Notes on 2-6

1. CHAPTER 2
SECTION 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 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. 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
Properties
• The 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
7) X = 3 7) Substitution
Given: 3x + 7 Prove: x = 3
2
= 8
Statements Reasons