There are several properties of equalities. These properties will allow you to balance, solve and manipulate equations. The following properties assume you are working with real numbers.
Reflexive Property of Equality
Any number is equal to itself
Examples:
3 = 3
a = a
Symmetric Property of Equality
The order of the equation does not change equlaity
Example:
x + 3 = 2y
is the same as
2y = x + 3
Transitive Property of Equality
Two quantities equal to the same quantity are equal to each other.
Examples:
if x = y and z = y then x = z
if 3a + b = c and x/4 = c then 3a + b = x/4
Substitution Property of Equality
A quantity may be substituted for an equal quantity in any expression.
Examples:
if x = 5 then 3x = 3(5) = 15
if x = a and 4a + 6 = 12 then x can be substituted for a to get 4x + 6 = 12
if b = 5a and b + 8 = 24 then 5a can be substituted for b to get 5a + 8 = 24
Addition Property of Equality
The addition property says that when you add a number to both sides of an equation, the two sides remain equal.
Example:
if a = b then a + 3 = b + 3
Subtraction Property of Equality
The subtraction property says that when you subtract a number from both sides of an equation, the two sides remain equal.
Example:
if a = b then a - 8 = b - 8
Multiplication Property of Equality
The multiplication property says that when you multiply a number to both sides of an equation, the two sides remain equal.
Example:
if a = b then a(4) = b(4)
Division Property of Equality
The division property says that when you divide both sides of an equation by a number, the two sides remain equal.
Example:
if a = b then a/2 = b/2