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Reasoning with Properties from Algebra

Reasoning with Properties from Algebra. Properties 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 =. Addition (Subtraction) Property of Equality. Properties of Equality. If a = b, then: ac = bc. If 4x = 32, Then x = 8

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Reasoning with Properties from Algebra

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  1. Reasoning with Properties from Algebra

  2. Properties 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 = Addition (Subtraction) Property of Equality

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

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

  5. Properties of Equality If a = b and b = c, then a = c If 2x = y and y = 48, then 2x = 48 Why? Transitive Prop. Transitive Prop. of = 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.

  6. Distributive Property -x(3x + 2) = 27 -3x2 – 2x = 27 Why? Distributive Prop. a(b + c) = ab + ac. a(b – c) = ab – ac.

  7. 5x – 18 = 3x + 2 Given Step Reason Solve: 5x – 18 = 3x + 2and give a reason for each step. 2x – 18 = 2 Subtraction POE 2x = 20 Addition POE x = 10 Division POE

  8. 55z – 3(9z + 12) = -64 Given Step Reason Solve: 55z – 3(9z + 12) = -64and give a reason for each step. Not Multiplication Property!!! 55z – 27z – 36 = -64 Distributive Prop 28z – 36 = -64 Simplify 28z = -28 Addition POE z = -1 Division POE

  9. What is the reason for each step in the solution? Step Reason 1. 1. Given 2. 10 – 8n = –6 2. Multiplication POE 3. – 8n = –16 3. Subtraction POE 4. n = 2 4. Division POE

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