Algebra Properties of Equality

Transitive Property of Equality

If a=b and b=c, then a=c If 3x = 15 and 15 = q, then 3x = q.

Division Property of Equality

If a=b and c=0, then a/c=b/c If 12x = 84, then x = 7

Substitution Property of Equality

If a=b, then a can be substituted for b in any expression or equation. If 2x + y = 5 and x = y, then 2x + x = 5.

Addition Property of Equality

If a=b, then a+c=b+c If 3x - 3=12, then 3x=15

Subtraction Property of Equality

If a=b, then a-c=b-c If 2x + 4=16, then 2x=12

Multiplication Property of Equality

If a=b, then ac=bc If M<A = 15, then 3 M<A = 45

Symmetric Property of Equality

If a=b, then b=a 8 + 7=7 +8

Identity of Addition

a + 0 = a 5 + 0 = 5

Identity of Multiplication

a • 1 = a 5 • 1 = 5

Distributive Property

a(b+c) = ab + ac 2(4x + 6) = 8x + 12

Reflexive Property of Equality

a=a 8=8