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
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3(4y + 3) = 9
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12y + 9 = 9
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12y + 9 - 9 = 9 - 9
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12y + 0 = 0
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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)
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4y + 5 = 3(x + 1)
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4(4) + 5 = 3(x + 1)
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16 + 5 = 3(x + 1)
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21 = 3(x + 1)
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=
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7 = 1(x + 1)
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7 = x + 1
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7 - 1 = x + 1 - 1
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6 = x + 0
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6 = x
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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