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SECTION 2-6

SECTION 2-6. Algebraic Proofs. 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 SUBSTITUTION -- If a=b then a may be used in any equation instead of b. DISTRIBUTIVE -- a(b+c) = ab+ac

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SECTION 2-6

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  1. SECTION2-6 Algebraic Proofs 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 equation instead 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. SHOW ME - THEN DO IT • WHEN WE ADD, SUBTRACT, MULT, OR DIV BOTH SIDES OF THE EQUATION, SHOW ME WHAT YOU ARE GOING TO DO FIRST • THE NEXT STEP IS THE DO IT STEP

  7. Given: 2x+5=17Prove x=6 Start by stating the given. The reason will be GIVEN Statement Reason 1) Given 1) 2x + 5 = 17

  8. Given: 2x+5=17Prove x=6 Statement Reason 1) Given 1) 2x + 5 = 17 2) Subtraction Property 2) 2x + 5 – 5 = 17 - 5

  9. Given: 2x+5=17Prove x=6 Statement Reason 1) Given 1) 2x + 5 = 17 2) Subtraction Property 2) 2x + 5 – 5 = 17 - 5 3) Substitution 3) 2x = 12

  10. Given: 2x+5=17Prove x=6 Statement Reason 1) Given 1) 2x + 5 = 17 2) Subtraction Property 2) 2x + 5 – 5 = 17 - 5 3) Substitution 3) 2x = 12 4) 2x / 2 = 12 / 2 4) Division Property

  11. Given: 2x+5=17Prove x=6 Statement Reason 1) Given 1) 2x + 5 = 17 2) Subtraction Property 2) 2x + 5 – 5 = 17 - 5 3) Substitution 3) 2x = 12 4) 2x / 2 = 12 / 2 4) Division Property 5) X = 6 5) Substitution

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

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