Properties
of Equality
Equation Rules
Equivalence properties and algebra rules for manipulating equations are listed below.
Definitions 
1. a = b means a is equal to b.
2. a ≠ b means a does not equal b.

Operations 
1. Addition: If a = b then a + c = b + c.
2. Subtraction: If a = b then a – c = b– c.
3. Multiplication: If a = b then ac = bc.
4. Division: If a = b and c ≠ 0 then a/c = b/c. 
See
also
Inequality
rules, trichotomy, side of an equation
