Rules of Symmetry

Hello, was reading my pre-algebra book again and it stated something that I'm having a hard time understanding. The books text states as follows:

The rules of symmetry also means that in any equation, we may exchange sides (IF 15 = 2X + 7), then we are allowed to write (2X + 7 = 15). Thus the rules of algebra tells us what we are allowed to write.

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Here is my question. The book does not explain why 2x + 7 = 15. The book also states in several places the that the value of x or -x when by it's self is equal to 1, or -1 and also that 2x + 7 would then equal 7x. What's going on with this symmetry thing, why is (2x + 7 = 15)?

The reason you are allowed to do that is because either way the equation is balanced. Solve for x on both equations and you will get the same answer.

BTW just in case you do not know: Symmetric means equally balanced on both sides.