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Pre-Algebra - 5.2 Equations with Variables on Both Sides

Added Jan 29, 2021 •

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Isolated the Variable. When there is a Variable on BOTH sides on an Equation, You just need to make a choice of an INVERSE OPERATION to clear out a term AND Keep your work BALANCED on both sides of the equation

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5:2 and this is more practice a solving equations with these right here nothing really complicated about it 5 - 2 solving equations with variables mold on both sides now I'm going to go look at this example 1/3 x equals x + 8 they use here let's look at in follow on here's your ex algebra tiles here's your ex out of house and here's your constant your ones not it that's eight so we got three X's equals 8 notice right here what did they do let's both of them have an excess throw an axe let's throw an excellent I got this balance remember it's equal equal means a seesaw that goes nowhere free x equals x + 8 since both sides have an X in common if this was a scale we can go rid of it only exists if I get rid of One X I would have to and then I would have none to X's would equal 8 but they turned it around so you can see like this I got two exes and they're equal to 8 but if I divide evenly each group e-checks goes with for that's with for suicide making it equal and even so f equals 2x equals 8 / 2X equals 4 button showing the work look what they did what do you move to what and that's the key variables on both sides which one do you decide to move the stash you do both and I'll show it to you so what I'm going to say is this so let's just redo this 3 x equals x + 8 + 3 x equals X Plus when you get variables on both sides which variable do you move it doesn't matter cuz as long as work stays equal you can do that I'm going to show you the way that would do more work so let's say I want to get rid of 3x instead cuz you need to make a choice and that's the thing about variables on two sides you as the person doing the work need to make a decision which ex do you move first somebody might move this so I subtract 3 X on this side of the equal sign I got to keep it balanced and subtract 3x on this side of the equal sign 3x - 3x equals 0 1 x - 3x is -2X and then I got a plus 880 equals negative 2x + 8 that doesn't really work out and then you need is that alright the variables on this side I got to move the constant to that side subtract 8 subtract 8 8 - 8.0 leaves me with -2 x 0 -8 divided by -2 negative 2 divided by negative is a positive one that's an x negative divided by negative is positive 8 / 2 same answer it's the whole thing is what you bear that's the whole thing it's moves that variable then add the clear out the constant but which variable that's why I need to make a choice instead of moving 3x we could subtract just X on both side notice the work is different but negative x equals negative X the work is balanced so 3x - 1 x that's a 2 x X - x is 0 bring down the eighth the positive it so that's one thing a lot of guys mess up on if that was the x - 8 Aladdin only brought down the 8th you forget you need to bring down the sign that goes with it when it's positive you don't need to write it but when it's negative you do but anyways I just put it down just so you can visually see it / 2 x equals 4 they both got you the same answer send me guys freak out halfway through your work and then you erase all of it and start over finish it if you halfway if you already started it just finish it to something lot of us realized man if I just did the other one to be quicker but having to erase it and start over your spending even more time but I'm just showing you should do it two different ways so right now one a try this one on your own make sure you know what to do I'm going to do both ways just to let you know so try this one on your own 7 x equals 5x + 4 make sure you could do it I'm going to give you 30 seconds cuz we need to move on try it on your own some you guys are moving your hands some you guys which I'm about to kick out cuz your cameras off you're not in class you will be removed you should never turn your camera off there's no reason to have your camera off the reason you're having your camera off means you're doing something else the right there thank you thank you thank you all you guys have the right answer but I'm going to show both ways to show it doesn't matter which way you do it you get the same answer I always show the more work we first so I'm going to subtract 7X that's it 0 equals 5x - 7 x negative 2x + 4 let me subtract 4 -4 equals -2X divided by -2 2 equals X subtract 5 x instead 7 x - 5 x 2 x that's a z bring that down you get a 4 / 2 x equals to Shorter one cuz the whole goal is to get the variable on one side the constant on the other so look at this starting back noticed we got variables on both sides we got variables on both sides but notice the constant is on this side so if you only have a concert here what moves the variable over to the other side then your whole goes to get variable equals constant and after you just divided by the coefficient this right here this site didn't have a constant and then decide to move the variable with the constant look at that it created one extra step of work so there's no right or wrong next one try this one on your own when you have a variable and a constant on both sides 3x - 2 equals x + 4 this and I'm going to do both ways try this on your own remember why you got to send all right what do I do first when you got very the constants on both sides you make a decision just make a decision and move one thing first and actually thought she do a lot of different you can do for different things you do this for different ways but they're pretty much the same price I'm going to do loops I'm in a mess up my  I'm going to do this problem 4 different ways to start with I'm just rewriting it 3 x - 2 equals x + 4 thank you thank you so the whole thing your number one goal. has one giant problem look at it as undoing everything to you have a variable on one side and the not variable constant on the other you're getting a variable by itself isolating the variable all right I got a bunch of answers and imma do it for different ways so I'm not going to move my variable first I remove my constant first and I will decide to move the minus I'm going to get rid of a minor and that's the thing when you have variables and constants on both sides you need to make a decision of what to make a 0 or a 1 versed I'm going to make a negative 2 into a zero I'm going to add to plus two notice I line up my constant I don't put it under the X I put it under my 4:00 because it's a constant not a variable 3x and that's a zero I get x + 6 and now notice I got no Austin on this side but I got a variable and a constant on that side so that means I should move this variable to this side so I subtract x minus X and technically that's a 1X x minus X is a 0 I'm left with 6 3 X - 1 x 2 x 2 x x so how do I undo a x i / 2X 3 I'm going to do it again but instead of moving the plus two I'm going to subtract 3x first -3x - 3 I'm going to make that a 1X 3 x - 3x that says 0 on my bring down this negative 2 1 x - 3 x negative 2x + 4 notice they looked print my whole line is different because I decided to move the 3x instead but does that mean it's wrong no let's follow the work because my variables decide now I got to move my constant to that side for - 400 so I bring down the negative 2x -2 - 4 + -6 divided by -2 negative divided by negative is a positive 6 / 2/3 instead of x equals 3 3 equals x same thing but you know what I'm going to do it again a different way instead of moving 2 or the 3x I'm going to move the X instead subtract X retract 1 x 3X - 1 x I get to X bring down the negative 2 x minus X is zero at bring down the for my variables on this side and I have a constant by itself that means all the constants should follow here so to get this constant to that side do the inverse operation of adding two 2x + -2 + 204 + 2 is a 6 hey very similar to that right there divided by 2 x equals 3 so this ends up being a simple look at this stuff right here that line is totally different but we ended up getting to the same work that's fine and then let's finish this one off instead of so I removed the two remove the negative 3x remove the X the only thing left is the four well let's do the four so let's see track for instead 3x nothing combines with that bring it down -2 and -4 makes a -6x comes down 4 - 400 3x - 6 there's no such thing as a 3X - 6 notice all those lines are pretty much different so the variable is by itself on this side I got a variable and constant on this side so since the variables on this side there subtract 3x and successive 3x let's make this a 1X 3 x - 3 x 0 I bring down the negative 6 -3 x 1 x -3 x -2X divided by -2 -2 / negative to positive one leaving me with just an X all of these get me the same answer let me zoom out so you can get a nice little view of everything you need problems like this I don't need to see all for you as the I need to decide which term do I move first and it's a choice if you follow the work correctly even though they look different and your friend if you work with a partner might do different things in the end when the steps get closer to the end they're the same thing ones just the negative the others just a positive but in the end if your work comes out correctly you would all get x equals 3 or 3 was X it does not matter which one you do first you just need to make sure your work is equal your work is balanced and literally I don't need to show the other examples but it's just this let's go the next ones so good thank you y'all got a C with her yes again you do not need to show all the version you just need to do one but but on that Calif s back test the smarter balanced whatever academic I forgot what the C stands for test they would say what are the four versions they won't make you do them but don't have a diagram all the different ones which one of these which which are the four ways to show this problem and you would have to look at all my are they doing the math right eye so which four and so you would actually have to choose the four methods yes that's on this all right let's go example to so that's what this at equations with variables on each side notice that right there zoom in and follow along so they only did one way their whole thing is and this right here this Logic for some reason it's how we think so some people think some people always say I want my variable on the left side some people say I always want to pause variable well 7y + 4y if I move the 7y over I get a negative I don't want a negative variable but if I move the four way over here stays positive so how do you get rid of a 4y you subtract for a while both sides notice and staying balanced that's what the red is subtraction property of equality If I subtract the same thing from both sides it stays balanced 7 y - 4 y 3 4 y - 4 y 0 but you have this negative 10 leftover now look at this the variables on this side there's no variable on that side so I got to move the constant so that's I'd how do you get rid of a plus 8 the inverse operation is the track if you subtract on both sides it stays balanced 8 - 8 is a 0 negative 10 minus 8 is -18 3y equals -18 y equals negative 6 and sometimes test always ask you to check your answer how do you check your answer you go back to the original problem 7 y + 8 equals 4 y - 10 you substitute didn't your variable -6 / where why is notice you plug it in both times -42 + 8 + -24 - 10 they both equal -34 and just to show you it doesn't matter I'm going to do it one more way so instead of moving the four why I'm going to move something else I'm going to show you already did it doesn't matter which one you do so do this one on your own so try this out to at plus 3 equals 3x - 2 solve this on your own and once you're done with that let's just do both of them at the same time 5 p + 15 equals P -49 do these two problems right here on your own try it on your own if you can only do one do one June 1st I'm going to give you a little bit of time to do that one too some guys are not riding that's how I know you're not doing anything you're not even listening to me your watch something else on TV or you're watching a show and I'm going to choose my way to go over it your way not be the same as mine you have a 25% of doing the same exact worked idea cuz there's four different ways for each problem each one of these problems yes has four possible ways and I only want you to do one of them the first one you do some of you guys will get same answer tell me if you guys will do the same work messages I choose but if you want three out of four of you will do the problem a different way but get the same answer that's all I wants its and then finish this one once you're done and then we'll read through the word problem and set it up watch your arithmetic two of you I know where you got that answer I'm not going to call you out but check your arithmetic and your Stein your sign got you you wrote that you forgot or messed up on one of the sign that's why that number came up so check your work check work that's why they say check your work yes yes it is on the first one good job plug it in and you should always plug it in the Czech pasta. For those of you that are yet you can this person says how did these people finish affect all right I'm going to one thing to you and you only cuz you're a small writer people who write who don't write super small use up paper they write faster you spend too much time focusing on save space stop doing that track your crack let's work it out this work it was almost done finish up I am going to move let's see which one I am going to I'm going to add to I will add to most of you guys probably did not do that 2x + 5 equals 3x notice each time I rewrite and make a new equation you're starting over each time I added to now I have a brand-new equation 2x + 5 equals 3x I subtract ux I'll bring it down to x minus 2805 equals 1 x x equals 5 you should still have gotten if you moved one of the other ones first you should still get the same work all right this one right here I'm going to add 49 I'm going to add 49 -49 + 49 that's a zero that leaves me only with PE that's not a negative pee that's where some guys messed up it's an egg the positive p + 49 fish something that'll help an extra stuff for some of you guys so some of you guys are visual Learners and you're still having trouble with sign on the first terms that's not a negative put a positive symbol there so if you decide to move things around you know that's a positive v p and a positive p so that negative is a -49 that's what's up positive T and then I got a plus positive I pee and then what is that 64 14 + 64 subtract 5 P cuz I got to get rid of the + 5 P subtract 5 p see that's the negative symbol messed you guys up 64 equals 1 P -5 P -4 P divided by -4 positive / negative your answers going to be negative watch out for that and then that's a p 64 / 4 One Time -16 will go back over it Sol Vista fry word problem I want I want to work. So this next time is no different literally word problems you just need to know how to translate so let's go do the last one together I don't want to you can read this on your own it shows you just a lot of times this doesn't help people a person a personal trainer charges a one-time fee of $60 so no matter what you always get that's a constant Plus $25 for each individual session so you need to know how to translate that no matter what it is it over no matter what it's $60 plus $25 for each individual session we don't know how many sessions someone might pay for those 25 x however many sessions so that's the variable that always changes so 25s a new fitness club charges a yearly fee of $450 $10 for each session with a personal trainer so $10 for each session notice we are two different problems right there so right write and solve an equation to determine for what number of sessions will the cost be equal so we're paying for $60 here we're paying $450 here but cheaper more expensive session most you might say that's a lot but at some point they're equal so one time so look at this right here 60 25 s equals 450 + tennis and then it just becomes a problem word problem setting it up so you have an equation a variable equation to solve and once you have that it just becomes all the steps what takes 26 sessions if you pay for 26 individual sessions to work out with the trainer cuz you know you want to you want to look all fit and you're like oh my God personal trainer Charlie is so cute and you pay and that's the whole thing you're thinking this sounds cheap if you go 26 sessions with a personal trainer Charlie you be like yeah but here after that on your 27th this is actually cheaper cuz every session is 10 bucks this gets higher each time cuz when you get to 26 sessions working with Charlie these bowls equal button on the 27th this one becomes cheaper because look is $10 and that's 25 so if you think it like you going to work out with Charlie more than 26 times choose this one so let's go do this one together Redbird cruises charges $85 per day plus a one-time fee of 75 dollars for taxes and gratuities so we don't know how many days were going on red cruises so red red cruises let's use bread instead why you nice purple red is no matter what $85 per day we don't know how many days so $85 per day and a one time fee of $75 for your taxes so no matter what one day if you go one day cruise you still got to pay that $75 you go to days you only pay so your father Hugo 100 day cruise cuz you don't want to set foot on land 400 Days are you paying the $75 for taxes same as person that only goes one day now it's going to the next one what's the color purple King cruises charges $100 per day we don't know how many days that is but no matter what plus a fee of $30 no matter what everyone pays thirty bucks write and solve an equation to determine what number of days the charges for the cruises will be the same so if we take away this be right here look at this for one day the increase is more expensive to date King cruises will always be more expensive because it's $100 a day but you got the charge that extra surcharge though King cruises charges Verde it's cheaper in terms of the tax you pay that one time he's got to pay 75 no matter what but when is it the same if they're the same it means they are equal 85 d 75 equals 100 D + 30 notice this right here was the hardest part of the equation did you hide the translated and that's that's any word problem is translating so some limit and you just need to make a decision what you want to move I'm going to subtract 85 days from that cuz I want positive variables and that means I got 75 equals what is that 15 days + 30 I subtract 30 days I get 45 and then 15 days and then he $45 / 15 45 divided by 15 is 3 if you do a 3-day cruise with both of them you can if you pay the same amount after that one more expensive than the other and literally this right here writing the equation of the word problem is the hardest thing let me go see what the assigned

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Pre-Algebra - 5.2 Equations with Variables on Both Sides

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