Auntie Donna: Hi Matthew!
Matthew: I have a math test tomorrow and I was wondering if you could test me with a couple of algebra questions.
Auntie Donna: Oh, sure. Hmm... Let me think of one... How about n+3-5n+12.
Matthew: Hmm... I think the answer is -6n+15
Auntie Donna: Your answer is incorrect, Matthew. Let's simply go back and take a look at how to do this question, and what you did wrong while solving it.
Matthew: Oh, shucks! Well, alright...
Auntie Donna: Well, first you must re-group the numbers to make it easier to solve. Therefore it should be, n-5n+3+12.Then combine like terms and solve it. Which means combine all the terms that are the same. Now, it should be, -4n+15. Now you have simplified it.
Matthew: Well, what did I do, to get my incorrect answer?
Auntie Donna: Hmm... Well, if we go back and look at it, you added -n and -5n instead of subtracting -5n from n.
Matthew: Oh, I see I see... Can you give me one more question?
Auntie Donna: Sure. How about, 2+4(3n+8).
Matthew: Okay, I'll try it. Uh... I came up with 12n+10.
Auntie Donna: Once again, you're incorrect. Let's go back and do step by step again.
Matthew: Aww... okay.
Auntie Donna: Okay, so with this question, there is distributive property going on. You can underline it so that you know where it happens. So, put the 2 first because you know that it's going to stay because it's not part of the distributive property. Now, take the number beside the bracket and multiply the two terms inside the brackets. It should now be, 2+12n+32. Now re-group it. It should be, 12n+2+32. Combine the like terms like last time. It should be, 12n+34. And that should be your simplified expression.
Matthew: Oh, right. Well, explain to me what I did wrong.
Auntie Donna: Oh yeah. Well, when you first looked at the question, instead of multiplying both terms in the bracket, you just multiplied the first one, and added the last two integers. Which is why you got the answer 12n+10.
Matthew: Ooooohhh. I get it now. It really is easy now that you've explained it all. Thanks Auntie Donna! I hope I do well on my math test.
Auntie Donna: Oh, I'm sure you will, but just remember to go step by step. It's okay to use lots of paper because we recycle!
ATTENTION PLEASE ! : On, my title of the picture there, I meant to put DIVISIVE, not DIVISITIVE. Thank you. :)
Divisive: First, I isolated the variable by multiplying n by 2. Then I got 2n/2. I also did it on the other side to balance it out. Then I crossed out the 2 and the 2, because they cancel eachother out. Then I solved 4(2) and I got n=8. Finally, I verifiedby plugging in the what n equals where n is supposed to go.