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Contents Lesson 9-1Properties Lesson 9-2Solving Addition Equations Lesson 9-3Solving Subtraction Equations Lesson 9-4Solving Multiplication Equations Lesson 9-5Solving Two-Step Equations Lesson 9-6Functions Lesson 9-7Graphing Functions

Lesson 1 Contents Example 1Use the Distributive Property Example 2Apply the Distributive Property Example 3Identify Properties Example 4Identify Properties Example 5Apply Properties

Example 1-1a Find mentally using the Distributive Property. Write 43 as Distributive Property Multiply 6 and 40 mentally. Add 240 and 18 mentally. Answer: 258

Example 1-1b Find mentally using the Distributive Property. Answer: 231

Example 1-2a 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 cost of 5 meals Method 2 Find the cost for 1 person. Then multiply by 5. cost for 1 person

Example 1-2b Evaluate either expression. Answer: The total cost is $275. Distributive Property Multiply. Add.

Example 1-2c 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

Example 1-3a Answer: This is the Commutative Property of Addition. The order in which the numbers are added changes. Identify the property shown by the equation

Example 1-3b Answer: Commutative Property of Multiplication Identify the property shown by the equation

Example 1-4a Answer: This is the Associative Property of Multiplication. The grouping of the numbers to be multiplied changes. Identify the property shown by the equation

Example 1-4b Answer: Associative Property of Addition Identify the property shown by the equation

Example 1-5a 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

Example 1-5b Find mentally. Answer: 117

Lesson 2 Contents Example 1Solve an Equation by Subtracting Example 2Solve an Equation Using Zero Pairs

Example 2-1a Method 1Use models.

Example 2-1b Method 2 Use symbols. Write the equation. Answer: The solution is 1. Subtract 4 from each side to “undo” the addition of 4 on the left.

Example 2-1c Answer:

Example 2-2a Method 1Use models. Check your solution.

Example 2-2b

Method 2 Use symbols. Write the equation. Subtract 11 from each side to undo x plus 11. Check Write the equation. Replace x with –4. This sentence is true. Answer: The solution is –4. Subtract 11 from each side.

Example 2-2c Answer: –6

Lesson 3 Contents Example 1Solve an Equation by Adding Example 2Solve a Subtraction Equation Example 3Use an Equation to Solve a Problem

Example 3-1a Method 1Use models.

Example 3-1b Method 2 Use symbols. Write the equation. Add 5 to each side. Simplify. Add 5 to each side to undo the subtraction of 5 on the left. Answer: The solution is 15.

Example 3-1c Answer: 12

Example 3-2a Check your solution. Write the equation. Add 5 to each side. Simplify. Answer: The solution is 4. Check Write the original equation. Replace x with 4. This sentence is true.

Example 3-2b Check your solution. Answer: 3

Example 3-3a 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 The record high temperature is 119  F. Write the equation. Definition of subtraction Subtract 54 from each side. Simplify. Solve the Test Item You need to find the record high temperature. Write and solve an equation. Let x represent the high temperature.

Example 3-3b Answer:

Example 3-3c 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:

Lesson 4 Contents Example 1Solve a Multiplication Equation Example 2Solve a Multiplication Equation Example 3Use an Equation to Solve a Problem

Example 4-1a Check your solution.

Example 4-1b

Example 4-1c Check Write the original equation. Replace x with 3. This sentence is true. Answer: The solution is 3.

Example 4-1d Check your solution. Answer: 5

Example 4-2a Write the equation. Divide each side by –5. Answer: The solution is –3. Check this solution.

Example 4-2b Answer: –7

Example 4-3a 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

Example 4-3b Write the equation. Divide each side by 4. Simplify. Answer: The length of the rectangle is 36 inches. Check

Example 4-3c 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

Lesson 5 Contents Example 1Solve a Two-Step Equation Example 2Solve a Two-Step Equation Example 3Use an Equation to Solve a Problem

Example 5-1a

Answer: The solution is –3.

Example 5-1b Answer: 2

Example 5-2a 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.

Example 5-2b Answer: 4

Example 5-3a 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? The cost of 2 large popcorns plus 3 tickets is $24. Two popcorns at $p each plus tickets costs $24 Words Variable Equation 2p2p

Example 5-3b 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?

Example 5-3c 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

Lesson 6 Contents Example 1Complete a Function Table Example 2Find a the Rule for a Function Table Example 3Solving a Problem Using a Function

Example 6-1a Complete the function table. The function rule is 3n. Multiply each input by 3. Input Output –1 – –1 Output (3n) Input (n) Answer: –3 1 0

Example 6-1c Complete the function table Output Input Answer: 3 5 4

Example 6-2a Find the rule for the function table Output Input Input Output The output is three less than the input. Answer: So, the function rule is n – 3. Study the relationship between each input and output.

Example 6-2b Find the rule for the function table Output Input Answer:

Example 6-3a 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 with the number of workdays after Nina’s first day, 7.

Example 6-3b Replace d with 7. Multiply 2 and 7. Add 14 and Answer: Nina spends $18.50 on coffee in her first 8 workdays.

Example 6-3c 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

Lesson 7 Contents Example 1Graph a Function Example 2Make a Function Table for a Graph

Example 7-1a Step 1 Record the input and output in a function table. List the input and output as ordered pairs. Make a function table for the rule Use input values of –4, 0, and 4. Then graph the function. 4 0 –4 (x, y)(y)( )(x) Ordered Pairs OutputFunction RuleInput –2 (–4, –2) 2 (0, 2) 6(4, 6)

Example 7-1b 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

Example 7-1c Answer:

Example 7-1d Make a function table for the rule Use input values of –2, 1, and 5. Then graph the function. (5, 2)25 – 35 (1, –2)–21 – 31 (–2, –5)–5–2 – 3–2 (x, y)(y)(x – 3)(x) Ordered Pairs OutputFunction RuleInput Answer:

Example 7-1e Answer:

Example 7-2a Make a function table for the graph. Then determine the function rule. Use the ordered pairs to make a function table.

Example 7-2b Study the input and output. Look for a rule. Input (x)Output (y)(x, y) –48(–4, 8) –24(–2, 4) 00(0, 0) 2–4(2, –4) Input Output –4 8 – –4 Each input is multiplied by –2 to get the output. Answer: The function rule is

Example 7-2d Make a function table for the graph. Then determine the function rule. Answer: