Unit 3 Using Properties of Algebra

1. Unit 3 Using Properties of Algebra

2. If a = b, then a + c = b + c If a = b, then a – c = b – c If a = b, then ac = bc If a = b, then a/c = b/c If a(x + b), then ax + ab If a = b, then b can be substituted in for a

3. a = a If a = b, then b = a If a = b and b = c, then a = c Reflexive Repeats Symmetric Switches

4. 1. Use the property to complete the statement. a. Multiplication Property of Equality: If m1 = m2, then 3m1 = ____________. b. Substitution Property of Equality: If a = 20, then 5a = __________. 3m2 5(20) = 100

5. Distributive Prop 9 + 2 = 9 + 2 Reflexive Prop Subtraction Prop If 4x + 7 = 11, then 4x = 4. If 4x = 4, then x = 1. Transitive Prop Addition Prop 4 + 5 = 5 + 4 Symmetric Prop Division Prop

6. PROOFS! All proofs start and end the same. It is very helpful to have a picture to refer to. We are given information and then are told to prove something.

7. Format of Proofs Picture Given: Prove: Statements Reasons 1. 2. 3. … What you are given 1. 2. 3. … Given To Prove

8. Complete the logical argument by writing a reason for each step. given Addition Prop Division Prop

9. Complete the logical argument by writing a reason for each step. given Subtraction Prop Addition Prop Division Prop

10. Complete the logical argument by writing a reason for each step. given Distributive Prop Combine Like Terms Subtraction Prop Addition Prop

11. 4. Solve the equation. Write a reason for each step 4x – 9 = 2x + 11 1. 1. Given 4x – 9 = 2x + 11 2. 2. Subtraction Prop. 2x – 9 = 11 3. 2x= 20 3. Addition Prop. 4. x = 10 4. Division Prop.

12. 5. Solve the equation for y. Write a reason for each step. 12x – 3y = 30 1. 12x – 3y = 30 1. Given 2. –3y = -12x + 30 2. Subtraction Prop. 3. y = 4x – 10 3. Division Prop.

13. HW Problem # 17 1. 12 – 3y = 30x 1. Given 2. –3y = 30x – 12 2. Subtraction Prop. 3. y = –10x + 4 3. Division Prop.