1-4 The Distributive Property1-5 Equations

CCSS: A.SSE.1a, A.SSE.2, A.CED.1

Example 1: Evaluate ExpressionsJohn burns approximately 420 calories per

hour by inline skating. The chart below shows the time he spent inline skating in one week.

Day Mon Tue Wed Thu Fri Sat Sun

Time (h)

1 ½ 0 1 0 2 2 ½

Determine the number of calories burned for the week

Example 2: Real World

A group of 7 adults and 6 children are going to a University of South Florida Bulls baseball game. Use the Distributive Property to write and evaluate an expression for the total ticket cost

Ticket Cost ($)

Adult Single Game

5

Children Single Game (12 and

under)

3

Groups of 10 or more Single

Game

2

Senior single game (65 and

over)

3

Example 3: Algebraic Expressions

2

7(3 5)

(6 3)4

(8 4 )2

6( 3 )

(3 5 )( 3)

4( 8 3 )

w

v v

n

r g t

q

m

Vocabulary

Use your textbook to define the following terms: Like Terms Simplest Form Coefficient

Like Terms- terms that contain the same variables, with corresponding variables having the same power

Simplest Form- contains no like terms or parentheses

Coefficient- the numerical factor

Example 4: Combine Like Terms

2

Simplify 17 25

Simplify 6 3

Simplify 6 4

u u

t t t

n n

2

3

2

Simplify 13 13

Simplify 4 2 8 5

Simplify 7 4 6 2

b b

y y y

a a a

Example 5: Write and Simplify Expressions

Use the expression twice the difference of 3x and y increased by five times the sum of x and 2y

a. Write an algebraic expression for the verbal expression

b. Simplify the expression and indicate the properties used

Use the expression five times the difference of q squared and r plus eight times the sum of 3q and 2r

a. Write an algebraic expression for the verbal expression

b. Simplify the expression and indicate the properties used

Example 6: Common Core

The red cross is holding blood drives in two locations. In one day, Center 1 collected 715 pints and Center 2 collected 1035 pints. Write and evaluate an expression to estimate the total number of pints of blood donated over a 3 day period.

Example 7: Common Core

2Use the distributive property to simplify 6 [(3 4) (4 2)]x x x

Vocabulary

Open SentenceEquationSolvingSolutionReplacement SetSetElementSolution SetIdentity

Open Sentence- a mathematical statement that contains algebraic expressions and symbols

Equation- a sentence that contains an equals signSolving- finding a value for a variable that makes a sentence trueSolution- replacement valueReplacement Set- a set of numbers from which replacements for

a variable may be chosenSet- collection of objects or numbers, shown using bracesElement- each object or number in the setSolution Set- set of elements from the replacement setIdentity- an equation that is true for every value of the variable

Example 8

Find the solution set of the equation 2 15 13

if the replacement set is 2,3,4,5,6

q

Find the solution set of the equation if the replacement set is 0,1,2,3

8 7 17

28 4(1 3 )

m

d

Example 9: Solutions of Equations

27 (4 10) 10n

(3 2) 6 5 (10 3)n n

Example 10: Identities

Solve (2 5 8)(3 6) [(2 ) 6]2h h h

2Solve 12(10-7)+9g=g(2 5) 36

3Solve 2 (2 5) 10(5 2) (12 6)d d

Example 11: Common Core

The perimeter of a regular octagon is 128 inches. Find the length of each side

Example 12: Common Core

Blood flow rate can be expressed as

Where F is the flow rate, p1 and p2 are the initial and final pressure exerted against the blood vessel’s walls, respectively, and r is the resistance created by the size of the vessel.

a. Write and solve an equation to determine the resistance of the blood vessel for an initial pressure of 100 millimeters of mercury, a final pressure of 0 millimeters of mercury, and a flow rate of 5 liters per minute

1 2p pF

r

c. Use the equation to complete the table belowInitial Pressure

Final Pressure

Resistance Blood Flow Rate

100 0 5

100 0 30

5 40 4

90 10 6