**Problem : ** Name the property shown:*x* = 12 and 12 = *y*. Thus, *x* = *y*

**Problem : ** Name the property shown:

4(2*x*) = 8*x*

**Problem : ** What number, when multiplied by 3, is equal to 1?

**Problem : ** What number, when multiplied by , is equal to 1?

**Problem : ** Name the property or operation used in each step:

Solve for *x*: - 16 = - 4

- - 16 = - 4
- - 16 + 16 = - 4 + 16
- + 0 = 12
- = 12
- 12() = 12(12)
- 1
*x*= 144 *x*= 144

- Given
- Addition Property of Equality
- Addition
- Additive Identity Property
- Multiplication Property of Equality
- Multiplication
- Multiplicative Identity Property

**Problem : ** Name the property or operation used in each step:

Solve for *y*: 3(4*y* + 3) = 9

- 3(4
*y*+ 3) = 9 - 12
*y*+ 9 = 9 - 12
*y*+ 9 - 9 = 9 - 9 - 12
*y*+ 0 = 0 - 12
*y*= 0 - 12 = 0
*ory*= 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: 4*y* + 5 = 3(*x* + 1)

- 4
*y*+ 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

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