Intro to Proofs - Properties of Equality

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What is the Addition Property of Equality?

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The Addition Property of Equality states that if you add the same number to both sides of an equation, the two sides remain equal.

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What is the Division Property of Equality?

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The Division Property of Equality states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.

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What is the Substitution Property?

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The Substitution Property states that if two values are equal, one can be substituted for the other in any expression.

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What is the Reflexive Property?

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The Reflexive Property states that any quantity is equal to itself, expressed as a = a.

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What is the Subtraction Property of Equality?

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The Subtraction Property of Equality states that if you subtract the same number from both sides of an equation, the two sides remain equal.

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How does the Addition Property of Equality apply in solving equations?

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It allows you to isolate a variable by adding the same value to both sides of the equation.

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Can you give an example of the Division Property of Equality?

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If 4x = 20, then by applying the Division Property, x = 20/4, which simplifies to x = 5.

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What is an example of the Substitution Property in use?

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If x = 2 and you have the expression 3x + 1, you can substitute 2 for x to get 3(2) + 1 = 7.

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What is the significance of the Reflexive Property in proofs?

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It is often used to establish equality in geometric proofs and algebraic manipulations.

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How can the Subtraction Property of Equality be used in problem-solving?

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It can be used to eliminate terms from one side of an equation to isolate the variable.