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Lesson 10-1 Simplifying Algebraic Expressions

Lesson 10-2 Solving Two-Step Equations

Lesson 10-3 Writing Two-Step Equations

Lesson 10-4 Sequences

Lesson 10-5 Solving Equations with Variables on Each Side

Lesson 10-6 Problem-Solving Investigation: Guess and Check

Lesson 10-7 Inequalities

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Five-Minute Check (over Chapter 9)

Main Idea and Vocabulary

Targeted TEKS

Example 1: Write Expressions With Addition

Example 2: Write Expressions With Addition

Example 3: Write Expressions With Subtraction

Example 4: Write Expressions With Subtraction

Example 5: Identify Parts of an Expression

Example 6: Simplify Algebraic Expressions

Example 7: Simplify Algebraic Expressions

Example 8: Real-World Example


• equivalent expressions– Expressions that are equal no

matter what X is

• Term– A “part” of an Alg. Expression

separated by + or -

• Coefficient– The number in front of a

variable

• Use the Distributive Property to simplify algebraic expressions.

• like terms– Look alike! – Same vars!

• Constant– A number w/o a variable

• simplest form– All like terms combined

• simplifying the expression– Combining all the like terms


NOTES

Quick Review Session

Distributive Property

a (b + c) = ab + ac I can only combine things in math that ?????

LOOK ALIKE!!!!!!!

In Algebra, if things LOOK ALIKE, we call them “like terms.”

The Distributive Property

http://www.glencoe.com/sec/math/brainpops/00112041/00112041.html


Write Expressions With Addition

Use the Distributive Property to rewrite 3(x + 5).

3(x + 5) = 3(x) + 3(5)

= 3x + 15 Simplify.

Answer: 3x + 15


A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. x + 8

B. x + 12

C. 2x + 6

D. 2x + 12

Use the Distributive Property to rewrite 2(x + 6).


Use the Distributive Property to rewrite (a + 4)7.

(a + 4)7 = a ● 7 + 4 ●7

= 7a + 28 Simplify.

Answer: 7a + 28

Write Expressions With Addition


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 3a + 27

B. 3a + 18

C. 3a + 9

D. a + 18

Use the Distributive Property to rewrite (a + 6)3.


Write Expressions With Subtraction

Use the Distributive Property to rewrite (q – 3)9.

(q – 3)9 = [q + (–3)]9 Rewrite q – 3 as q + (–3).

= (q)9 + (–3)9 Distributive Property

= 9q + (–27) Simplify.

= 9q – 27 Definition of subtractionAnswer: 9q – 27


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. q – 16

B. q – 10

C. 8q – 16

D. 8q – 10

Use the Distributive Property to rewrite (q – 2)8.


Write Expressions With Subtraction

Use the Distributive Property to rewrite –3(z – 7).

Answer: –3z + 21

–3(z – 7) = –3[z + (–7)] Rewrite z – 7 as z + (–7).

= –3(z) + (–3)(–7) Distributive Property

= –3z + 21 Simplify.


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. –2z + 8

B. –2z – 8

C. –2z – 4

D. –2z

Use the Distributive Property to rewrite –2(z – 4).


Identify Parts of an Expression

Identify the terms, like terms, coefficients, and constants in 3x – 5 + 2x – x.

3x – 5 + 2x – x = 3x + (–5) + 2x + (–x)

Definition of

subtraction

= 3x + (–5) + 2x + (–1x)

Identity

Property;

–x = –1x

Answer: The terms are 3x, –5, 2x, and –x.The like terms are 3x, 2x, and –x.The coefficients are 3, 2, and –1.The constant is –5.


Identify the terms, like terms, coefficients, and constants in 6x – 2 + x – 4x.

Answer: The terms are 6x, –2, x, and –4x.The like terms are 6x, x, and –4x.The coefficients are 6, 1, and –4.The constant is –2.


Simplify Algebraic Expressions

Simplify the expression 6n – n.

6n – n are like terms.

Answer: 5n

6n – n = 6n – 1n Identity Property; n = 1n

= (6 – 1)n Distributive Property

= 5n Simplify.


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 10n

B. 8n

C. 7n

D. 6n

Simplify the expression 7n + n.


Simplify Algebraic Expressions

Simplify 8z + z – 5 – 9z + 2.

8z, z, and –9z are like terms. –5 and 2 are also like terms.

Answer: –3

8z + z – 5 – 9z + 2

= 8z + z + (–5) + (–9z) + 2

Definition of subtraction

= 8z + z + (–9z) + (–5) + 2

Commutative Property

= [8 + 1+ (–9)]z + [(–5) + 2]

Distributive Property

= 0z + (–3) or –3

Simplify.


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. –z

B. –z + 2

C. z –1

D. –2z

Simplify 6z + z – 2 – 8z + 2.


THEATER Tickets for the school play cost $5 for adults and $3 for children. A family has the same number of adults as children. Write an expression in simplest form that represents the total amount of money spent on tickets.

Words $5 each for adults and $3 each for the same number of children

Variable Let x represent the number of adults or children.

Expression 5 ● x + 3 ● x


Simplify the expression.

5x + 3x = (5 + 3)x Distributive Property

= 8x Simplify.

Answer: The expression $8x represents the total amount of money spent on tickets.


A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. $2.50x

B. $7.50x

C. $15.50x

D. $17.50x

MUSEUM Tickets for the museum cost $10 for adults and $7.50 for children. A group of people have the same number of adults as children. Write an expression in simplest form that represents the total amount of money spent on tickets to the museum.


Five-Minute Check (over Lesson 10-1)


Targeted TEKS

Example 1: Solve Two-Step Equations

Example 2: Solve Two-Step Equations

Example 3: Equations with Negative Coefficients

Example 4: Combine Like Terms First


• two-step equation– Contains TWO operations that need to be

“undone”

• Solve two-step equations.


NOTES

The Goal of solving EVERY algebra equation is to GET THE VARIABLE BY ITSELF!!!

I can only combine things in math that ????

To PUT SOMETHING TOGETHER, you follow the directions.

In math, to put an expression together, we used a specific order of operations.

PEMDAS

If you want to take something APART you REVERSE the directions.

To solve Algebra equations, REVERSE PEMDAS

SADMEP

BrainPop: Two-Step Equations






Solve Two-Step Equations

Solve 5x + 1 = 26.

Method 1 Use a model.

Remove a 1-tile from the mat.



Separate the remaining tiles into 5 equal groups.

There are 5 tiles in each group.



Method 2 Use Symbols

Use the Subtraction Property of Equality.

Write the equation.

Subtract 1 from each side.



Use the Division Property of Equality.

Answer: The solution is 5.

Divide each side by 5.

Simplify.

BrainPop: Two-Step Equations






A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 6

B. 8

C. 9

D. 12

Solve 3x + 2 = 20.



Write the equation.

Answer: The solution is –18.


Simplify.

Multiply each side by 3.

Simplify.


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 14

B. 8

C. –26

D. –35


Equations with Negative Coefficients


Write the equation.

Definition of subtraction


Simplify.

Divide each side by –3.

Simplify.


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. –3

B. –1

C. 2

D. 5

Solve 5 – 2x = 11.


Combine Like Terms First

Write the equation.

Identity Property; –k = –1k

Combine like terms;–1k + 3k = (–1 + 3)k or 2k.Add 2 to each side.

Simplify.


Simplify.


Check

14 = –k + 3k – 2 Write the equation.


Combine Like Terms First

14 = –8 + 3(8) – 2 Replace k with 8.?

14 = –8 + 24 – 2 Multiply.?

14 = 14 The statement is true.


A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 3

B. 5

C. 8

D. 10

Solve 10 = –n + 4n –5.



Main Idea

Targeted TEKS

Example 1: Translate Sentences into Equations






• Write two-step equations that represent real-life situations.


CONVERTING ENGLISH SENTENCES TO MATH SENTENCES!

There are 3 steps to follow:

1) Read problem and highlight KEY words.

2) Define variable (What part is likely to change OR What do I not know?)

3) Write Math sentence left to Right (Be careful with Subtraction!.)


Notes – CONT.

Looks for the words like:

• is, was, total– EQUALS

• Less than, decreased, reduced, – SUBTRACTION - BE CAREFUL!

• Divided, spread over, “per”, quotient– DIVISION

• More than, increased, greater than, plus– ADDITION

• Times, Of– MULTIPLICATION


Translate Sentences into Equations

Translate three more than half a number is 15 into an equation.

Answer:


A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Translate five more than one-third a number is 7 into an equation.

A.

B.

C.

D.



Translate nineteen is two more than five times a number into an equation.

Answer: 19 = 5n + 2


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 15 = 3n + 6

B. 15 = 6n + 3

C. 15 = 3(n + 6)

D. 15 = 6(n + 3)

Translate fifteen is three more than six times a number into an equation.



Translate eight less than twice a number is –35 into an equation.

Answer: 2n – 8 = –35


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 3(n – 6) = –22

B. 6(n – 3) = –22

C. 3n – 6 = –22

D. 6n – 3 = –22

Translate six less than three times a number is –22 into an equation.


TRANSPORTATION A taxi ride costs $3.50 plus $2 for each mile traveled. If Jan pays $11.50 for the ride, how many miles did she travel?

Words $3.50 plus $2 per mile equals $11.50.

Variable Let m represent the number of miles driven.

Equation 3.50 + 2m = 11.50


3.50 + 2m = 11.50 Write the equation.

3.50 – 3.50 + 2m = 11.50 – 3.50 Subtract 3.50 from each side

2m = 8

Simplify.

Answer: Jan traveled 4 miles.


Simplify.


A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 200 miles

B. 250 miles

C. 300 miles

D. 325 miles

TRANSPORTATION A rental car costs $100 plus $0.25 for each mile traveled. If Kaya pays $162.50 for the car, how many miles did she travel?


DINING You and your friend spent a total of $33 for dinner. Your dinner cost $5 less than your friend’s. How much did you spend for dinner?

Words Your friend’s dinner plus your dinner equals $33.

Variable Let f represent the cost of your friend’s dinner.

Equation f + f – 5 = 33


f + f – 5 = 33 Write the equation.

2f – 5 = 3 Combine like terms.

2f – 5 + 5 = 33 + 5 Add 5 to each side.

2f = 38 Simplify.

Answer: Your friend spent $19 on dinner. So you spent $19 – $5, or $14, on dinner.

f = 19 Simplify.



A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. $22

B. $26

C. $28

D. $30

DINING You and your friend spent a total of $48 for dinner. Your dinner cost $4 more than your friend’s. How much did you spend for dinner?




Targeted TEKS

Example 1: Identify Arithmetic Sequences

Example 2: Describe an Arithmetic Sequence


Example 4: Test Example


• Sequence– An ordered list of numbers

• Term– A specific number in a sequence

• common difference– The difference between EVERY term is the SAME

• arithmetic sequence– Where the terms all have a common difference

• Write algebraic expressions to determine any term in an arithmetic sequence.


NOTES

To Identify Arithmetic Sequences Look for a pattern that has a common difference

If one exists, the sequence is arithmetic

Ex: 15, 13, 11, 9, 7, ….

To find the “rule” that describes a sequence1. Write the terms on top of the sequence number (1,2,3…)

2. Find the “common difference.”

3. Write down common difference followed by the variable

4. Find out how much you need to ADD or SUBTRACT to get to the first term.

5. Check your rule for the rest of the terms

-2 -2 -2 -2


Identify Arithmetic Sequences

State whether the sequence 23, 15, 7, –1, –9, … is arithmetic. If it is, state the common difference. Write the next three terms of the sequence.

Answer: The terms have a common difference of –8, so the sequence is arithmetic.

23, 15, 7, –1, –9 Notice that 15 – 23 = –8, 7 – 15 = –8, and so on.

–8 –8 –8 –8

Continue the pattern to find the next three terms.

Answer: The next three terms are –17, –25, and –33.

–9, –17, –25, –33

–8 –8 –8


Answer: arithmetic; –2; 19, 17, 15

State whether the sequence 29, 27, 25, 23, 21, … is arithmetic. If it is, state the common difference. Write the next three terms of the sequence.


Describe an Arithmetic Sequence

Write an expression that can be used to find the nth term of the sequence 0.6, 1.2, 1.8, 2.4, …. Then write the next three terms of the sequence.

Use a table to examine the sequence.

Answer: An expression that can be used to find the nth term is 0.6n. The next three terms are 0.6(5) or 3, 0.6(6) or 3.6, and 0.6(7) or 4.2.

The terms have a common difference of 0.6. Also, each term is 0.6 times its term number.


Write an expression that can be used to find the nth term of the sequence 1.5, 3, 4.5, 6, …. Then write the next three terms.

Answer: 1.5n; 7.5, 9, 10.5


TRANSPORTATION This arithmetic sequence shows the cost of a taxi ride for 1, 2, 3, and 4 miles. What would be the cost of a 9-mile ride?

The common difference between the costs is 1.75. This implies that the expression for the nth mile is 1.75n. Compare each cost to the value of 1.75n for each number of miles.


Each cost is 3.50 more than 1.75n. So, the expression 1.75n + 3.50 is the cost of a taxi ride for n miles. To find the cost of a 9-mile ride, let c represent the cost. Then write and solve an equation for n = 9.


c = 1.75n + 3.50 Write the equation.

c = 1.75(9) + 3.50 Replace n with 9.

c = 15.75 + 3.50 or 19.25 Simplify.

Answer: It would cost $19.25 for a 9-mile taxi ride.


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. $18.75 B.$21.50

C. $24.50 D.$27.00

TRANSPORTATION This arithmetic sequence shows the cost of a taxi ride for 1, 2, 3, and 4 miles. What would be the cost of a 15-mile ride?


Which expression can be used to find the nth term in the following arithmetic sequence, where n represents a number’s position in the sequence?

A. n + 3

B. 3n

C. 2n + 1

D. 3n – 1


Read the Test Item You need to find an expression to describe any term.

Solve the Test Item The terms have a common difference of 3 for every increase in position number. So the expression contains 3n.

Answer: D

• Eliminate choices A and C because they do not contain 3n.

• Eliminate choice B because 3(1) ≠ 2.• The expression in choice D is correct for all the listed

terms. So the correct answer is D.


A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 7n

B. 4n – 3

C. 7 – n

D. 4n + 3

Let n represent the position of a number in the sequence 7, 11, 15, 19, … Which expression can be used to find any term in the sequence?



Main Idea

Targeted TEKS

Example 1: Equations with Variables on Each Side

Example 2: Equations with Variables on Each Side



• Solve equations with variables on each side.


NOTES

The goal of solving EVERY Algebra equation you will ever see for the rest of your life is??????

GET THE VARIABLE BY ITSELF!!

To solve equations with variables on each side of the equation:

1. Add or subtract all VARIABLES on ONE side to get rid of them on that side.

2. Add or subtract all the NUMBERS on OTHER side to move them to the side without the variables.

3. Solve it like we’ve been doing all year!

4. HINT: Get rid of the SMALLEST variable term!


Equations with Variables on Each Side

Solve 7x + 4 = 9x. Check your solution.


Subtract 7x from each side.Write the equation.

Simplify by combining like terms.Mentally divide each side by 2.

To check your solution, replace x with 2 in the original equation.Check

Write the equation.

Replace x with 2.

The sentence is true.

?


A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. –5

B. –3

C. –1

D. 1

Solve 3x + 6 = x. Check your solution


Equations with Variables on Each Side

Solve 3x – 2 = 8x + 13.

Write the equation.


Subtract 8x from each side.

Simplify.

Add 2 to each side.

Simplify.

Mentally divide each side by –5.


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. –4

B. –7

C. –10

D. –12

Solve 4x – 3 = 5x + 7.


GEOMETRY The measure of an angle is 8 degrees more than its complement. If x represents the measure of the angle and 90 – x represents the measure of its complement, what is the measure of the angle?

Words 8 less than the measure of an angle equals the measure of its complement.

Variable x and 90 – x represent the measures of the angles.

Equation x – 8 = 90 – x


x – 8 = 90 – x Write the equation.

x – 8 + 8 = 90 + 8 – x Add 8 to each side.

x = 98 – x

x + x = 98 – x + x Add x to each side.

2x = 98

Answer: The measure of the angle is 49 degrees.


x = 49


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 39 degrees

B. 42 degrees

C. 47 degrees

D. 51 degrees

GEOMETRY The measure of an angle is 12 degrees less than its complement. If x represents the measure of the angle and 90 – x represents the measure of its complement, what is the measure of the angle?



Main Idea

Targeted TEKS

Example 1: Guess and Check


• Guess and check to solve problems.


8.14 The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. (C) Select or develop an appropriate problem-solving strategy from a variety of different types, including…systematic guessing and checking…to solve a problem.


Guess and Check

THEATER 120 tickets were sold for the school play. Adult tickets cost $8 each, and child tickets cost $5 each. The total earned from ticket sales was $840. How many tickets of each type were sold?

Explore You know the cost of each type of ticket, the total number of tickets sold, and the total income from ticket sales.

Plan Use a systematic guess and check method to find the number of each type of ticket.


Guess and Check

Solve Find the combination that gives 120 total tickets and $840 in sales. In the list, a represents adult tickets sold, and c represents child tickets sold.

Check So, 80 adult tickets and 40 child tickets were sold.

Answer: 80 adult and 40 child


A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 90 adult tickets, 60 child tickets

B. 100 adult tickets, 50 child tickets

C. 110 adult tickets, 40 child tickets

D. 120 adult tickets, 30 child tickets

THEATER 150 tickets were sold for the school play. Adult tickets were sold for $7.50 each, and child tickets were sold for $4 each. The total earned from ticket sales was $915. How many tickets of each type were sold?



Main Idea

Targeted TEKS

Example 1: Write Inequalities with < or >

Example 2: Write Inequalities with < or >

Example 3: Write Inequalities with ≤ or ≥

Example 4: Write Inequalities with ≤ or ≥

Example 5: Determine the Truth of an Inequality

Example 6: Determine the Truth of an Inequality

Example 7: Graph an Inequality

Example 8: Graph an Inequality


• Write and graph inequalities.


NOTES

Translating English to Mathlish Inequalities is similar to converting to equations.

Look for the following clues:

SOLVING INEQUALITIES

1. Solve inequalities just like you do equations … GET THE VARIABLE BY ITSELF!


NOTES - CONTINUED

To check your answer, pick 3 numbers and check them to see if they work in your answer.

1. Pick a number higher

2. Pick a number lower

3. Pick the actual number to see if you need a greater than or equal to sign (or a less than or equal to).

TO DETERMINE IF INEQUALITIES ARE TRUE PLUG IN WHAT YOU KNOW AND SEE IF IT’S TRUE!!

TO GRAPH INEQUALITIES1. Graph the point on a number line

2. Figure out if the point should be filled in or not.

3. Use an arrow to show which direction the inequality should go.


Write Inequalities with < or >

SPORTS Members of the little league team must be under 14 years old. Write an inequality for the sentence.

Let a = person’s age.

Answer: a < 14


A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. a < 10

B. a ≤ 10

C. a > 10

D. a ≥ 10

SPORTS Members of the peewee football team must be under 10 years old. Write an inequality for the sentence.


Write Inequalities with < or >

CONSTRUCTION The ladder must be over 30 feet tall to reach the top of the building. Write an inequality for the sentence.

Let b = ladder’s height.

Answer: b > 30


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. h < 300

B. h ≤ 300

C. h > 300

D. h ≥ 300

CONSTRUCTION The new building must be over 300 feet tall. Write an inequality for the sentence.


Write Inequalities with ≤ or ≥

POLITICS The president of the United States must be at least 35. Write an inequality for the sentence.

Let a = president’s age.

Answer: a ≥ 35


1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. p > 7

B. p ≥ 7

C. p < 7

D. p ≤ 7

SOFTBALL The home team needs more than 7 points to win. Which of the following inequalities describes how many points are needed to win?


CAPACITY A theater can hold a maximum of 300 people. Write an inequality for the sentence.

Let p = theater’s capacity.

Answer: p ≤ 300

Write Inequalities with ≤ or ≥


A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. p < 10,000

B. p ≤ 10,000

C. p > 10,000

D. p ≥ 10,000

CAPACITY A football stadium can hold a maximum of 10,000 people. Write an inequality for the sentence.


Determine the Truth of an Inequality

For the given value, state whether the inequality is true or false.

x – 4 < 6; x = 0

Answer: Since –4 is less than 6, –4 < 6 is true.

–4 < 6 Simplify

0 – 4 < 6 Replace x with 0.?

x – 4 < 6 Write the inequality.


1. A

2. B0%0%


x – 5 < 8; x = 16

A. true

B. false


Determine the Truth of an Inequality


3x ≥ 4; x = 1

Answer: Since 3 is not greater than or equal to 4, the sentence is false.

3x ≥ 4 Write the inequality.

3(1) ≥ 4 Replace x with 1.?

3 ≥ 4 Simplify.


1. A

2. B

0%0%

A. true

B. false


2x ≥ 9; x = 5


Graph an Inequality

Graph n ≤ –1 on a number line.

Place a closed circle at –1. Then draw a line and an arrow to the left.

Answer:


Answer:

Graph n ≤ –3 on a number line.


Graph an Inequality

Graph n > –1 on a number line.

Answer:

Place an open circle at –1. Then draw a line and an arrow to the right.


Answer:

Graph n > –3 on a number line.


Five-Minute Checks

Image Bank

Math Tools

Graphing Equations with Two Variables

Two-Step Equations


Lesson 10-1 (over Chapter 9)

Lesson 10-2 (over Lesson 10-1)






To use the images that are on the following three slides in your own presentation:

1. Exit this presentation.

2. Open a chapter presentation using a full installation of Microsoft® PowerPoint® in editing mode and scroll to the Image Bank slides.

3. Select an image, copy it, and paste it into your presentation.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 10

B. 12

C. 22

D. 30

Use the histogram shown in the image. How many people were surveyed?

(over Chapter 9)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 2

B. 6

C. 8

D. 12

Use the histogram shown in the image. How many people drink more than 3 carbonated beverages per day?

(over Chapter 9)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 12 percent

B. 20 percent

C. 30 percent

D. 40 percent

Use the histogram shown in the image. What percentage of people drink 2–3 carbonated beverages per day?

(over Chapter 9)

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. about 26.1; 25; none

B. about 26.1; 17; none

C. about 26.1; 25; 17

D. about 26.1; 17; 40

Find the mean, median, and mode for the following set of data. 20, 27, 40, 17, 25, 33, 21

(over Chapter 9)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 17

B. 23

C. 25

D. 40

Find the range for the following set of data.20, 27, 40, 17, 25, 33, 21

(over Chapter 9)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. histogram

B. box-and-whisker plot

C. circle graph

D. line graph

Select an appropriate display for the number of people who prefer skiing to all of the winter sports.

(over Chapter 9)

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 8y – 3

B. y – 24

C. 8y – 24

D. 8y + 24

Use the Distributive Property to rewrite the expression 8(y – 3).

(over Lesson 10-1)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. –22m + 2n

B. –22m – n

C. –11m + n

D. –11m – n

Use the Distributive Property to rewrite the expression –2(11m – n).

(over Lesson 10-1)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 15k

B. 16k

C. 17k

D. 18k

Simplify 7k + 9k.

(over Lesson 10-1)

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 3h – 3

B. –3h + 3

C. –3h – 3

D. 3h + 3

Simplify 14h – 3 – 11h

(over Lesson 10-1)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 3x – 2

B. 3x + 2

C. 4x – 2

D. 4x + 2

Sara has x number of apples, 3 times as many oranges as apples, and 2 peaches. Write an expression in simplest form that represents the total number of fruits.

(over Lesson 10-1)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 5x + 1

B. 3x

C. 2x – 1

D. 6x

Which expression represents the perimeter of the triangle?

(over Lesson 10-1)

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Solve 3n + 2 = 8. Then check your solution.

(over Lesson 10-2)

A. 2

B.

C.

D. 4

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

Solve 6n – 3 = 21. Then check your solution.

(over Lesson 10-2)

A.

B. 3

C.

D. 4

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. –5

B. –1

C. 1

D. 5

Solve 2 = 3 – a. Then check your solution.

(over Lesson 10-2)

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. –16

B. –6

C. 6

D. 16

Solve –5 + 2a – 3a = 11. Then check your solution.

(over Lesson 10-2)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

Jack traveled 5 miles plus 3 times as many miles as Janice. He traveled 23 miles in all. How far did Janice travel?

(over Lesson 10-2)

A. 18 miles

B.

C.

D. 6 miles

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

If 3x – 2 = 16, which choice shows the value of 2x – 3?

(over Lesson 10-2)

A.

B. 6

C. 9

D. 15

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 3 – n = 10; 7

B. 3 – n = 10; –7

C. 3n – 5 = 10; –5

D. 3n – 5 = 10; 5

Translate the sentence into an equation. Then find the number. The difference of three times a number and 5 is 10.

(over Lesson 10-3)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

Translate the sentence into an equation. Then find the number. Three more than four times a number equals 27.

(over Lesson 10-3)

A. 4n + 3 = 27; 6

B. 3 – 4n = 27; –6

C.

D.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

Translate the sentence into an equation. Then find the number. Nine more than seven times a number is 58.

(over Lesson 10-3)

A.

B. 7n + 9 = 58; 7

C.

D.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Translate the sentence into an equation. Then find the number. Four less than the quotient of a number and three equals 14.

(over Lesson 10-3)

A.

B.

C.

D.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. $2.33

B. $3.20

C. $3.61

D. $6.50

Jared went to a photographer and purchased one 8 x 10 portrait. He also purchased 20 wallet-sized pictures. Jared spent $97 in all, and the 8 x 10 cost $33. How much is each of the wallet-sized photos?

(over Lesson 10-3)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 35

B. 55

C. 70

D. 105

What is the value of x in the trapezoid?

(over Lesson 10-3)

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. arithmetic; +6; 62, 68, 74

B. arithmetic; –6; 50, 44, 38

C. not arithmetic; 62, 68, 74

D. not arithmetic; 84, 126, 189

State whether the sequence is arithmetic or not arithmetic. If it is arithmetic, state the common difference. Write the next three terms of the sequence. 32, 38, 44, 50, 56, …

(over Lesson 10-4)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

State whether the sequence is arithmetic or not arithmetic. If it is arithmetic, state the common difference. Write the next three of the sequence.15, 17, 20, 24, 29, …

(over Lesson 10-4)

A. arithmetic; +2; 31, 33, 35

B. arithmetic; +3; 32, 35, 38



1. A

2. B

3. C

4. D

0%0%0%0%

A B C D


(over Lesson 10-4)

A. arithmetic; –5; 20, 15, 10

B.

C.


A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. arithmetic; +48; 120, 168, 216

B. arithmetic +2; 74, 76, 78




(over Lesson 10-4)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 64, 58, 52, 46

B. 76, 70, 64, 58

C. 76, 82, 88, 94

D. 70, 64, 58, 52

What are the first 4 terms of an arithmetic sequence with a common difference of (–6) if the first term is 76?

(over Lesson 10-4)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

Which sequence is arithmetic?

(over Lesson 10-4)

A. 4, 8, 16, 32, 64, ...

B. 4, 6, 10, 12, 16, ...

C. 4, 1, –2, –5, –8, ...

D.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Solve 8b – 12 = 5b. Then check your solution.

(over Lesson 10-5)

A. –4

B.

C.

D. 4

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. –6

B. –4

C. 4

D. 6

Solve 5c + 24 = c. Then check your solution.

(over Lesson 10-5)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 5

B. 1

C. –1

D. –5

Solve 3x + 2 = 2x – 3. Then check your solution.

(over Lesson 10-5)

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 5

B. 2

C. –2

D. –5

Solve 4n – 3 = 2n + 7. Then check your solution.

(over Lesson 10-5)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 400 + 0.20x = 500 – 0.15x; $285.70

B. 400 + 0.20x = 500 + 0.15x; $2,000

C. 0.20x – 400 = 500 – 0.15x; $2,571.40

D. 0.20x – 400 = 500 + 0.15x; $18,000

Todd is trying to decide between two jobs. Job A pays $400 per week plus a 20% commission on everything sold. Job B pays $500 per week plus a 15% commission on everything sold. How much would Todd have to sell each week for both jobs to pay the same? Write an equation and solve.

(over Lesson 10-5)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 3

B. 4

C. 5

D. 6

Find the value of x so that the pair of polygons shown in the image has the same perimeter.

(over Lesson 10-5)

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 25 and 27

B. 57 and 59

C. 157 and 159

D. 1,681 and 1,682

The product of two consecutive odd integers is 3,363. What are the integers? Solve using the guess and check strategy.

(over Lesson 10-6)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 2 keychains, 4 cups, 3 pens

B. 4 keychains, 3 cups, 2 pens

C. 3 keychains, 4 cups, 2 pens

D. 3 keychains, 2 cups, 4 pens

Jorge decided to buy a souvenir keychain for $2.25, a cup for $2.95, or a pen for $1.75 for each of his 9 friends. If he spent $22.05 on these souvenirs and bought at least one of each type of souvenir, how many of each did he buy? Solve using the guess and check strategy.

(over Lesson 10-6)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 27

B. 31

C. 29

D. 25

A number squared is 729. Find the number. Solve using the guess and check strategy.

(over Lesson 10-6)

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 5 quarters, 5 dimes, 9 nickels

B. 7 quarters, 9 dimes, 3 nickels

C. 2 quarters, 13 dimes, 4 nickels

D. 6 quarters, 3 dimes, 10 nickels

Candace has $2.30 in quarters, dimes, and nickels in her change purse. If she has a total of 19 coins, how many of each coin does she have? Solve using the guess and check strategy.

(over Lesson 10-6)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 4 people

B. 5 people

C. 6 people

D. 7 people

In the Brown home, there are 30 total legs on people and pets. Each dog and cat has 4 legs, and each family member has 2 legs. The number of pets is the same as the number of family members. How many people are in the Brown family home? Solve using the guess and check strategy.

(over Lesson 10-6)

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