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Multi-Step Equations with Parenthesis and Stuff

Added Dec 10, 2018 •

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okay so today we're going to solve the more equations we love solving equations this time the equations that we're going to solve multi-step equations and they're going to have parentheses in there and I stop that make them a little more complicated and by the time we got done with this lesson we should be able to solve all kinds of different equations really well and be ready to be equation-solving machines okay so the first kind of equations ever look at our equations where you have to use the distributive property because I've got parentheses in there and we remember then when you see those parentheses with a 10 in the front what we're really saying is that a plus two is getting x 10 so it's going to be 10 * a + 10 * 2 so our first step is going to be to Use the distributive property to distribute that 10 + now it's going to be 5 + 10/8 + 20 because we did 10 times a to get 10 I-10 a and 10 times 2 to get 20 so hopefully you remember that disturb property idea and why the 10 x parentheses 8 + 2 turns into 10 a + 20 it's cuz the whole 8 plus two is getting X by 10 today is getting * by 10 and the 2 is getting * by 10 we got it now what the heck we have to do next to solve this equation well what you'll notice is that we have a 5 and we have a 20K and those 5 and 20 are like terms so we can put them together and make 25 so really like the 10 a plus 25 adds up to 35 and now we're just going to solve it like a normal two step equation take 25 away from both sides at 25 cancel out you just have to attend a 35-25 which is 10 set a course at this point you would divide both sides by 10 where 10 10/10 comes out to what I didn't write the / 10/10 on both sides but I think you get the idea they're so the distributive property is what we're going to use whenever we see parentheses all right let's try a couple more examples how about this one we got eight and there's parentheses t plus 2 but on this one there's a negative in front of the 8K so that - 8 has to get distributed it's not just 8 x t it's - 8 x t so it's -18 and it's not just 8 * 2 it's -8 * 2 so we're going to get Negative 80 and then we're going to get -16 here okay now that we took care of that we got to look for anything that we can switch together like for instance 20 t - 80 those are like terms and if you're not a hundred percent sure on how to put those together correctly I like to think of it as whatever kind of a word starts with a T like if you have 20 tomato send you take away eight Tomatoes you have 12 Tomatoes right so I'm going to take that 20 - 80 and I'm going to turn it into a 12T now again I got a normal regular old two step equation do + 16 on both sides to cancel out the -16 and then I'll just have 12T on the left and -12 on the right and I'm going to divide both sides by 12 to get T by itself and when I do -12 / I should get -1 as my solution to this equation all right so sometimes we have to use parentheses and the distributive property sometimes you got a smushed together like terms and sometimes there are no parentheses you just have to look for like terms right off the bat so in this case our first thing is we got 5A + 10A we got five apples + 10 apples we're just going to say that's 15 apples right so we're going to simplify this whole equation by just combining like terms together and making it shorter and sweeter so 15 a plus 5 equals 35 and then I can swap the fives what I just have 15 a.m. 35 - 5 is 30 / Side by 15 and 30 / 15 comes out to 2 okay so that would make sense I hope so one more example problem then we'll be just about ready to go this one's a little trickier because the bee and the bee are right next to each other but hopefully you can see that you've got five bananas and then you're going to take away two bananas so far bananas -2 bananas is 3 bananas + 11 cuz the + 11 is just still there nothing happened with that and the 50 is hanging out over there on the right by itself until we start canceling out this 11 we're going to take 11 away from the 50 and now all we're going to have on the left side is 3B and what we're going to have remaining on the right side is 50 - 11 vs 39 the three can't talk and I have just be left over I'm left side and I'll have my solution on the right side because 39 / 3 is 13 all right so oh I forgot on all these example problems I wasn't plugging my answer be you've got to plug your answer back into check to see if you did it correctly right but on a problem like this I'm not just going to plug 13in for that be I've also got the plug 13in for that P don't I so on these kind of more complex multi-step equations plugging in your answer as a little bit more time consuming but I think you could figure this out so at the first part 5 * 13 is 65 + 11 so that's 76 and then you're going to take away 2 * 13 which is 26 of 76 - 2613 or 100% hundred percent confident super super confident that we actually got this problem correct we know for a fact that Vehicles 13 and we can move on feeling good about ourselves and our lives and city of solving equations so how about you walk away from this equation feeling good about yourself by Distributing simplifying solving and then check your answer to see what I actually equals and then once you're done with that you can try and oh my goodness I bet if you combine some lifetime terms there this probably isn't going to be as complicated as you think so try to smoke together the terms that are like terms and then simplify this and then solve it and see what x comes out to all right we'll see how we did on these two practice problems in class tomorrow and see you next time

Uploaded by Jeff Marbut.

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