# Reasoning with Properties from Algebra. Properties of Equality Addition (Subtraction) Property of Equality If a = b, then: a + c = b + c a – c = b – c.

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Reasoning with Properties from Algebra

Properties of Equality Addition (Subtraction) Property of Equality If a = b, then: a + c = b + c a – c = b – c If x + 8 = 20, Then x = 12 Why? Subtract Prop. of =

Properties of Equality Multiplication (Division) Property of Equality If a = b, then: ac = bc If 4x = 32, Then x = 8 Why? Division Prop. of =

Properties of Equality Reflexive Prop. of = a = a3 = 3 Why? Reflex Prop = Symmetric Prop. of = If a = b, then b = a. If 54 = x, then x=54 Why? Symm. Prop =

Properties of Equality Transitive Prop. of = If a = b and b = c, then a = c If 2x = y and y = 48, then 2x = 48 Why? Transitive Prop. Substitution Prop. of = If a = b, then a can replace b in an equation If 4x + 5 = 3y and x =-2, then 4(-2) + 5 = 3y Why? Substitution Prop.

Distributive Property a(b + c) = ab + ac. a(b – c) = ab – ac. -x(3x + 2) = 27 -3x 2 – 2x = 27 Why? Distributive Prop.

Solve: 5x – 18 = 3x + 2 and give a reason for each step. 5x – 18 = 3x + 2Given StepReason 2x – 18 = 2Subtraction POE 2x = 20Addition POE x = 10Division POE

Solve: 55z – 3(9z + 12) = -64 and give a reason for each step. 55z – 3(9z + 12) = -64Given StepReason 55z – 27z – 36 = -64Distributive Prop 28z – 36 = -64Simplify/Substitution 28z = -28Addition POE z = -1Division POE

What is the reason for each step in the solution? 2. 10 – 8n = –62. Multiplication POE 1. Given1. StepReason 3. – 8n = –163. Subtraction POE 4. n = 24. Division POE

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