1-4 SOLVING EQUATIONSProperties of Equality

Reflexive Property of Equality Symmetric Property of Equality Transitive Property of Equality Substitution

PROPERTIES OF EQUALITY

Reflexive Property

• a + b = a + b

The same expression is written on both sides of the equal sign.

PROPERTIES OF EQUALITY

• If a = b then b = a

• If 4 + 5 = 9 then 9 = 4 + 5

Symmetric Property

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

ADDITIONAL PROPERTIES OF REAL NUMBERS

Substitution Property

• If a = b, then a can be replaced by b.

• a(3 + 2) = a(5)

NAME THE PROPERTY

• 5(4 + 6) = 20 + 30• 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) = 20 + 30 then 5(10) = 20 + 30

• Distributive• Substitution• Reflexive• Symmetric

• Commutative• Transitive

MORE PROPERTIES OF EQUALITYIF THE OPERATION DONE TO ONE SIDE IS ALSO DONE TO THE OTHER THEN

THE VALUE OF THE EQUATION DOES NOT CHANGE

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 = 12

+ 3 If x = 12,

then x – 3 = 12 – 3

If x = 12, then x ∙ 3 = 12 ∙

3 If x = 12,

then x / 3 = 12 / 3

Definition Examples

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 .

Solve . Check your solution.

Original equation

Add 5.48 to each side.

Simplify.

Check: Original equation

Answer: The solution is 5.5.

Simplify.

Substitute 5.5 for s.

Example 1

YOUR TURN What is the solution of 12b=18?

12b / 12 = 18 / 12 Divide each side by 12

b = 3 / 2 Simplify

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.

YOUR TURN What is the solution of -27 + 6y = 3(y – 3)?

-27 + 6y = 3(y – 3) -27 + 6y = 3y – 9 Distributive

Property 6y = 3y + 18 Add 27 to each side. 3y = 18 Subtract 3y from each

side y = 6 Divide each side by

3.

YOUR TURN What is the solution of 3( 2x – 1) – 2(3x +

4)=11x?

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

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

YOUR TURN

PROBLEM 4 PAGE 29

PROBLEM #5 PAGE 29

ANOTHER LITERAL EQUATION Distance = Rate x Time or d = r ∙ t

Solve for r

Solve for t