Elementary and Intermediate Algebra (with CengageNOW 2-Semester, Personal Tutor with ...

901 Pages·2010·15.95 MB·English

How to Be Successful in a Math Course
Being successful in algebra depends most on having good study skills. We list study skills and other good habits to
develop to be successful in this course at the beginning of the first few chapters. Here's a recap.
Make a Good Start (Chapter 1)
Put Yourself on a Schedule
Make a schedule for yourself in which you set aside 2 hours each day to work on algebra.
Find Your Mistakes and Correct Them
Always check your answers against the answers in the back of the book.
Gather Information about Available Resources and Help
You should anticipate that you will need extra help sometime during the course, so gather information about the
resources (tutors, study groups, online practice) available to you.
Organize Your Work—And You Won’t Get Nervous! (Chapter 2)
Imitate Success
Your work should look like the work you see in this book and the work your instructor shows.
List Difficult Problems
Begin to make lists of problems that give you the most difficulty.
Begin to Develop Confidence with Word Problems
Instead of telling yourself in advance that you can’t do word problems, decide to do whatever it takes to master
them.
Be Attentive (Chapter 3)
Review with the Exam in Mind
Each day you should review material that will be covered on the next exam.
Pay Attention to Instructions
Train yourself to pay attention to the instructions that accompany a problem as you work through your home-
work problems.
Focus on Being a Success in the Course (Chapter 4)
Be Focused, Not Distracted
Don’t dwell on questions and worries about the class that can become excuses for not doing well.
Be Resilient
Don’t let setbacks keep you from your goals.
Intend to Succeed
Set out to master the material, no matter what it takes.
Develop Good Habits (Chapter 5)
Continue to Set and Keep a Schedule
Even if you are doing well in the course, you should not slacken your efforts.
Increase Effectiveness
Spend time on study activities that produce the best results for you, so that you can use success to build success.
Continue to List Difficult Problems
Don’t let down your guard. List difficult problems so that you can prepare for the next exam effectively.
The Blueprint for Problem Solving is a general outline that you can use to help you solve application problems.
BLUEPRINT FOR
PROBLEM SOLVING
STEP 1: Read the problem, and then mentally list the items that are known
and the items that are unknown.
STEP 2: Assign a variable to one of the unknown items. (In most cases this
will amount to letting x ⫽ the item that is asked for in the problem.)
Then translate the other information in the problem to expressions
involving the variable.
STEP 3: Reread the problem, and then write an equation, using the items
and variables listed in steps 1 and 2, that describes the situation.
STEP 4: Solve the equation found in step 3.
STEP 5: Write your answer using a complete sentence.
STEP 6: Reread the problem, and check your solution with the original words
in the problem.
Here is a Blueprint for Problem Solving that you can use specifically for problems about systems of equations (be-
ginning in Chapter 3).
BLUEPRINT FOR PROBLEM SOLVING
USING A SYSTEM OF EQUATIONS
STEP 1: Read the problem, and then mentally list the items that are known
and the items that are unknown.
STEP 2: Assign variables to each of the unknown items; that is, let x ⫽ one
of the unknown items and y ⫽ the other unknown item. Then trans-
late the other information in the problem to expressions involving
the two variables.
STEP 3: Reread the problem, and then write a system of equations, using
the items and variables listed in steps 1 and 2, that describes the
situation.
STEP 4: Solve the system found in step 3.
STEP 5: Write your answers using complete sentences.
STEP 6: Reread the problem, and check your solution with the original
words in the problem.
Resources
By gathering resources early in the term, before you need help, the information about these resources will be avail-
able to you when they are needed.
INSTRUCTOR
Knowing the contact information for your instructor is very important. You may already have this information from
the course syllabus. It is a good idea to write it down again.
Name Office Location
Available Hours: M T W TH F
Phone Number ext. E-mail Address
TUTORING CENTER
Many schools offer tutoring, free of charge to their students. If this is the case at your school, find out when and
where tutoring is offered.
Tutoring Location Phone Number ext.
Available Hours: M T W TH F
COMPUTER LAB
Many schools offer a computer lab where students can use the online resources and software available with their
textbook. Other students using the same software and websites as you can be very helpful. Find out where the
computer lab at your school is located.
Computer Lab Location Phone Number ext.
Available Hours: M T W TH F
VIDEO LESSONS
A complete set of video lessons is available to your school. These videos feature the author of your textbook pre-
senting full-length, 15- to 20-minute lessons from every section of your textbook. If you miss class, or find yourself
behind, these lessons will prove very useful.
Video Location Phone Number ext.
Available Hours: M T W TH F
CLASSMATES
Form a study group and meet on a regular basis. When you meet try to speak to each other using proper mathe-
matical language. That is, use the words that you see in the definition and property boxes in your textbook.
Name Phone E-mail
Name Phone E-mail
Name Phone E-mail
ELEMENTARY AND
INTERMEDIATE ALGEBRA
A COMBINED COURSE
THIRD EDITION
Charles P. McKeague
CUESTA COLLEGE
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Brief Contents
CHAPTER 1 THE BASICS 1
CHAPTER 2 LINEAR EQUATIONS AND INEQUALITIES 83
CHAPTER 3 GRAPHING AND SYSTEMS OF EQUATIONS 155
CHAPTER 4 EXPONENTS AND POLYNOMIALS 229
CHAPTER 5 FACTORING 285
CHAPTER 6 RATIONAL EXPRESSIONS 337
CHAPTER 7 TRANSITIONS 391
CHAPTER 8 EQUATIONS AND FUNCTIONS 465
CHAPTER 9 RATIONAL EXPONENTS AND ROOTS 535
CHAPTER 10 QUADRATIC FUNCTIONS 595
CHAPTER 11 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 657
CHAPTER 12 CONIC SECTIONS 711
CHAPTER 13 SEQUENCES AND SERIES 743
Contents
CHAPTER 1 The Basics 1
1.1 Notation and Symbols 3
1.2 Real Numbers 11
1.3 Addition of Real Numbers 22
1.4 Subtraction of Real Numbers 29
1.5 Properties of Real Numbers 36
1.6 Multiplication of Real Numbers 43
1.7 Division of Real Numbers 51
1.8 Subsets of the Real Numbers 58
1.9 Addition and Subtraction with Fractions 66
Summary 76
Review Test 79
Projects 81
CHAPTER 2 Linear Equations and Inequalities 83
2.1 Simplifying Expressions 85
2.2 Addition Property of Equality 93
2.3 Multiplication Property of Equality 99
2.4 Solving Linear Equations 106
2.5 Formulas 112
2.6 Applications 122
2.7 More Applications 131
2.8 Linear Inequalities 139
Summary 148
Review Test 151
Projects 152
iv
Contents v
CHAPTER 3 Graphing and Systems of Equations 155
3.1 Paired Data and Graphing Ordered Pairs 157
3.2 Solutions to Linear Equations in Two Variables 164
3.3 Graphing Linear Equations in Two Variables 170
3.4 More on Graphing: Intercepts 178
3.5 Slope and the Equation of a Line 184
3.6 Solving Linear Systems by Graphing 194
3.7 The Elimination Method 200
3.8 The Substitution Method 208
3.9 Applications 215
Summary 222
Review Test 225
Projects 227
CHAPTER 4 Exponents and Polynomials 229
4.1 Multiplication with Exponents 231
4.2 Division with Exponents 239
4.3 Operations with Monomials 249
4.4 Addition and Subtraction of Polynomials 255
4.5 Multiplication with Polynomials 259
4.6 Binomial Squares and Other Special Products 265
4.7 Dividing a Polynomial by a Monomial 270
4.8 Dividing a Polynomial by a Polynomial 274
Summary 279
Review Test 282
Projects 283
CHAPTER 5 Factoring 285
5.1 The Greatest Common Factor and Factoring by Grouping 287
5.2 Factoring Trinomials 293
5.3 More Trinomials to Factor 297
5.4 The Difference of Two Squares 303
5.5 The Sum and Difference of Two Cubes 308
5.6 Factoring: A General Review 311
vi Contents
5.7 Solving Equations by Factoring 315
5.8 Applications 321
Summary 330
Review Test 333
Projects 334
CHAPTER 6 Rational Expressions 337
6.1 Reducing Rational Expressions to Lowest Terms 339
6.2 Multiplication and Division of Rational Expressions 348
6.3 Addition and Subtraction of Rational Expressions 356
6.4 Equations Involving Rational Expressions 362
6.5 Applications 367
6.6 Complex Fractions 375
6.7 Proportions 380
Summary 385
Review Test 387
Projects 388
CHAPTER 7 Transitions 391
7.1 Review of Solving Equations 392
7.2 Equations with Absolute Value 404
7.3 Compound Inequalities and Interval Notation 408
7.4 Inequalities Involving Absolute Value 417
7.5 Review of Systems of Linear Equations in Two Variables 423
7.6 Systems of Linear Equations in Three Variables 434
7.7 Linear Inequalities in Two Variables 442
7.8 Systems of Linear Inequalities 450
Summary 458
Review Test 462
Projects 463
CHAPTER 8 Equations and Functions 465
8.1 The Slope of a Line 466
8.2 The Equation of a Line 481
8.3 Introduction to Functions 492