Originally Posted by

**JeffM**
You did it right.

The different uses of the + sign and - sign are a source of confusion to the beginner. + and - are used in at least three different senses in math. At a very fundamental level these senses are all coherent, but that coherence is not intuitive at first to the beginner. So be patient.

Additive inverses: For a given number a (which may be positive or negative) there is an ADDITIVE INVERSE indicated as (- a) such that a + (- a) = 0.

Operations: + means addition and - means subtraction.

The rule is that (a - b) = [a + (- b)] where the first minus sign means the operation of subtraction and the second minus sign means additive inverse. So your "removing the subtraction" is CORRECT. It may add a step but if it prevents mistakes, SO WHAT?

Now consider an expression like [a - (c * d)]. That is equal to {a + [-(c * d)]}, where [-(c * d)] is the additive inverse of (c * d). Now, in general, the additive inverse of (c * d) is NOT [(-c) * (-d)] because (c * d) + [(-c) * (-d)] = (c * d) + (c * d) = 2(c * d). The additive inverse of (c * d) = [(-c) * d] = [c * (-d)] = - (c * d).

So when "you remove the subtraction" from 4(x + 3) - 2(x - 1) = 4(x + 3) + {- [2(x - 1)]} you have a choice.

You can compute {- [2(x - 1)]} = (- 2) * (x - 1) = - 2x + 2, or you can compute {- [2(x - 1)]} = 2[- (x - 1)] = 2(- x + 1) = - 2x + 2.

Clear now?

Thanks JeffM for your thorough explanation. The more I do this kind of problem the more I can kind of do it in my head.

Code:

4(x + 3) - 2(x - 1)
| | | |
1 2 3 4 <-- I look at it in four steps
| | | |
4(x) 4(3) -2(x) -2(-1) <-- 1, 2, 3, 4
| | | |
4x + 12 + (-2x) + 2 <-- stick a bunch of + signs in there
2x + 14 <-- reorder and simplify

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