Algebra II help! PLEASE!?

Question

okay, I need to figure out what property and stuff was used (like distributive and inverse) to get to the next part of the problem, it sounds confusing kind of. Here are the actual directions:

Show that a+(a+2)=2(a+1) for all values of a by justifying the steps using the properties of addition and multiplication.

Here is the problem:

a+(a+2)=(a+a)+2

a+(a+2)=(1 x a + 1 x a) + 2

a+(a+2)=(1+1)a+2

a+(a+2)=2a+2 x 1

a+(a+2)=2(a+1)

I need help! =O

Answer 1

a+(a+2)=(a+a)+2   -- addition is associative

a+(a+2)=(1 x a + 1 x a) + 2  --- identity property of multiplication

a+(a+2)=(1+1)a+2 --- distributive property

a+(a+2)=2a+2 x 1 --- 1+1 = 2 and identity property of multiplication

a+(a+2)=2(a+1)  --- distributive property

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