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Section 2-4 Reasoning with Properties from Algebra

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Properties of Equality

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Addition property Adding something to each side of an equation Given + 18 Therefore, the Addition Property of (=) was applied. Example:

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subtraction property Subtracting from each side of an equation Given Therefore, the Subtraction Property of (=) was applied. Example:

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Multiplication property Multiplying something to each side of an equation Example: Given 7 7 Therefore, the Multiplication Property of (=) was applied.

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division property Dividing something on each side of an equation Example: Given 22 Therefore, the Division Property of (=) was applied.

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Reflexive property Same exact thing on each side of the equal sign! Examples:

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Symmetric property The sides of an equation are switched. (Nothing else is done with the equation.) Examples:

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Transitive property * Relates to the Law of Syllogism!

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Examples:

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substitution property Plugging in something in place of another thing in any equation or expression. Example:

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Distributive property a(b+c) = ab +ac *Helps to get rid of parentheses Example: 4(x+y) Given = 4x + 4y Therefore, the Distribution Property was applied.

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Simplification To combine like terms Example: x= 3 + 5 Given = 8 Therefore, the Simplification was applied.

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