1. Standard:
MCC9-12.A.REI.1 – Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

2. Properties of Equality
Vocabulary:
Properties of Equality
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Substitution
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality

3. Properties of Equality
Reflexive Property
a + b = a + b
The same expression is written on both sides of the equal sign.

4. Properties of Equality
Symmetric Property
If a = b then b = a
If = 9 then 9 = 4 + 5

5. Properties of Equality
Transitive Property
If a = b and b = c then a = c
If 3(3) = 9 and 9 = 4 +5, then 3(3) = 4 + 5

6. Properties of Equality If the operation done to one side is also done to the other then the value of the equation does not change
Definition
Examples
Addition: If a=b, then
a + c = b + c
Subtraction: If a=b, then a – c = b – c Multiplication: If a=b, then a ∙ c = b ∙ c
Division: If a = b, then
a / c = b / c (c≠0)
If x = 12,
then x + 3 =
then x – 3 = 12 – 3
then x ∙ 3 = 12 ∙ 3
If x = 12,
then x / 3 = 12 / 3

7. Additional Properties of Real Numbers
Substitution Property
If a = b, then a can be replaced by b.
a(3 + 2) = a(5)

8. Additional Properties of Real Numbers
Distributive Property
If a ( b + c ) = ab + ac
2(3 + 2) = 6 + 4

9. y=-19 Solve Prove: y=-19 Reason Statement Given
Distributive Properties
Combine Like terms
Addition Properties
Division Properties
y=-19
Symmetric Property
Example 3-5a

10. Your turn What is the solution of -27 + 6y = 3(y – 3)?
Statement Reason
y = 3(y – 3) Given
y = 3y – 9 Distributive Property
-27+3y = Subtraction Property
3y=18 Addition Property
y = Division Property

11. Your turn What is the solution of 3( 2x – 1) – 2(3x + 4)=11x?
6x – 3 – 6x – 8 = 11x Distributive Property
– 11 = 11x Combine Like Terms
– 1 = x Divide each side by – 11
x = – 1 Symmetric Property