Algebraic Properties of Equality

The equal sign that depicts the fact that both sides of it are equal is a very strange symbol with many properties. It tells you various traits of each side, and it allows you to manipulate each side in specific ways. Here are the different properties of that sign:

Property	Definition	Example
Reflexive	For all a, a=a
Symmetric	If a = b, then b = a
Transitive	If a = b & b = c, then a = c	If 8 = (4)(2) and (4)(2) = (2)(4), then 8 = (2)(4)
Substitution	If a = b, then one can replace a with b.	$x-6=14\,$ $x=20\,$
Subtraction	You can subtract one number from both sides $x+6-6=14-6\,$ $x=8\,$
Multiplication	You can multiply both sides by a same number $x=108\,$
Division	You can divide both sides by a same number different from zero $x=3\,$