[Bear_in_RoseBear]

You start off with the equation, N+6=10.

Subtract 6 from each side.

6-6=0, so the left side becomes N+0, right side becomes 10-6 or 4.

Solution is N=4.

[Rose in RoseBear]

Yes, isn't this an illustration of an axiom?

If you do the exact same thing to both sides of an equation, then you've essentially done nothing to the equation. Therefore, if you subtract 6 from both sides of the equation, you simplify the equation:

N + 6 - 6 = 10 - 6
N = 4

The parentheses are there to make sure you execute the subtraction in the right order.

An example of the reflexive property of equality.