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Reasoning with Properties from Algebra

Explore how to apply algebraic properties in equations, such as the properties of equality and substitution, to solve mathematical problems with clear reasoning steps. Understand the significance of properties like division and distribution in solving equations effectively.

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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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