Holt McDougal Florida Larson Algebra 1 - RJSSOLUTIONS.COM

490 Pages·2009·8.59 MB·English

Holt McDougal
Florida
Larson Algebra 1

Chapter Resources
Volume 1: Chapters 1-6

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All rights reserved.

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Printed in the United States of America

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retains title to the materials and they may not be resold. Resale of examination copies is
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Possession of this publication in print format does not entitle users to convert this
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ISBN 13: 978-0-547-25017-5

ISBN 10: 0-547-25017-7

1 2 3 4 5 6 7 8 9 XXX 15 14 13 12 11 10 09

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Algebra 1
Chapter Resource Book
iii

Contents

Chapter 1 Expressions, Equations, and Functions

Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–4

1.1 Evaluate Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–10

1.2 Apply Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–19

1.3 Write Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20–25

1.4 Write Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26–32

1.5 Use a Problem Solving Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33–39

1.6 Represent Functions as Rules and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40–46

1.7 Represent Functions as Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47–57

Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Chapter 2 Properties of Real Numbers

Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61–64

2.1 Use Integers and Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65–73

2.2 Add Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74–79

2.3 Subtract Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80–87

2.4 Multiply Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88–94

2.5 Apply the Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95–101

2.6 Divide Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102–107

2.7 Find Square Roots and Compare Real Numbers . . . . . . . . . . . . . . . . . . . . 108–117

Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

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Algebra 1
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Chapter 3 Solving Linear Equations

Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119–122

3.1 Solve One-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123–129

3.2 Solve Two-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130–138

3.3 Solve Multi-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139–144

3.4 Solve Equations with Variables on Both Sides . . . . . . . . . . . . . . . . . . . . . . 145–152

3.5 Write Ratios and Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153–159

3.6 Solve Proportions Using Cross Products . . . . . . . . . . . . . . . . . . . . . . . . . . 160–165

3.7 Solve Percent Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166–174

3.8 Rewrite Equations and Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175–181

Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Chapter 4 Graphing Linear Equations and Functions

Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183–186

4.1 Plot Points in a Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187–198

4.2 Graph Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199–212

4.3 Graph Using Intercepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213–222

4.4 Find Slope and Rate of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223–231

4.5 Graph Using Slope-Intercept Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232–246

4.6 Model Direct Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247–255

4.7 Graph Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256–265

Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

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Algebra 1
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Chapter 5 Writing Linear Equations

Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267–270

5.1 Write Linear Equations in Slope-Intercept Form . . . . . . . . . . . . . . . . . . . . 271–277

5.2 Use Linear Equations in Slope-Intercept Form . . . . . . . . . . . . . . . . . . . . . 278–283

5.3 Write Linear Equations in Point-Slope Form . . . . . . . . . . . . . . . . . . . . . . . 284–296

5.4 Write Linear Equations in Standard Form . . . . . . . . . . . . . . . . . . . . . . . . . 297–303

5.5 Write Equations of Parallel and Perpendicular Lines . . . . . . . . . . . . . . . . 304–310

5.6 Fit a Line to Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311–320

5.7 Predict with Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321–330

Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

Chapter 6 Solving and Graphing Linear Inequalities

Chapter Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333–336

6.1 Solve Inequalities Using Addition and Subtraction . . . . . . . . . . . . . . . . . . 337–345

6.2 Solve Inequalities Using Multiplication and Division . . . . . . . . . . . . . . . . 346–355

6.3 Solve Multi-Step Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356–367

6.4 Solve Compound Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368–378

6.5 Solve Absolute Value Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379–388

6.6 Solve Absolute Value Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389–397

6.7 Linear Inequalities in Two Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398–409

Chapter Review Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410

Gridded Response Answer Sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

Resource Book Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1–A72

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Algebra 1
Chapter Resource Book
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Contents

Descriptions of Resources
This Chapter Resource Book is organized by lessons within the chapter in order to make
your planning easier. The following materials are provided:

Family Letter This guide helps families contribute to student success by providing
an overview of the chapter along with questions and activities for families to work on
together.

Graphing Calculator Activities with Keystrokes Keystrokes for two models of
calculators are provided for each Graphing Calculator Activity in the Student Edition.

Activity Support Masters These blackline masters make it easier for students to
record their work on selected activities in the Student Edition.

Practice A, B, and C These exercises offer additional practice for the material in each
lesson, including application problems. There are three levels of practice for each lesson:
A (basic), B (average), and C (advanced).

Review for Mastery These two pages provide additional instruction, worked-out
examples, and practice exercises covering the key concepts and vocabulary in each lesson.

Problem Solving Workshops These blackline masters provide extra problem solving
opportunities in addition to the workshops given in the textbook. There are three types of
workshops: Alternative Methods, Worked-Out Examples, and Mixed Problem Solving.

Challenge Practice These exercises offer challenging practice on the mathematics of
each lesson.

Chapter Review Game This worksheet offers fun practice at the end of the chapter
and provides an alternative way to review the chapter content in preparation for the
Chapter Test.

Gridded Response Answer Sheet This page provides 12 answer grids for the teacher
to copy and distribute as needed for use with the gridded response questions in the Problem
Solving Workshops.

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1
Algebra 1
Chapter 1 Resource Book

CHAPTER
1

Chapter Overview One way you can help your student succeed in Chapter 1 is by discussing
the lesson goals in the chart below. When a lesson is completed, ask your student the following ques-
tions. “What were the goals of the lesson? What new words and formulas did you learn? How can you
apply the ideas of the lesson to your life?”

Lesson Title
Lesson Goals
Key Applications

1.1: Evaluate Expressions
Evaluate algebraic expressions
and use exponents.
• Movies
• Storage Cubes
• Football

1.2: Apply Order of
Operations

Focus on Reasoning

Use the order of operations to
evaluate expressions.
Determine whether statements are
always, sometimes, or never true.

• Litter Collection
• Sales
• Online Shopping

1.3: Write Expressions
Translate verbal phrases into
expressions.
• Tips
• Training
• Cycling

1.4: Write Equations
and Inequalities
Translate verbal sentences into
equations or inequalities.
• Mountain Biking
• Compact Discs
• Baking Measurements

1.5: Use a Problem
Solving Plan
Use a problem solving plan to
solve problems.
• Running
• Framing
• Hiking

1.6: Represent Functions
as Rules and Tables
Represent functions as rules and
as tables.
• Concert Tickets
• Yard Sale
• Savings

1.7: Represent Functions
as Graphs

Focus on Functions

Represent functions as graphs.

Determine whether a relation is
a function when the relation is
represented by a table or a graph.

• SAT Scores
• Guitar Sales
• Elections

Key Ideas for Chapter 1

In Chapter 1, you will apply the key ideas listed in the Chapter Opener (see page 1)
and reviewed in the Chapter Summary (see page 53).

1. Writing and evaluating algebraic expressions
2. Using expressions to write equations and inequalities
3. Representing functions as verbal rules, equations, tables, and graphs

Family Letter
For use with Chapter 1

CHAPTER
1

CHAPTER SUPPORT

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Algebra 1
Chapter 1 Resource Book

CHAPTER
1
Family Letter continued
For use with Chapter 1

Key Ideas Your student can demonstrate understanding of key concepts by working
through the following exercises with you.

Lesson
Exercise

1.1
Find the volume of a cube-shaped CD player, where each side s is 23 centimeters.
Use the formula V 5 s3.

1.2
Evaluate 10(x 2 3) 1 6 and 10x 2 3 1 6 when x 5 5.

Focus on
Reasoning
Tell whether the statement is always, sometimes, or never true: For a given whole
number x, the product 6x is an odd whole number.

1.3
The student council is holding a craft show as a fundraiser. Each exhibitor is
charged $40 for a table and the admission price is $3.50 per person. Write an
expression for the amount (in dollars) raised. There are 38 exhibitors and
420 people attend the craft show. Find the amount raised.

1.4
It costs $380 to attend a leadership conference. The school will contribute $75. You
can save $35 per week. Use the inequality 35w 1 75 ≥ 380 to model the situation.
What does w represent? How many weeks will it take to save enough money?

1.5
You are framing a picture that is 9.5 inches long and 7 inches wide. The picture is
bordered by 2-inch matting. The wood to make the frame is 1.5 inches wide. Find
the length and width of the frame. What is the total area of the framed picture? Use
a problem solving plan to find the solution.

1.6
Make a table for the function y 5 2x 2 2 with domain 1, 2, 3, 4, and 5.
Identify the range of the function.

1.7
Graph the function y 5 3x 1 1 with domain 0, 1, 2, 3, and 4.

Focus on
Functions
Tell whether the pairing of x-values and y-values is necessarily a function: A teacher
makes a table that lists the year x and the population of Miami y each year during a
ten-year period.

Home Involvement Activity

Directions Use exactly five 5’s and grouping symbols to make each whole

number from one to ten. For example, 1 5 5
}
5 1 1 5 2 5
}
5 2 .

Answers

1.1: 12,167 cm3 1.2: 26; 53 Focus on Reasoning: never 1.3: 40e 1 3.5p; $2990 1.4: w represents
the number of weeks needed to save; 9 weeks 1.5: 16.5 in.; 14 in.; 321 in.2
1.6:
x
1
2
3
4
5

y
0
2
4
6
8

; range: 0, 2, 4, 6, 8 1.7

x

y

O
1
2
3

2

4
5

4
6
8
10
12
14
Focus on Functions: yes

CHAPTER SUPPORT

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Algebra 1
Chapter 1 Resource Book

CHAPTER
1

CAPÍTULO
1

Vistazo al capítulo Una manera en que puede ayudar a su hijo a tener éxito en el Capítulo 1
es hablar sobre los objetivos de la lección en la tabla a continuación. Cuando se termina una lección,
pregúntele a su hijo lo siguiente: “¿Cuáles fueron los objetivos de la lección? ¿Qué palabras y fórmulas
nuevas aprendiste? ¿Cómo puedes aplicar a tu vida las ideas de la lección?”

Título de la lección
Objetivos de la lección
Aplicaciones clave

1.1: Evaluar expresiones
Evaluar las expresiones
algebraicas y usar exponentes
• Películas
• Almacenaje
• Fútbol americano

1.2: Aplicar el orden de
las operaciones

Enfoque en el
razonamiento

Usar el orden de las operaciones para
evaluar expresiones
Determinar si enunciados son siempre,
a veces o nunca verdaderos

• Recolecta de basura
• Ventas
• De compras en línea

1.3: Escribir expresiones
Convertir frases verbales en
expresiones
• Pautas
• Entrenamiento
• Ciclismo

1.4: Escribir ecuaciones
y desigualdades
Convertir oraciones verbales en
ecuaciones o desigualdades
• Bicicletas de montañas
• Discos compactos
• Medidas de cocina

1.5: Usar un plan de
resolución de
problemas

Usar un plan para resolver
problemas
• Correr
• Enmarcar
• Alpinismo

1.6: Representar
funciones como
reglas y tablas

Representar funciones como reglas
y tablas
• Entradas de concierto
• Mercadillo
• Ahorros

1.7: Representar funciones
como gráfi cas

Enfoque en las
funciones

Representar funciones como gráfi cas

Determinar si una relación es una
función cuando la relación se
representa por una tabla o una gráfi ca

• Puntajes del SAT
• Ventas de guitarras
• Elecciones

Ideas clave para el Capítulo 1

En el Capítulo 1, aplicarás las ideas clave enumeradas en la Presentación del capítulo
(ver la página 1) y revisadas en el Resumen del capítulo (ver la página 53).

1. Escribir y evaluar expresiones algebraicas
2. Usar expresiones para escribir ecuaciones y desigualdades
3. Representar funciones como reglas verbales, ecuaciones, tablas y gráficas

Carta para la familia
Usar con el Capítulo 1

CHAPTER SUPPORT

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Algebra 1
Chapter 1 Resource Book

CHAPTER
1

CAPÍTULO
1
Carta para la familia continúa
Usar con el Capítulo 1

Ideas clave Su hijo puede demostrar la comprensión de las ideas clave al hacer los
siguientes ejercicios con usted.

Lección
Ejercicio

1.1
Halla el volumen de un tocador de CD en forma de cubo, donde cada lado I mide
23 centímetros. Usa la fórmula V 5 P.

1.2
Evalúa 10(x 2 3) 1 6 y 10x 2 3 1 6 cuando x 5 5.

Enfoque en el
razonamiento
Determina si cada enunciado es siempre, a veces o nunca verdadero: Para un
número entero x, el producto 6x es siempre un número entero impar.

1.3
El consejo escolar planifica una exhibición de manualidades para recaudar dinero.
Se le cobran $40 a cada expositor para una mesa y el costo de entrada es $3.50 por
persona. Escribe una expresión para el total (en dólares) que se recaudó. Había 38
expositores y 420 personas fueron a la exhibición. Halla el total de dinero recaudado.

1.4
Cuesta $380 para asistir a una conferencia de liderazgo. Tu escuela pagará $75.
Tú puedes ahorrar $35 por semana. Usa la desigualdad 35s 1 75 ≥ 380 para hacer
un modelo de la situación. ¿Qué representa s? ¿Por cuántas semanas tendrás que
ahorrar hasta tener el dinero suficiente?

1.5
Vas a enmarcar un cuadro que mide 9.5 pulgadas de largo y 7 pulgadas de ancho.
El cuadro se borda por una esfera de 2 pulgadas. La madera que se usa para hacer
el marco mide 1.5 pulgadas de ancho. Halla la longitud y el ancho del marco. ¿Qué
es el área total del cuadro enmarcado? Usa un plan para resolver el problema.

1.6
Grafica la función y 5 2x 2 2 con el dominio 1, 2, 3, 4 y 5. Identifica el rango de
la función.

1.7
Grafica la función y 5 3x 1 1 con el dominio 1, 2, 3 y 4.

Enfoque en
las funciones
Determina si la combinación de valores x e y es una función: Un maestro hace una
tabla que enumera el año x y la población de Miami y cada año durante un período
de diez años.

Actividad para la familia

Instrucciones Usa precisamente cinco 5 y símbolos de agrupación para formar

cada número entero desde el uno hasta el diez. Por ejemplo, 1 5 5
}
5 1 1 5 2 5
}
5 2 .

Respuestas

1.1: 12,167 cm3 1.2: 26; 53 Enfoque en el razonamiento: nunca 1.3: 40e 1 3.5p; $2990 1.4: s
representa el número de semanas necesarias para ahorrar; 9 semanas 1.5: 16.5 pulg; 14 pulg; 321 pulg2
1.6:
x
1
2
3
4
5

y
0
2
4
6
8

; rango: 0, 2, 4, 6, 8 1.7

x

y

O
1
2
3

2

4
5

4
6

8
10
12

14
Enfoque en las funciones: sí

CHAPTER SUPPORT

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5
Algebra 1
Chapter 1 Resource Book

LESSON
1.1
Practice A
For use with pages 2–7

Name the operation indicated by the expression.

1. 19x
2. 5 2 b
3. 14 4 m
4.
a 1 24

Evaluate the expression.

5. y 1 7 when y 5 5
6. 13 2 x when x 5 2
7. 4a when a 5 2.1

8. 9 1 m when m 5 8.2
9. h 1 6 when h 5 1.7
10. 42 4 g when g 5 2

11. x
}
5 when x 5 100
12. 52
}
d when d 5 13
13. 2
}
3 p t when t 5 6

14. r(8.3) when r 5 10
15.
w 1 1
}
4 when w 5 3
}
4
16. n
}
14 when n 5 28

Write the power in words and as a product.

17. 72
18. 45
19. 28

Write the power represented by the words or product.

20. 5 p 5 p 5
21. six squared
22. x p x p x p x

Evaluate the power.

23. 32
24. 24
25. 15

Evaluate the expression.

26. x2 when x 5 5
27. y3 when y 5 3
28. m8 when m 5 1

29. Window Treatments You are ordering custom blinds for your bedroom windows.
The ordering instructions are to measure the width of the window in inches and add
a half-inch to this measurement. So, the blind width you order is given by the
expression w 1 0.5 where w is the width of your window.

a. One of your windows measures 27 inches wide. What width blind should you

order?

b. The other window measures 28.5 inches wide. What width blind should you

order?

30. Skateboarding A skate park charges $10 per person for an all-day admission to the
park. The total cost for n people to go to the park all day is 10n. Eight friends go to
the park on Saturday. What is the total cost of admission?

31. Geometry The area of a square with a side length of s is given by the expression s2.
What is the area of the square shown?

4 in.

4 in.

LESSON 1.1

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6

Algebra 1
Chapter 1 Resource Book

Evaluate the expression.

1.
y 1 12 when y 5 29
2. 47 2 x when x 5 38
3. 0.8a when a 5 7.5

4. 12.5 1 m when m 5 7.6
5. r(4.6) when r 5 8.1
6. 6.25 4 g when g 5 2.5

7.
x}
0.9 when x 5 54
8. 62
}d when d 5 3.1
9.
4}7 p t when t 5 7}8

10.
r(8.3) when r 5 10.2
11. w 1 2}5 when w 5 1}2
12.
n
}
2.4 when n 5 12

Write the power in words and as a product.

13. 87
14. (0.1)4
15.
x5

Evaluate the power.

16. 92
17. 26
18. (0.4)3

Evaluate the expression.

19.
x2 when x 5 1}5
20. m4 when m 5 0.6
21. 2y3 when y 5 4

22.
Side Table A side table has interior storage space in the shape of a cube. What is the
volume of the storage space if the interior length is 12 inches?

12 in.

12 in.

12 in.

23.
Playing Cards There are 52 cards in a standard deck of playing cards. You are
combining decks of cards so that you can play a game with a large number of
people. The expression 52d represents the number of cards in d decks. If you
combine 4 decks of cards, how many cards will you have altogether?

24.
Sales Tax An item costs c dollars and 6% sales tax is charged. The total cost
including sales tax is given by the expression 1.06c. You are buying a skateboard
that costs $75. What is the cost of the skateboard including sales tax?

25. Flower Arranging You are creating a fl ower arrangement for a friend. The total cost

(in dollars) for one vase and f fl owers is given by the expression 8 1 2.5f. How
much will it cost to make an arrangement with 8 fl owers?

Practice B
For use with pages 2–7

LESSON
1.1

LESSON 1.1

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7
Algebra 1
Chapter 1 Resource Book

Practice C
For use with pages 2–7

Evaluate the expression.

1. 5y when y 5 6
2. 18 2 x when x 5 7
3. 0.4a when a 5 32

4. 4 1 m when m 5 9.7
5. h 2 3 when h 5 5.1
6. 48 4 g when g 5 3

7. x
}
8 when x 5 72
8. 60
}
d when d 5 1.5
9. 4
}
9 p t when t 5 7
}
16

10. 2x 1 y when x 5 3 and y 5 2
11. m
}
5 2 n when m 5 4 and n 5 2
}
3

12. 12b
}
a when a 5 2.4 and b 5 0.6
13. 4.5x
}
y when x 5 8.4 and y 5 1.5

Evaluate the power.

14. (0.5)4
15. 1 1
}
3 2
5

16. 1 4
}
5 2
3

Evaluate the expression.

17. 6x when x 5 3
18. (4y)2 when y 5 5

19. (a 2 b)5 when a 5 10 and b 5 6
20. 4m 1 n3 when m 5 7 and n 5 10

21. 3x4 1 2y when x 5 5 and y 5 13
22. (3y)2 2 x2 when x 5 9 and y 5 4

23. Baseball Display A baseball display case is in the shape

9.8 cm

9.8 cm
9.8 cm

of a cube. What is the volume of the display case if the
side length is 9.8 centimeters?

24. Sales Tax An item costs c dollars and 6.25% sales tax is charged. The total cost
including sales tax is given by the expression 1.0625c. You are buying a skateboard
that costs $82. What is the cost of the skateboard including sales tax? Round your
answer to the nearest cent.

25. Planter You are creating concrete planters for a
11 in.

11 in.

15 in.

15 in.

15 in.

11 in.

garden border by placing the concrete in a large
cube and then placing a smaller cube inside. The
amount of concrete you need can be found using
the expression V 2 v where V is the volume of the
larger cube and v is the volume of the smaller
cube. How much concrete do you need to make
one planter?

26. Music A music store sells new CDs for $13.95 and used CDs for $6.50. The total
cost of buying x new CDs and y used CDs can be found using the expression
13.95x 1 6.5y. You buy 3 new CDs and 4 used CDs. Find the total cost.

LESSON
1.1

LESSON 1.1

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Copyright © Holt McDougal. All rights reserved.

8
Algebra 1
Chapter 1 Resource Book

Evaluate algebraic expressions and use exponents.

Vocabulary
A variable is a letter used to represent one or more numbers.

An algebraic expression, or variable expression, consists of numbers,
variables, and operations.

To evaluate an expression, substitute a number for the variable,
perform the operation(s), and simplify the result if necessary.

A power is an expression that represents repeated multiplication of the
same factor.

A power can be written in a form using two numbers, a base and an
exponent. The exponent represents the number of times the base is
used as a factor.

GOAL

Review for Mastery
For use with pages 227

LESSON
1.1

Evaluate algebraic expressions

Evaluate the expression when x 5 5.

a. 7x

b. 12 1 x

Solution

a. 7x 5 7(5)
Substitute 5 for x.

5 35
Multiply.

b. 12 1 x 5 12 1 5
Substitute 5 for x.

5 17
Add.

Exercises for Example 1

Evaluate the expression for the given value of the variable.

1. 15 2 a when a 5 3
2. 3b when b 5 7

3. 11 1 c when c 5 10
4. 28
}
d when d 5 4

5. 1
}
2 n when n 5 18
6. 0.4f when f 5 8

EXAMPLE 1

LESSON 1.1

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9
Algebra 1
Chapter 1 Resource Book

Evaluate an expression

The cost of fi lling a car’s gas tank can be represented by the expression xy where x
is the price per gallon of gasoline and y is the number of gallons purchased. You
purchase 10 gallons of gasoline when the price per gallon is $2.35. Find the total
cost.

Solution
Total Cost 5 xy
Write expression.

5 2.35(10)
Substitute 2.35 for x and 10 for y.

5 23.50
Multiply.

The total cost is $23.50.

Exercises for Example 2

7. You purchase 5 gallons of gasoline when the price of gasoline is $2.26 per
gallon. Find the total cost.

8. You purchase 8 gallons of gasoline when the price of gasoline is $2.20 per
gallon. Find the total cost.

EXAMPLE 2

Read and write powers

Write the power in words and as a product.

a. 83
b. m6

Solution
a. eight to the third power, or eight cubed; 8 p 8 p 8
b. m to the sixth power; m p m p m p m p m p m

Exercises for Example 3

Write the power in words and as a product.

9. 48
10. 1 1
}
3 2
4
11. x2

EXAMPLE 3

Review for Mastery continued
For use with pages 227

LESSON
1.1

LESSON 1.1

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