1. 2-6: Algebraic Proof

2. Properties Reflexive property – every # equals itself; a=a, 1=1, etc. Symmetric property – You can switch the sides of the equation. If a=b, then b=a. Transitive property – If a=b and b=c, then a=c. Addition property of equality – you can add to both sides. Subtraction property of equality – you can subtract from both sides.

3. More Properties Multiplication property of equality – you can multiply both sides. Division property of equality – you can divide both sides. Substitution property – If a=b, then you can substitute a for b. Distributive property – a(b+c)=ab+ac

4. Give a reason for each statement. 1. Nick is the same height as Jermaine, and Jermaine is the same height as Randy, so Nick is the same height as Randy. 2. 3(x+5)=3x+15 3. If m<1=m<2, then m<2=m<1. 4. If x+1=10, then x=9. 5. XY=XY

5. Algebraic Proof Given: 2x-4=10 Prove: x=7 StatementsReasons 1) 2x-4=101) 2)2) Addition property of equality 3) x=73)

6. Given: 8x-5=2x+1 Prove: x=1 StatementsReasons 1) 8x-5=2x+11) 2) 8x-5-2x=x+1-2x2) 3)3) Substitution 4) 6x=64) 5)

7. StatementsReasons 1) 2) 3) 4) 5) 6) 7) Given; XZ=ZY, XZ=4x+1, and ZY=6x-13. Prove: x=7

9. Assignment p. 97; 9, 14-25all