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Need some clarity for re-arranging equations

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Hey guys, I'm a lot further through the Practical Algebra book I'm going through, but I've run into a problem that seems rather confusing. In the first chapter of the book, the following is stated:
Quote:
When adding, the order of the numbers may be changed. Thus, b + 9 = 9 + b. When subtracting, the order of the numbers may not be changed. Thus b - 9 != 9 - b.
Then in chapter 3:
Quote:
Once you know how to re-arrange polynomials in convenient order, you can use this skill to assist you when adding them. Example: (3x - y) + (2y + x) Removing the parenthesis and grouping like terms, we get: (3x + x) + (2y - y)
Surely that's just gone and re-arranged the order of the numbers, which the subtraction rules says you can't? I've plugged in numbers, and I can see that it works, but the rule is totally confusing me and preventing me from understanding why you can do it in the first place. Can someone elaborate for me please? Thanks in advance, -hellz

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You swapped values around a + sign -- no problem, addition is commutative.

The thing to remember is that (a+b)=(b+a) but that (a-b)=-(b-a).

Or you could think of (a-b) as (a+(-b)), so (a-b)=(-b+a)

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Hey dude,

Thanks for the reply. So does that mean that you can't re-arrange signs of operations outside of terms, but you can re-arrange within the terms themselves, or have I misunderstood?

-hellz

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