Simpliying Variable Expressions using multiple properties?

Question

Hi, this is comlicated for me, so if I don't ask clearly it's because I'm not 100 percent sure of my question. I'm studing some pre algebra and I have to simplify some equations using different properties such as the distributive property and the alternate form of the distributive property. The question I'm working on involves combining like terms.

So the example I'm working on is simplify 12z-8a+3-16z+8. 
I got the whole thing about combining them but how do you know which sign to put next? Sorry, let me try to state that clearly.
If you combine 12z and 16z how do you know if you should add them or subtract them? Do I use the sign after the first number of before the second? 

The answer I came up with was 12z-16z+8a+8a+3 which in turn goes to -4z+16a+3.... but when I did that math the answer I had was different then the book. So I must have combined them wrong.

If you know what I'm talking about, I know I'm not being very clear, please give me a hand and explain this the easiest way you know. 

Thank you so much in advance

kartoonkid49 · Accepted Answer

In the 2nd paragraph you asked: If you combine 12z and 16z how do you know if you should add them or subtract them? Do I use the sign after the first number of before the second?" The answer is to use the sign that comes before the second number. For example, 5A-7A, is the same as 5A+ - 7A. So the answer is -2A. Its sorta confusing. But in your question (12Z - 8A +3 -16Z + 8), you take the 8A and since there's no other terms with an A, you leave it. Then go to the next alphabetical letter: Z. 12Z+ the other Zterm, -16Z is egual to: -4Z. So far, the answer is 8A- 4Z. Now you must move on to the terms with no variable:3 and 8. Take the +3 (positive 3) and add a +8. This is equal to 11. The answer is 8A-4Z+11. 

PS- I have no idea how you took 12z-8a+3-16z+8 and turned it into:12z-16z+8a+8a+3. How did you end up with two 8A's? Was it a typo? Im assuming you typed the original equation correctly.

mom · Answer

12z-8a+3-16z+8
------------------
do the letters, and numbers separately

12z-16z = -4z

-8a (I think you copied yours incorrectly)

+3+8=11

answer -8a -4z +11

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Simpliying Variable Expressions using multiple properties?

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