# Expressions and Equations

## Problems 5

Summary Problems 5

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 : What number, when multiplied by , is equal to 1? (the reciprocal of )

Problem : Name the property or operation used in each step:
Solve for x: - 16 = - 4

1. - 16 = - 4
2. - 16 + 16 = - 4 + 16
3. + 0 = 12
4. = 12
5. 12( ) = 12(12)
6. 1x = 144
7. x = 144

1. Given
5. Multiplication Property of Equality
6. Multiplication
7. Multiplicative Identity Property

Problem : Name the property or operation used in each step:
Solve for y: 3(4y + 3) = 9

1. 3(4y + 3) = 9
2. 12y + 9 = 9
3. 12y + 9 - 9 = 9 - 9
4. 12y + 0 = 0
5. 12y = 0
6. 12 = 0ory = 0
7. Since 12âÉ  0, y = 0

1. Given
2. Distributive Property of Multiplication over Addition
3. Subtraction Property of Equality
4. Subtraction
6. Zero Product Property
7. (inference)

Problem : Name the property or operation used in each step:
Solve for x if y = 4: 4y + 5 = 3(x + 1)

1. 4y + 5 = 3(x + 1)
2. 4(4) + 5 = 3(x + 1)
3. 16 + 5 = 3(x + 1)
4. 21 = 3(x + 1)
5. = 6. 7 = 1(x + 1)
7. 7 = x + 1
8. 7 - 1 = x + 1 - 1
9. 6 = x + 0
10. 6 = x
11. x = 6

1. Given
2. Substitution Property
3. Multiplication