Identify rules of algebra with (x+3)-(x+3)=0

Taking any number x, and adding on its opposite -x, leads to x+(-x) = x-x = 0

This is the inverse property of addition.

A numeric example would be 7 + (-7) = 7-7 = 0

Going back to x-x = 0, we can replace x with any expression (whether simple or complicated) we want.

So in this case, we replace each 'x' with 'x+3' to get (x+3)-(x+3) = 0

The equation (x+3)-(x+3) = 0 has infinitely many solutions. The solution set is the set of all real numbers. We can replace x with any number and the original equation will simplify to a true statement.

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