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Aztec Bridge

Added May 25, 2022 •

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Multi - Step Equations

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welcome back Center of mass Bridge lesson they were talking about solving multi-step equations if you recalled two lessons go we're doing one step equations and then we will move on to two-step now runs a multi-step right so that's going to be any question requires more than two steps so our objective is to solve equations requiring more than two step including distribution and combining like terms to talk a little bit about distribution in the previous lesson right we said distribution is another word for multiplication when they talk about distribution they're referring to the most location operation and the difference between you know when we say multiplication in distribution is that when we refer to multiplication on its own or usually talking about multiplying two values and about Distributing it's one value be multiplied into multiple different values so at least you so for example we may have a number and a set of parentheses and decide those parentheses we met Constance meaning just a stand-alone number and a coefficient with a variable that's a number with the letter combination and we're going to have to multiply the number that's outside of those parentheses into the princes with Ali close to Bally's so we'll see. Hopefully in this lesson we've already explored that a little bit in the previous list come here we have an example of distributions this is what I was talking about we have a number we have a set of parentheses and inside those parentheses we have at least two values and I use the word values you can also use the word terms but when I say valleys I'm referring to visa for example this x variable and this number to the constant so what that means is I'm going to have to multiply 6 * x + 2 * 6 stupid reason why I can't just go x + 2 and combine those two terms is because those are unlike trims the x is a variable that's who is a constant in those two cannot be combined it together they're not like it's like trying to you know organized money and saying oh just put a nickel with the stack of Dimes right you can't do that. Those aren't like denominations of currency right so you put the times with the nickels with the nickels in the same is true with these terms or values you would combine like terms and therefore if I had another variable X I could combine that together I have another number that's a constant for example is 4 of this - 10 I can combine those together but not agreeable with the constant however I can multiply them together right now I can do so here we go we're taking the 6 and multiply that times the x 6 x whenever we take a number and multiply it times a variable the solution is just a number with a variable written next to each other essentially nothing changed here 6 * X is just ran a stick which means six times x they're just rewriting the same the same thing in a different form but this is this hasn't changed one bit 6 * 212 it's another way of taking care of the distribution now we can combine like terms and I'm going to begin combining like terms on one side so I'm going to do it on this side so the terms that I highlighted the 12 and the form those are like trims they're both Constance right so 12 - 4 that's going to give me Kate's cuz I'm going to take Eragon 12 - 4 gives me 8 now I need to continue combining like terms only this time I'm going to need a cross that equal sign in or to combine like so this eat and this negative 10 those are like terms they're both constants but I need to isolate the X can you get rid of this a try I want the ex to be alone but I have this age that's in my way turn order to get rid of it I first need to see what operation is currently happening that operation is addition so then in order to get rid of that eighth I do the opposite operation opposite of addition is packed and whatever I do to one side of the equation I do to both sides so if I subtract 8 from the left I also need to subtract 8 from the right so that's what's Happening Here subtract 8 from the left and I'm only left with 6X on the right I have - 10 - 8 that becomes -18 now I'm down to my final stuck again this whole time I'm trying to isolate the X that's ultimately what I want right but I don't have the X alone because I have this I like to say hanging out with with my variable so I need to get rid of it by doing the opposite operation of what's currently going on so what's really going on his multiplication the officer that would be Division and whatever I do to one side I do to boast so that means I'm going to need to divide both sides of the equation by 6 so the six is cancel out on the left and then on the right I have - 18 / 6 that gives me -3 so now I have my answer x equals negative 3 all right so I'm going to pull up text box so that we can show our work as we saw there so the first thing I need to do you know this is this is different then we're doing order of operations you know we did that lesson you know I'm not sure if it was in this level of math or either in the basics or hiset but we talked about the order of operations and that's what we follow when we don't have a variable right when we're only working with numbers first who would solve within the parentheses then go to exponents multiply divide and then finally add subtract but because we have a variable you know the process is first we're going to distribute if you need to then we're going to combine like terms and then finally were going to isolate the variable so it's a different protocol for algebraic equations I need to do is I'll take a look at that that three that's outside the parentheses the first thing I need to do is I need to distribute that three into the parentheses meaning I need a multiply 3 * 2X and I also need * 3 * 3 read my 12x That Remains the Same it doesn't change so my 3 x 2 x that's going to become 6x my three times is going to give me a nine that's all you put 245 now I already distributed so now I need to move on to step to combine like terms well I have one pair of like on the left hand side of the equation the 12 x and the Styx X those are like terms because they contain the same variables the variable X is going to give me 18 x alright I'm still on Step 2 combining like terms now my second pair of like terms are separated by the equal sign and those are the number 9 and the number 45 need a combined those two terms and you know I can kill two birds with one stone because I need to combine like terms and I also need to isolate the X so makes it makes the most sense for how to get rid of the 9 on the left and when I do that his first time I determine what's currently going on that's going to be addition so now to get rid of it I do the opposite operation to both sides of the equation that means I'm going to subtract about the equation I'm going to have an 18 X on the left on the right first I subtract 5 that's 40 and then another form that's going to be 36 all right so now the nine is eliminated from the left on the I subtract 9 from 4536 now I move on to step three step three is isolate the variable now to isolate the variable when I say that I mean I just Axe Cologne but I have this 18 butts in my way so again it's all the same protocol first I look at the prom and see what's going on currently so what's going on currently is multiplication I need to do the opposite Opera both sides of the equation that means I need to divide both sides by 18 on the left hand side of the equation the 18th are going to cancel I'll just be left with chi-x and then on the right hand side of the equation is 36 / 18 that's going to give me 2 so do you have it I'm going to scroll down to you guys come to work again first thing we did was distribute that was step number one and that's the number one may not always be included in every problem not you're not going to have distribution in every single multi-step algebraic equation but in this one we did so that's the first thing we did was distribute and then we combine like terms and then we are so those are the three steps all right I said sometimes you will see questions that have a variable on both sides of equal sign like this example all right so you see we have a 7 x here and a 5x here you know what we could take a step further we can all see you know this is one set of like terms 7x + 5x we have another set of like terms the nine and the 87 better also opposite sides of the equation you know we're we're we're moving values across the equal sign either way it so it makes no difference to us now you know when you have this problem you can go that is for different route so you can go beginning with the variables I could either subtract 7x from both sides of the equation more I could add 5x to go equation in both of those scenarios I'm doing the opposite operation that's currently going on to both sides of the equation my recommendation and the way that I operate is I always pick the option that's going to avoid running into the negative so in this case you know if I had to pick between subtracting 7x from both sides of the equation for adding 5 x to both sides I'm going to go with adding five and again the reason I do that is so that I don't end up with a negative in my equation there's nothing wrong with having a negative it's just you're better off avoiding them no you can be to increases the likelihood that you run into Miss and it just makes it more challenging as opposed to going to easier up same thing here you know you could subtract 87 from both sides but then you would have to move this 12 to the other side of the equation so the easiest thing to do is just add 9 to both sides so you know this whole time there's the combining like terms notice there was no distribution in this step but they just went directly to combining like terms and then here now all they have to do is isolate the variable right and they're going to do it through Division and divide both sides by 12 to 12 is going to cancel out on the left turn on the right you're just going to have 8 as your answer all right notice on this problem doesn't know District either the way that you know if I need to distribute is you're going to look for a set of parentheses a number to the left and at least two terms inside the parentheses let's go ahead and solve this one 7 + 5x equals 2x + 10 so you know you can choose to start with your variables are you can start with your consonants just for me to remain consistent what I'm going to do is I'm going to focus on the variables first then the constant so I have a choice I could subtract 5x from both sides or I could subtract 2x from both sides if I were to subtract 5x from both sides I would end up with a negative 3x on the right and again I don't want to deal with negative so I'm going to opt out talking to X on both sides gummy 7 now I'm going to have positive 3x on the left and then a pain on the right side of the all right now I can go two ways right I could subtract 7 from both sides or I could subtract 10 from both sides will makes you the most sense for me is just at 7. now I'm left with three x equals 3 now this final step I'm isolating the variable divide both sides by 3 Northern like after the -7 in the three and there's a. For some reason like when you type on the text and you put spaces it'll automatically put a. But it's not intentional I'm not a placing and then 3 / 3 do you guys see the process here does the two things one was combine the like terms and then isolate the variable so there you have it all right so says let's try when their car is a few more steps okay so this one does include distribution right we know that because you know we have the current season the number outside outside of the prince is right and then after we take care of the distribution we're only going to combine like terms and the final step will be to ice Luther Burger 1 things keep in mind is you always take the sign to the left of the number what I mean by that is for example you don't adjust distribute before you don't just go 4 * 2X and four times for you also include the sign to the left so everything that I highlighted here is where you're going to multiply so you're going to include this minus sign and again I've said this before I want you guys to think of addition as being interchangeable with positive and subtraction being interchangeable with negative because they function in the same way so we're going to multiply the 2X and the 4 * -4 once they do that they end up here in this line right here that Tyler's it says now we can see that there are like terms to combine on the left and right side so that we are familiar with we did that in a few days, we start sending the like terms across the equal sign to combine them all right you still need to get are the extremes together so they're they're just working on combining the variables she had the right here that you know they're at two steps away from the answer if they still have to get the 16 across and then finally now they can isolate the variable so I'll have to do is divide by 3 and we have our answer alright you guys want to take a moment to try this one out and then I went to get some rest then we can go ahead and share so I'll give you guys a moment try this one out and then once I get to my sponsor then we'll go ahead and review together I'll give you guys a hint the first thing you're going to do is the distribution that's over here all right cuz I don't have a response that's what I'll do is I'll start working out slowly and then and then we'll catch up with with what every step you guys are on all right so this is original problem right I just copied it down over here so again the first thing I would do is a distribution that's what comes first that means I go 3 x 5 x that's 15 x remind me to sign 3 * 6 + 18 now I combined lights terms so I have one set of like terms on the left hand side of the equation that's the 6 - 18 if I have six and I subtract 18 that's going to be -12 and on the right hand side of the equation I have one set of like shrimps that's the 2x + 5x so that's going to be seven it now my life's rooms are across you know one across one from another from across from each other inside so you know what makes the most sense is subtract 7x from both sides so that I don't run into a negative so I'm going to go like Donna 15 - 7 is 8x and now I'm going to add 12 to both sides of the equation again I'm doing the opposite operation all right so that's going to give me 72 - 84 + 12 is going to bring me to negative 70 to think of it as you having a $84 debt you paid $12 of that debt now your debt has reduced down to $72 so you know the first line of my what is distribution all the other lines leading up to the current one we're about combining like terms and now my final Line This is Where I isolate the variable so can we go I'm in / 8 and then I have x equals negative again the signs are different when I'm dividing I have one negative or positive because find the difference that means my answers are going to be negative we got down so you can see it see my work against the light back on but just to recap in this line right here the second line that's where we distributed from from the third line all the way to the second to last line is where we can ended like terms and then from this line right here down to the answer all we did was isolate the variable all right you have a different one now you may be unsure as to whether this is a disc you should come or not because we do have the parentheses right but we don't have a number outside of the parentheses so you know maybe I'm sure as to whether we distribute here or not but this is a distribution problem we do distributive so this is a minus sign really nice try to do some minus time but again we have to think of a minus sign and a negative sign as interchangeable right because they function the same way so we're going to actually distribute this into the parentheses so think of this as a negative and this is going to change the signs of of the terms inside of so this is going to become a negative 2X and this is going to become a positive for or a plus for that's what they going to do here your day Peter portrayed as a negative sign but in reality this is a subtraction but you know we have to think of it as interchangeable so here they are the Distributing the negative sign now becomes to look at the original one originally was positive 2x now it's minus 2x it was - 4/8 + 4 all right now that they are done Distributing they combine the like terms and the end up here they're still not done combining like terms with this 9 and the 29 subtract 9 from both sides all right they do that and now it's this stuff there at the final step that's just where we again isolate the variable so divided. they have their answer here so this one is identical to the one we just saw where we to distribute or negative so the first thing we do is the distribution right we have this minus sign outside of the parentheses that's going to be distributed inside so this for is going to be -4 - 3x is going to become plus that's what happens when I distribute the minus sign okay now I can buy him like terms on the left hand side of the equation 10x + 3x + 13x all right so now I need to combine like terms so I'm continuing to my life but now that are across from each separated by the equal sign so my best route to go is 2 subtract 2X that way I don't run into the negatives with the various it's going to bring me down to 11 x - or he was 29 all right now I need to get rid of this - 4 app work mugshots 11x 29 + 4 free and now at this point in my problem I am now isolating the variable that means I'm going to divide both sides by 11 equal scroll down Siesta Key to work again I'm just going to recap at 3 so the first line is our original problem second line is where we distribute the minus sign gets to shoot it into the parentheses so this for becomes - 4 - 3x becomes + 3x and then what distributed then I can go ahead and combine the light trim the 10x with the 3x back its combined it and then once I do that then I combine like terms across equal sign so the 2X and the 13 x if I minded do subtraction that gets that goes me to 11 X now hear this minus for buying for both sides at 11:33 and that this isolate the variable divided by 11 equals 3 are you guys we are all set you know I know that was a lot of new information you know we were adding new information to a previous knowledge but my recommendation is to review the video so that you guys can good can get those Concepts I'll memorize

Uploaded by Daniel Gomez.

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