2.3 Diagrams and 2.4 Algebraic Reasoning

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• P. 88, 23

Justify each step. What type of reasoning is this?

4 (6 ) 2(2 10)x x x

Addition Property of Equality.If a = b, then a + c = b + c

Subtraction Property of Equality.If a = b, then a – c = b – c

Multiplication Property of Equality. If a = b, then ac = bc

Division Property of Equality. If a = b, then a/c = b/c

Substitution Property of Equality. If a = b, then a can be substituted for b in any eq.

3( 7) 3 9 12x x x

Distributive Propertya(b + c) = ab + ac a(b – c) = ab – ac

Reflexive Propertya = a

Symmetric PropertyIf a = b, then b = a

Transitive PropertyIf a = b and b = c, then a = c.