SOLUTION: How do I simplify the expression and justify each step? By justify I mean each time you simplify would that step be distributive, associative, commutative etc. 29c + (-29c)

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Question 673284: How do I simplify the expression and justify each step? By justify I mean each time you simplify would that step be distributive, associative, commutative etc.
29c + (-29c)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
WARNING:
Different books/teachers may give slightly different names to the same properties.

IF YOU MUST CHOOSE JUST ONE PROPERTY, AS IN A MULTIPLE CHOICE QUESTION,
then it would be simple.
I could say that -29c obviously means the additive inverse of 29c.
Then I would say that
29c+%2B+%28-29c%29=0 is the Additive Identity Property.

IF A FULL EXPLANATION IS EXPECTED,
it may be more complicated.
Unfortunately, I suspect they want to make it more complicated, and we would need to invoke 3 or more properties.
If it is interpreted as just -29c=-29%2Ac, we could say that
29c+%2B+%28-29c%29=%2829%2B%28-29%29%29%2Ac is the application of the Distributive Property.
Then,
%2829%2B%28-29%29%29%2Ac=0%2Ac Additive Identity Property,
and finally,
0%2Ac=0 Zero Property

IF THEY WANT TO MAKE YOU EXPLAIN EVEN MORE:
The Distributive Property is usually represented in the form
c%28a%2Bb%29=c%2Aa%2Bc%2Ab.
In this case we have a%2Ac%2Bb%2Ac=%28a%2Bb%29c, with a=29 and b=-29.
That is usually referred to as "taking out a common factor".
a%2Ac%2Bb%2Ac=%28a%2Bb%29c is the same (read backwards) as
the usual %28a%2Bb%29c=a%2Ac%2Bb%2Ac distributive property.
c%28a%2Bb%29=c%2Aa%2Bc%2Ab and %28a%2Bb%29c=a%2Ac%2Bb%2Ac are the same thing,
because of the Commutative Properties for Addition and Multiplication.