent and so you say well one one thing I can do is just multiply all these together so 1 times 7 7 times 2 is 14 times 2 is 28 so I could go after a 28 okay and that this is gonna be our easiest little task here so if you want this to be a 28 so again this is what I'm looking for as a fraction the fraction a fraction and fraction but I all want them to have 28 that's my goal here on this step so I can do that well this one's going to need to be multiplied in my 28 so 28 times 1 yes 28 times 2 that's 56 times X this one I need it to be a 28 so I'm going to multiply by 4 so I've got my 28 that's going to be an 8x up there on the top crossing over the equals sign I'm still looking for 28 this one's going to need to be multiplying by 14 that'll give me a 14 and this one also is going to need to be multiplied by 14 and the bottom is 28 and the top is whatever 17 times 14 is so 17 times 14 yeah that's what I get to 38 so once you've got all your common denominator work and that's the hard part then what you do is say I don't need those denominators anymore I know that 56 X minus 8 X has to equal 14 X plus 2 38 let me just kind of set this over to the side so I don't accidentally do something with it I don't need to okay so let's work on one side at a time we can combine those 56 minus 8 that looks like about 48 nothing to combine over here so I'm just going to rewrite it I'll now bring my X's to one side so that means I would need to subtract to get those out of way what you do the one do to the other so for my every 34 axes is equal to 238 so now what I need to do is divide by 34 so I can get that down to 1x and now we need to figure out what is 238 divided by 34 so we've got let's see what times what okay so what can I multiply and you say hmm I don't know let's see 7 times 4 would be 28 let's try that 7 times 4 is 28 carry the 2 21 23 perfect we found something that went in evenly good I even didn't go in evenly I would just sit there and reduce the fraction maybe keep cutting it in half until you finally get down or you can use a calculator so it's perfectly fine right thing next question same kind of concept this is the last one in our review and I want to show you a little trick right here you notice how this problem is different in that I've got a denominator but I've got more than one term up here that throws a lot of students off so let me give you an insider tip here put parentheses if you've got multiple terms up there you know here's an X to the negative 3 all over that little denominator here is an accident - it's a good habit to just put that in parenthesis now let's go back and work it like we've done the others so I've got a fraction - fraction the fraction so I'm on the hunt for a common denominator see what's 5 times 2 is 10 times 3 how about 30 let's go after a 30 so could I get a 30 here a 30 here and a 30 here so what do you multiply my six so that would give me eight Toni X's on the top this one would have to be multiplied by 15 so that would give me a 15 times X minus 3 you notice I didn't get fancy right there I just wrote 15 times whatever that is we'll say that next thing for the next step same here I multiplied by 10 but then I'm just gonna save that for my next step math is very step by step so my goal was to get a common denominator did that so that tells me I don't need any to worry about those denominators anymore this is what I'm looking at and now you'll see why those parentheses were important because I need to distribute that to each term there so we're looking at copy it down over here we're looking at a negative 15 times X a negative times a negative so that's going to be a positive 15 times 3 makes 45 10 times my X is just 10 X and 10 times my 2 is just 20 see I'm just very set by step through here let's take this side can I combine some turner's you bet so there's 3 X is there nothing to combine over here so I'll just wait copy that no problem I'll move my X's to one side too which type doesn't matter I typically move them to the left let's just have it more than anything so 3 - ten gives me negative seven I'm going slowly step by step through here wants you to see just very important I'm going to subtract my 45 turn now and that gives me a negative 7x is equal to 20 minus 45 negative 25 divided by your negative 7 and so X is equal to notice here I've got a negative divided by a negative so a positive 25 divided by seven it doesn't divide evenly like that thing so I just leave it as 25 or seven a check there's no way that's going to reduce any further so there's my answer that'll take us into nice solving equations make sure you can if you want to just stop right here go into the exercise and practice some of those we're going to take this another step a little bit little bit deeper so that will conclude this review part