1. 1-4 Solving Equations Properties of Equality
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Substitution

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

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

4. 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

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

6. Distributive Substitution Reflexive Symmetric Commutative Transitive
Name the property
5(4 + 6) =
5(4 + 6) = 5(10)
5(4 + 6) = 5(4 + 6)
If 5(4 + 6) = 5(10) then 5(10) = 5(4 + 6)
5(4 + 6) = 5(6 + 4)
If 5(10) = 5(4 + 6) and 5(4 + 6) = then 5(10) =
Distributive
Substitution
Reflexive
Symmetric
Commutative
Transitive

7. More 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

8. Solve the Equation
Solving an equation that contains a variable means finding all the possible values that make the equation true. The first step is to isolate the variable to one side of the equation by using inverse operations.
Inverse operations undo operations.
Addition, subtraction are inverse operations as are multiplication, and division .

9. Example 1 Solve . Check your solution. Original equation
Add 5.48 to each side.
Simplify.
Check:
Original equation
Substitute 5.5 for s.
Simplify.
Answer: The solution is 5.5.
Example 3-4a

10. Your turn What is the solution of 12b=18?
12b / 12 = 18 / 12 Divide each side by 12
b = 3 / 2 Simplify

11. Distributive and Substitution Properties
Solve
Original equation
Distributive and Substitution Properties
Commutative, Distributive, and Substitution Properties
Addition and Substitution Properties
Division and Substitution Properties
Answer: The solution is –19.
Example 3-5a

12. Your turn What is the solution of -27 + 6y = 3(y – 3)?
y = 3y – 9 Distributive Property
6y = 3y Add 27 to each side.
3y = 18 Subtract 3y from each side
y = 6 Divide each side by 3.

13. 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

16. Your turn
Suppose the flower carpet from Problem 3 had a perimeter of 320 meters. What would the dimensions of the flower carpet be?

17. Problem 4 Page 29

18. Problem #5 Page 29

19. Another Literal Equation
Distance = Rate x Time or d = r ∙ t
Solve for r
Solve for t