1. CHAPTER 2 SECTION 6 Jim Smith JCHS

2. Properties we’ll be needing REFLEXIVE -- a = aREFLEXIVE -- a = a SYMMETRIC -- if x = 2 then 2 = xSYMMETRIC -- if x = 2 then 2 = x TRANSITIVE -- if a = b and b = c then a = cTRANSITIVE -- if a = b and b = c then a = c SUBSTITUTION -- If a = b then a may be used in any equation instead of bSUBSTITUTION -- If a = b then a may be used in any equation instead of b

3. DISTRIBUTIVE -- a(b+c) = ab+acDISTRIBUTIVE -- a(b+c) = ab+ac ADD and SUBTRACT -- if a = b then a+c = b+c and a-c = b-cADD 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 / cMULT 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. 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 Given: 2x+5 = 17 Prove x = 6 Statement Reason 1) 2x + 5 = 17 1) Given 2) 2x + 5 – 5 = 17 - 5 2) Subtraction Property 3) 2x = 12 3) Substitution 4) 2x / 2 = 12 / 2 4) Division Property 5) X = 6 5) Substitution Start by stating the given. The reason will be GIVEN

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

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