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CHAPTER 2 SECTION 6

Algebraic Proofs. CHAPTER 2 SECTION 6. Jim Smith JCHS. Properties we’ll be needing. REFLEXIVE -- a = a SYMMETRIC -- if x = 2 then 2 = x TRANSITIVE -- if a = b and b = c then a = c

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CHAPTER 2 SECTION 6

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  1. Algebraic Proofs CHAPTER 2SECTION 6 Jim Smith JCHS

  2. Properties we’ll be needing REFLEXIVE-- a = a SYMMETRIC-- if x = 2 then 2 = x TRANSITIVE-- if a = b and b = c then a = c SUBSTITUTION-- If a = b then a may be used in any equationinstead of b

  3. DISTRIBUTIVE-- a(b+c) = ab+ac ADD and SUBTRACT-- if a = b then a+c = b+c and a-c = b-c MULT and DIVIDE-- if a = b then ac = bc and a / c = b / c

  4. 2 COLUMN PROOFS Statements Reasons

  5. In An Algebraic Proof, You Must Show All Steps Used To Solve The Equation. Each Individual Step You Use Is A Statement In The Proof. You Then Give Each Statement A Reason.

  6. Given: 2x+5 = 17 Prove x = 6 Statement Reason Start by stating the given. The reason will be GIVEN 1) Given 1) 2x + 5 = 17 2) Subtraction Property 2) 2x + 5 – 5 = 17 - 5 3) 2x = 12 3) Substitution 4) 2x / 2 = 12 / 2 4) Division Property 5) X = 6 5) Substitution

  7. Remember !! • The SHOW ME steps will be Add,Sub, Mult, or Div or Distributive Properties • The DO IT steps will be Substitution

  8. Statements Reasons Given: 3x + 7 Prove: x = 3 2 = 8 • 3x + 7 = 8 1) Given • 2 • 2) 2 3x + 7 = 2 ( 8 ) 2) Mult Prop • 2 • 3x + 7 = 16 3) Substitution • 3x + 7 – 7 = 16 – 7 4) Subtraction Prop • 3x = 9 5) Substitution • 3x = 9 6) Division • 3 3 • 7) X = 3 7) Substitution

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