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Algebraic Properties of Equality

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Reflexive Property

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Every number is equal to itself.

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Symmetric Property

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If one number is equal to another, then those two numbers can be flipped and remain equal.

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Division Property of Equality

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If two numbers are equal, both sides of the equation can be divided by the same nonzero quantity and remain equal.

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Multiplication Property of Equality

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If two numbers are equal, both sides of the equation can be multiplied by the same quantity and remain equal.

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Transitive Property

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If one number equals a second, and the second equals a third, then the first equals the third.

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Subtraction Property of Equality

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If two numbers are equal, the same quantity can be subtracted from each without affecting the equality.

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Substitution Property

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A value may be substituted for its equal in any expression or equation.

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Addition Property of Equality

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If two numbers are equal, the same quantity can be added to each without affecting the equality.

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