Properties of Equality and Algebraic Proofs for Students

Addition Property

If _______________, then _______________________________.

Subtraction Property

If _______________, then _______________________________.

Multiplication Property

If _______________, then _______________________________.

Division Property

If _______________, then _______________________________.

Distributive Property

a(b + c), then a(b + c) = ______________________.

Substitution Property

If ____________ then a may be _____________________________ by b in any expression or equation.

Reflexive Property

For any real number a, __________________.

Symmetric Property

If ________________, then ________________.

Transitive Property

If _______________, and _______________, then ______________.

Proof Statement 1

If k = 3, then 3 = k.

Proof Statement 2

If 2x = 14, then x = 7.

Proof Statement 3

10y = 10y.

Proof Statement 4

If -5x - 1 = -11, then -5x = -10.

Proof Statement 5

If 10a = 2b and 2b = c, then 10a = c.

Proof Statement 6

-7(n - 4) = -7n + 28.

Proof Statement 7

If 6y = 24, then 6y - 3 = 24 - 3.

Proof Statement 8

If 10x + w = 41 and w = 1, then 10x + 1 = 41.

Proof Statement 9

If 3x = 2y and 2y = z, then 3x = z.

Proof Statement 10

If 7m = 35, then 7m + 4 = 35 + 4.

Proof Statement 11

If -2c = 18, then 18 = -2c.

Proof Statement 12

Given 3x2 + 1, if x = 5, then 3(5)2 + 1.

Proof Statement 13

If m = -2, then 8m = -16.

Two-Column Proof

The ______________________ (or steps) are listed on the LEFT SIDE.

Reasons for Proof

What can be used as reasons? __________________, __________________, __________________, ___________________.