Question

Solve the equation x-8=16 and state which axiom do you use here

Answer 1

x-8=16

add 8 to both sides:

x-8+8=16+8

simplify
x = 24

Have no idea what "axiom" that might be.

Answer 2

Associative property maybe?

Answer 3

Gawd...this gets goofy sometimes. I googled "what do you call adding a number to both sides" and damned if I didn't get some hits.

Apparently this falls under "properties of equality", and specifically subtitled "subtraction property of equality" and the "addition property of equality"

I don't know if that's what you're looking for or not, but there it is. :-)