Unit 3 Using Properties of Algebra Name Addition

Unit 3 Using Properties of Algebra

Name Addition Property of Equality If a = b, then a + c = b + c Subtraction Property If a = b, then a – c = b – c Multiplication Property Division Property If a = b, then ac = bc Distribution Property Substitution Property 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

Reflexive Property a=a Symmetric Property If a = b, then b = a Transitive Property If a = b and b = c, then a = c Reflexive Repeats Symmetric Switches

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

Statement If 4(x + 7), then 4 x + 28 9+2=9+2 If 2 x + 5 = 9, then 2 x = 4 Reason Distributive Prop Reflexive Prop Subtraction Prop If 4 x + 7 = 11, then 4 x = 4. If 4 x = 4, then x = 1. Transitive Prop If x – 7 = 2, then x = 9 Addition Prop 4+5=5+4 If 4 x = 12, then x = 3 Symmetric Prop Division Prop

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.

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

Complete the logical argument by writing a reason for each step. Statements 1. 8 x – 34 = 6 Reasons 1. given _________ 2. 8 x = 40 2. Addition Prop _________ 3. x=5 3. Division Prop _________

Complete the logical argument by writing a reason for each step. Statements Reasons 1. 4 x – 7 = 6 x + 7 1. given _________ 2. -2 x – 7 = 7 2. _________ Subtraction Prop 3. -2 x = 14 3. Addition Prop _________ 4. x = -7 4. Division Prop _________

Complete the logical argument by writing a reason for each step. Statements Reasons 1. 5(x – 3) + 1 = 4(x + 2) 1. given ____________ 2. 5 x – 15 + 1 = 4 x + 8 2. Distributive Prop ____________ 3. 5 x – 14 = 4 x + 8 3. Combine Like Terms ____________ 4. Subtraction Prop ____________ 5. Addition Prop ____________ 4. 5. x – 14 = 8 x = 22

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

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

HW Problem LT 3. 3 Page # Assignment Due 108 -111 3 -5, 7, 9, 17, 21 -26, 41, 42 # 17 Statements Reasons 1. 12 – 3 y = 30 x 1. Given 2. – 3 y = 30 x – 12 2. Subtraction Prop. 3. y = – 10 x + 4 3. Division Prop.