CHAPTER 2CHAPTER 2SECTION 6SECTION 6

Jim Smith JCHS

Properties we’ll be needingProperties we’ll be needing• REFLEXIVEREFLEXIVE -- -- a = aa = a

• SYMMETRICSYMMETRIC -- -- if x = 2 then 2 =if x = 2 then 2 = x x

• TRANSITIVETRANSITIVE -- -- if a = b and b = c if a = b and b = c then a = c then a = c

• SUBSTITUTIONSUBSTITUTION -- -- If a = b then a If a = b then a may may be used in any equationbe used in any equation instead of binstead of b

• DISTRIBUTIVEDISTRIBUTIVE -- a(b+c) = ab+ac-- a(b+c) = ab+ac

• ADD and SUBTRACTADD and SUBTRACT -- if a = b -- if a = b then a+c = b+c and a-c = b-cthen a+c = b+c and a-c = b-c

• MULT and DIVIDEMULT and DIVIDE -- if a = b -- if a = b then then ac = bc and a / c = b / cac = bc and a / c = b / c

2 COLUMN PROOFS2 COLUMN PROOFS

Statements ReasonsStatements Reasons

In An Algebraic Proof, You Must In An Algebraic Proof, You Must Show All Steps Used To Solve Show All Steps Used To Solve The Equation. Each Individual The Equation. Each Individual

Step You Use Is A Statement In Step You Use Is A Statement In The Proof. You Then Give Each The Proof. You Then Give Each

Statement A Reason.Statement A Reason.

Given: 2x+5 = 17 Prove x = 6 Given: 2x+5 = 17 Prove x = 6

Statement ReasonStatement Reason

1) 2x + 5 = 171) 2x + 5 = 17 1) Given1) Given

2) 2x + 5 – 5 = 17 - 52) 2x + 5 – 5 = 17 - 5 2) Subtraction Property2) Subtraction Property

3) 2x = 123) 2x = 12 3) Substitution3) Substitution4) 2x / 2 = 12 / 24) 2x / 2 = 12 / 2 4) Division Property4) Division Property

5) X = 65) X = 6 5) Substitution5) Substitution

Start by stating the given. The reason Start by stating the given. The reason

will be GIVENwill be GIVEN

Remember !!Remember !!• The The SHOW MESHOW ME steps will be steps will be Add,Add,

Sub, Mult, or Div or DistributiveSub, Mult, or Div or Distributive PropertiesProperties

• The The DO IT DO IT steps will be steps will be SubstitutionSubstitution

1)1) 3x + 73x + 7 = 8 1) Given = 8 1) Given 222) 2 2) 2 3x + 73x + 7 = 2 ( 8 ) 2) Mult Prop = 2 ( 8 ) 2) Mult Prop 223)3) 3x + 7 = 163x + 7 = 16 3) Substitution 3) Substitution4)4) 3x + 7 – 7 = 16 – 7 4) Subtraction Prop3x + 7 – 7 = 16 – 7 4) Subtraction Prop5)5) 3x = 9 5) Substitution3x = 9 5) Substitution6)6) 3x 3x = = 9 9 6) Division 6) Division 3 33 37) X = 3 7) Substitution7) X = 3 7) Substitution

GivenGiven: : 3x + 73x + 7 Prove: x = 3 Prove: x = 3 22

= = 88Statements ReasonsStatements Reasons