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Two-Step Equations

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alright everybody today we're going to talk about some more equations and we're going to talk about what two step equations and these equations are two step equations because they're going to be equations that required two steps when you saw them set up just one step when you sell them so  two step equations might look something like this and + 17 equals 21  the goal is to get em by itself so that we can figure out what and equals just like it always is when we're solving and it Asian when were solving an equation were always trying to figure out what that variable equals so we want to know what is an equal so we've got to get off which means we've got to get rid of that too and we've also got to get rid of that 17 the question is  do I subtract 17 first  or do I divide by to first you know you're going to have to get rid of the two and get rid of the 17 but how do we know which one get rid of first  well in this case we're going to get rid of the 17 first so we're going to do minus seen so that we can get rid of that 17 and then we're going to balance it out on the right as well and when you do that the 17th cancel each other out and on the left you just have to end on the right you're going to have 21-17 is 4 and then from here to be easy right because when too many calls for you know you just / 2 and / 2 and now we have End by itself and 4 divided by 2 equals to can you still plug to in back for n to check your solution yeah you always can check your solution whenever you're solving an equation no matter whether it's a simple equation I really complicated one if you plug two in for n it should work and in this situation what's 2 x - 4 what's 4 + 1720 and does it work yep it does work okay so this is a two-step equation because we had to subtract 17 from both sides and then we how to divide both sides by 2 but we had to do it in that order if we divided besides by to First it wouldn't come out right and so we're going to talk about that let's see at 5 x minus 10 equals 40 equation like that again we've got to get rid of the 5 and got to get what is the 10  do we add 10 because it's a - 10 or do we divide by 5 to get rid of the five we're going to have to do both but the question is what one do you do first the official way to do this the real rule here is get rid of the part that's not attached to the variable first in other words that 5 is attached to the variable it's right next to it they're stuck together so get rid of the part that's not stuck to the next burst that means get rid of the 10 first so we're going to add 10 to besides first but if you're not sure it which one to do first if you think we'll maybe I should / 5 first just pick one way do it that way and since you can always check your answer the if it doesn't come out right try it the other way one of the great things about math is trial and error you can always just keep trying until you find the and that works alright so if you were doing this problem what would your first step be well if you said First Step would be to add for to both sides you'd be correct how about this one take a second look at that you have to get rid of the V and you have what are the three which one you going to get rid of first on this problem you would subtract 3 from both sides first because you want to get rid of the three that's not attached did the axe first Danielle get rid of the five second metal be your second step of your two step equation how about this one negative two equals 2 + 4x or try to get the X by itself so what would our first step be what we're going to get rid of the four but that's attached to that EXT so we probably have to get rid of the to the positive two  first alright let's actually saw one of these so let's say you had 50 + 40 x equals 130 we just said that the first thing that need to do is get rid of the part that's not attached to the x that would be the 50 right so how do you get rid of a 50 well this is an addition problem rights 50 + 40 x so how you undo addition  subtraction can I subtract 50 from the left side of the equation and what will that give us  40 x right what would 40 x equal will now we have to balance this - 50 over here by -50 over here 130 - 50 is 80 now we're starting to see how this is going to play out so what's my next step my next step is to get rid of this 40 by dividing by 40 right because we run doing the multiplication there 40/40 cancels out is x equals well I've got to divide The Other Side by 40 as well how many times does 40 go into 80 twice how do I know the x equals to  when I plug two in here what's 40 * 280 what's 50 + 80 50 + 80 comes out to 130 therefore  check X actually does equal to in Reno that for sure let's try another example problem this one's a little bit different okay notice on this one X over 3 plus 1 equals 11 can we still solve this the same way sure what are we going to get rid of first the 3 or the 1 well get rid of the part that's not attached to the acts that means get rid of the one so the opposite of + 1 is -1 minus one cancels now we just have X over three equals what does it equal oh well I subtracted one from the right now I got to subtract 1 from the left easy 11-1 is 10 now how do I get X by itself I got to get rid this 3 right here right so how do I get rid of that three have to get rid of that three by doing the opposite of x divided by 3 which would be times 3 so that'll cancel out and give me the axe that I want and since I X the right by 3 I'm going to time the left by 3 is well and I'm going to get 30 calls X or x equals 30 and that's my answer plug it back in what's 30 divided 310 what's 10 + 1 11 check and we're good to go  alright now you try 25 equals 10 x + 5 you're going to have to do two steps on this one to get rid of the 5 and 1/2 get rid of the 10 and after you do both steps you'll have x equals something make sure you plug that solution in to see if it works all right there's only one more thing that we need to talk about your and that's making sure you know how to handle your negatives alright and something weird happens if you have 5-10 X we've got to get rid of the five first right because it's not attached to the x then we're going to do it on both sides to keep it balanced notice that what we end up with is the five gets cancelled out but this minus sign right here  has to stay there that's important okay because that minus next should still be a -10x even after you get rid of the 5 so that minus cast to stay there the negative has to stay there before you solve the rest of the problem okay I think you could probably see how the rest of that problem will go so why you to try another problem that's kind of similar but you have to make sure you handle that - in there correctly alright that's pretty much it so if you need to go back and review any of that review that make sure you what does to practice problems done show all your steps check your solution and we will recheck that solution and double-check that solution in class tomorrow

Uploaded by Jeff Marbut.

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Two-Step Equations

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