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2.5 – Reasoning Using Properties of Algebra Name Addition Property 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: 3m2 If m1 = m2, then 3m1 = ____________. b. Substitution Property of Equality: 5(20) = 100 If a = 20, then 5a = __________. Statement If 4(x + 7), then 4x + 28 9+2=9+2 If 2x + 5 = 9, then 2x = 4 Reason Distributive Prop Reflexive Prop Subtraction Prop If 4x + 7 = 11, then 4x = 4. If 4x = 4, then x = 1. Transitive Prop If x – 7 = 2, then x = 9 Addition Prop 4+5=5+4 If 4x = 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. 8x – 34 = 6 Reasons 1. given __________________ 2. 8x = 40 2. Addition Prop __________________ 3. x=5 3. Division Prop __________________ Complete the logical argument by writing a reason for each step. Statements Reasons 1. 4x – 7 = 6x + 7 1. given __________________ 2. -2x – 7 = 7 2. __________________ Subtraction Prop 3. -2x = 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. 5x – 15 + 1 = 4x + 8 2. Distributive Prop _______________________ 3. 5x – 14 = 4x + 8 4. 5. x – 14 = 8 x = 22 Combine Like Terms 3. _______________________ 4. Addition Prop _______________________ 5. Addition Prop _______________________ 4. Solve the equation. Write a reason for each step 4x – 9 = 2x + 11 Statements 1. 4x – 9 = 2x + 11 Reasons 1. Given 2. 2x – 9 = 11 2. Subtraction Prop. 3. 2x = 20 3. Addition Prop. 4. x = 10 4. Division Prop. 5. Solve the equation for y. Write a reason for each step. 12x – 3y = 30 Statements Reasons 1. 12x – 3y = 30 1. Given 2. –3y = -12x + 30 2. Subtraction Prop. 3. y = 4x – 10 3. Division Prop. HW Problem Section 2.5 Page # 108-111 Assignment Spiral ?s 3-5, 7, 9, 17, 21-26, 41, 42 12-17 # 17 Statements 1. 12 – 3y = 30x 2. –3y = 30x – 12 3. y = –10x + 4 Reasons 1. Given 2. Subtraction Prop. 3. Division Prop.