SOLUTION: How would I write a proof for the problem (4a+3)-3a= a+ 3?

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Question 484692: How would I write a proof for the problem (4a+3)-3a= a+ 3?
Found 2 solutions by richard1234, Edwin McCravy:
Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
Rewrite LHS as (4a + 3) + (-3a) then using the fact that addition is associative, you can say the LHS is equal to (4a - 3a) + 3 = a + 3, same as RHS. That's if you want to prove they're equal.

In reality though, we just say (4a + 3) - 3a is equal to a + 3 right off the back.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
The other tutor did not prove it.  Here is the proof.

 (4*a+3)-3*a =

 (4*a+3) + (-3*a)   by the definition of subtraction

 4*a + [3 + (-3*a)] by the associative principle for addition 

 4*a + [(-3*a) + 3] by the commutative principle for addition 

 [4*a + (-3*a)] + 3 by the associative principle for addition

 {[4 + (-3)]*a} + 3  by the distributive principle of multiplication 
                             over addition

 1*a + 3            by the operation of addition 4+(-3) = 1

   a + 3            by the identity property for multiplication.

Edwin
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