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Algebraic Proofs: Properties and Column Proofs Explained

Learn algebraic proof techniques including reflexive, symmetric, and transitive properties with examples of column proofs. Master solving equations step by step using properties. Show each step followed by the reason for it.

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Algebraic Proofs: Properties and Column Proofs Explained

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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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