Problem : Name the property shown:
x = 12 and 12 = y. Thus, x = y
Transitive Property of Equality
Problem : Name the property shown:
4(2x) = 8x
Associative Property of Multiplication
Problem : What number, when multiplied by 3, is equal to 1?
(the reciprocal of 3)
Problem : Name the property or operation used in each step:
Solve for y: 3(4y + 3) = 9

3(4y + 3) = 9

12y + 9 = 9

12y + 9  9 = 9  9

12y + 0 = 0

12y = 0

12 = 0ory = 0
 Since 12âÉ 0, y = 0
 Given
 Distributive Property of Multiplication over Addition
 Subtraction Property of Equality
 Subtraction
 Additive Identity Property
 Zero Product Property
 (inference)
Problem : Name the property or operation used in each step:
Solve for x if y = 4: 4y + 5 = 3(x + 1)

4y + 5 = 3(x + 1)

4(4) + 5 = 3(x + 1)

16 + 5 = 3(x + 1)

21 = 3(x + 1)

=

7 = 1(x + 1)

7 = x + 1

7  1 = x + 1  1

6 = x + 0

6 = x

x = 6
 Given
 Substitution Property
 Multiplication
 Addition
 Division Property of Equality
 Division
 Multiplicative Identity Property
 Subtraction Property of Equality
 Subtraction
 Additive Identity Property
 Symmetric Property of Equality