Transcript Answer

Lesson 9-1 Properties
Lesson 9-2 Solving Addition Equations
Lesson 9-3 Solving Subtraction Equations
Lesson 9-4 Solving Multiplication Equations
Lesson 9-5 Solving Two-Step Equations
Lesson 9-6 Functions
Lesson 9-7 Graphing Functions
Example 1 Use the Distributive Property
Example 2 Apply the Distributive Property
Example 3 Identify Properties
Example 4 Identify Properties
Example 5 Apply Properties
Find
mentally using the Distributive Property.
Write 43 as
Distributive Property
Multiply 6 and 40 mentally.
Add 240 and 18 mentally.
Answer: 258
Find
mentally using the Distributive Property.
Answer: 231
THEME PARKS Suppose admission to a theme park
costs $35 per person and meals cost $20 per person.
What is the cost for a family of 5 people?
Method 1 Find the cost of 5 admissions and 5 meals.
Then add.
cost of 5 admissions
Method 2
cost of 5 meals
Find the cost for 1 person. Then multiply by 5.
cost for 1 person
Evaluate either expression.
Distributive Property
Multiply.
Add.
Answer: The total cost is $275.
BOWLING Suppose the cost of bowling three games at
a local bowling alley is $6.50 and the cost of shoe rental
is $1.50. What is the cost for a group of 6 friends to
each rent a pair of shoes and bowl three games?
Answer: $48
Identify the property shown by the equation
The order in which the numbers are added changes.
Answer: This is the Commutative Property of Addition.
Identify the property shown by the equation
Answer: Commutative Property of Multiplication
Identify the property shown by the equation
The grouping of the numbers to be multiplied changes.
Answer: This is the Associative Property of Multiplication.
Identify the property shown by the equation
Answer: Associative Property of Addition
Find
mentally.
Since you can easily multiply 2 and 4, change the order.
Commutative Property
Now group the numbers. The parentheses tell you which to
perform first.
Associative Property
Multiply 2 and 4 mentally.
Multiply 8 and 12 mentally.
Answer: 96
Find
Answer: 117
mentally.
Example 1 Solve an Equation by Subtracting
Example 2 Solve an Equation Using Zero Pairs
Method 1
Use models.
Method 2
Use symbols.
Write the equation.
Subtract 4 from each
side to “undo” the
addition of 4 on the left.
Answer: The solution is 1.
Answer:
Check your solution.
Method 1
Use models.
Method 2
Use symbols.
Write the equation.
Subtract 11 from each
side to undo x plus 11.
Subtract 11 from each side.
Check
Write the equation.
Replace x with –4.
This sentence is true.
Answer: The solution is –4.
Answer: –6
Example 1 Solve an Equation by Adding
Example 2 Solve a Subtraction Equation
Example 3 Use an Equation to Solve a Problem
Method 1
Use models.
Method 2
Use symbols.
Write the equation.
Add 5 to each side to undo the
subtraction of 5 on the left.
Add 5 to each side.
Simplify.
Answer: The solution is 15.
Answer: 12
Check your solution.
Write the equation.
Add 5 to each side.
Simplify.
Check
Write the original equation.
Replace x with 4.
This sentence is true.
Answer: The solution is 4.
Check your solution.
Answer: 3
GRID-IN TEST ITEM The difference between the record
high and the record low temperatures in Oregon is
173F. The record low temperature is –54F. What is the
record high temperature in degrees Fahrenheit?
Read the Test Item
You need to find the record high temperature. Write and
solve an equation. Let x represent the high temperature.
Solve the Test Item
Write the equation.
Definition of subtraction
Subtract 54 from each side.
Simplify.
The record high temperature is 119F.
Answer:
GRID-IN TEST ITEM The difference between the age
of Julie’s mother and Julie’s age is 27 years. Julie’s
age is 6. What is the age of Julie’s mother?
Answer:
Example 1 Solve a Multiplication Equation
Example 2 Solve a Multiplication Equation
Example 3 Use an Equation to Solve a Problem
Check your solution.
Check
Write the original equation.
Replace x with 3.
This sentence is true.
Answer: The solution is 3.
Check your solution.
Answer: 5
Write the equation.
Divide each side by –5.
Answer: The solution is –3. Check this solution.
Answer: –7
GEOMETRY The area of a rectangle is 144 square
inches and the width is 4 inches. Write an equation to
find the length of the rectangle and use it to solve the
problem.
The area of a rectangle is equal to its length times its width.
144
Write the equation.
Divide each side by 4.
Simplify.
Check
Answer: The length of the rectangle is 36 inches.
GEOMETRY The area of a rectangle is 126 square feet
and the width is 7 feet. Write an equation to find the
length of the rectangle and use it to solve the problem.
Answer: 18 feet
Example 1 Solve a Two-Step Equation
Example 2 Solve a Two-Step Equation
Example 3 Use an Equation to Solve a Problem
Answer: The solution is –3.
Answer: 2
Check your solution.
Write the equation.
Add 2 to each side.
Simplify.
Divide each side by 4.
Simplify.
Answer: The solution is 2. Check this solution.
Answer: 4
MOVIE NIGHT Three friends went to the movies. The
tickets cost $6 each. They bought 2 large popcorns to
share. If they spent a total of $24 at the movies, how
much did a large popcorn cost?
Words
The cost of 2 large popcorns plus 3 tickets is $24.
Variable
Equation
Two popcorns at $p each plus tickets costs $24
2p
Write the equation.
Subtract 18 from each side.
Simplify.
Divide each side by 2.
Simplify.
Answer: A large popcorn cost $3. Is this answer
reasonable?
SHOPPING Jen went to her favorite store at the mall.
She bought 3 t-shirts which cost $12 each. She also
bought 2 pairs of the same jeans. If Jen spent a total of
$80 at the store, how much did each pair of jeans cost?
Answer: $22
Example 1 Complete a Function Table
Example 2 Find a the Rule for a Function Table
Example 3 Solving a Problem Using a Function
Complete the function table.
The function rule is 3n. Multiply each input by 3.
Answer:
Input
–1
Output
–3
0
0
1
3
Input
(n)
–1
0
1
Output
(3n)
–3
0
1
Complete the function table.
Answer:
Input Output
1
3
2
4
3
5
Find the rule for the function table.
Study the relationship between each input and output.
Input
10
8
5
Output
7
5
2
Input Output
10
7
8
5
5
2
The output is three less than the input.
Answer: So, the function rule is n – 3.
Find the rule for the function table.
Input Output
Answer:
11
4
10
3
9
2
COFFEE Nina buys a refillable mug for $4.50 on her
first day at a new job. Starting with her second day, she
gets a refill of coffee costing $2.00 every day on the
way to work. How much does she spend on coffee in
her first 8 workdays?
First, determine the function rule.
The function rule is
Then, replace d in the rule
workdays after Nina’s first day, 7.
with the number of
Replace d with 7.
Multiply 2 and 7.
Add 14 and 4.50.
Answer: Nina spends $18.50 on coffee in her first 8
workdays.
MOVIE RENTAL A video store offers a deal where the
first movie rented costs $5.25 and each movie rented
after the first costs $2.50. Find the total cost to rent 6
movies.
Answer: $17.75
Example 1 Graph a Function
Example 2 Make a Function Table for a Graph
Make a function table for the rule
Use input
values of –4, 0, and 4. Then graph the function.
Step 1
Record the input and output in a function table.
List the input and output as ordered pairs.
Input
Output
Ordered
Pairs
(y)
(x, y)
–4
–2
(–4, –2)
0
2
(0, 2)
4
6
(4, 6)
(x)
Function Rule
(
)
Step 2
Graph the ordered pairs on the coordinate plane.
Step 3
The points appear to lie on a line. Draw the line
that contains these points. The line is the graph
of
For any point on this line
Answer:
Make a function table for the rule
Use input
values of –2, 1, and 5. Then graph the function.
Answer:
Input
Function Rule
Output
Ordered
Pairs
(x)
(x – 3)
(y)
(x, y)
–2
–2 – 3
–5
(–2, –5)
1
1–3
–2
(1, –2)
5
5–3
2
(5, 2)
Answer:
Make a function table for the graph. Then determine
the function rule.
Use the ordered pairs to make a function table.
Input (x)
–4
–2
0
2
Output (y)
8
4
0
–4
(x, y)
(–4, 8)
(–2, 4)
(0, 0)
(2, –4)
Input
Output
–4
8
–2
4
0
0
2
–4
Study the input and output. Look for a rule.
Each input is multiplied by –2 to get the output.
Answer: The function rule is
Make a function table for the graph. Then determine
the function rule.
Answer: