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Multi-Step Equations with Parenthesis and Stuff

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okay so today we're going to solve some are equations we love solving equations this time equations that we're going to solve multi-step equations stuff to make him a little bit more, and by the time I'm 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 Art equations where you have to use the distributive property because I've got parentheses in there and remember that when you see those parentheses with a 10 in the front what we're really saying is that a plus two is getting * 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 a + 20 because we did 10 times a day to get 10 I-10 a + 10 x 2 to get 20 so hopefully you remember that Disturbed property idea and why the 10 x parentheses a + 2 turns into 10 a + 20 it's cuz the whole 8 plus 2 is getting Times by 10 today is getting Times by 10 and the twos getting Times 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 that 25 cancel out you just have to attend a 35-25 which is 10 but of course at this point you divide both sides by 10 where tendai 10/10 comes out to what I didn't write the / 10 / 10 on both sides but I think you get the idea there so the distributive property is what we're going to use whenever we see parentheses alright let's try a couple more examples how about this one we got eight and parenthesis 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 negative 18 and it's not just 8 * 2 -8 * 2 so we're going to get -80 and then we're going to get -16 here okay now that we took care of that we've got to look for anything that we can switch together like for instance 20 t - 8 T 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 and 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 a negative one as my solution to this equation alright so sometimes we have to use parentheses and the distributive property sometimes you got to smash 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 + 5 equals 35 and then I can't stop the 5 so I just have 15 a on the 35 - 5 is 30 divide both sides by 15 and 30 / 15 comes out to two Okay did that 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 aren't 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 sofa 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 cancelling out this 11 then 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 which is 39 and I'm going to buy both sides by threes can't talk and just be left over on the left side and I'll have my solution on the right side because 39/3 is 13 alright so oh I forgot on all these example problems I wasn't plugging my answer. you've got to plug your answer back in to 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 they don't 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 it the first part 5 * 13 is 65 + 11 so that's 76 and then you're going to take away two times 13 which is 26 is 76 - 26th 08 that does come out 250 GB does actually 13 100% what are percent confident super super confident that we actually got this problem correct we know for a fact that be equals 13 and we can move on feeling good about ourselves and our 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 a actually equals and then once you're done with that you can try and oh my goodness I bet if you combine some like terms there is probably isn't going to be as complicated as you think so try to together the terms that are like terms and then simplify this and then solve it and see what x comes out to alright we'll see how we did on these to practice problems in class tomorrow and see you next time

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Multi-Step Equations with Parenthesis and Stuff

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