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| Elementary and Intermediate Algebra Mark Dugopolski,
Southeastern Louisiana University
Table of ContentsPreface ixChapter 1: Real Numbers and Their Properties 1
1.1 The Real Numbers 2
1.2 Fractions 9
1.3 Addition and Subtraction of Real Numbers 19
1.4 Multiplication and Division of Real Numbers 25
1.5 Exponential Expressions and the Order of Operations 29
1.6 Algebraic Expressions 36
1.7 Properties of the Real Numbers 44
1.8 Using the Properties to Simplify Expressions 52
Collaborative Activities 58
Chapter Summary 59
Enriching Your Mathematical Word Power 61
Review Exercises 62
Chapter 1 Test 64
Chapter 2: Linear Equations in One Variable 65
2.1 The Addition and Multiplication Properties of Equality 66
2.2 Solving General Linear Equations 73
2.3 Identities, Conditional Equations, and Inconsistent
Equations 79
2.4 Formulas 86
2.5 Translating Verbal Expressions into Algebraic
Expressions 94
2.6 Number, Geometric, and Uniform Motion Applications 102
2.7 Discount, Investment, and Mixture Applications 108
Collaborative Activities 114
Chapter Summary 115
Enriching Your Mathematical Word Power 116
Review Exercises 116
Chapter 2 Test 119
Making Connections Chapters 1–2 120
Chapter 3: Inequalities in One Variable 121
3.1 Inequalities 122
3.2 Compound Inequalities 132
3.3 Absolute Value Equations and Inequalities 142
Collaborative Activities 150
Chapter Summary 157
Enriching Your Mathematical Word Power 152
Review Exercises 152
Chapter 3 Test 154
Making Connections Chapters 1–3 156
Chapter 4: Linear Equations in Two Variables and Their Graphs 157
4.1 Graphing Lines in the Coordinate Plane 158
4.2 Slope 170
4.3 Equations of Lines in Slope-Intercept and
Standard Form 181
4.4 The Point-Slope Form 190
4.5 Applications of Linear Equations 197
4.6 Introduction to Functions 203
Collaborative Activities 213
Chapter Summary 214
Enriching Your Mathematical Word Power 215
Review Exercises 216
Chapter 4 Test 219
Making Connections Chapters 1–4 221
Chapter 5: Polynomials and Exponents 223
5.1 Addition and Subtraction of Polynomials 224
5.2 Multiplication of Polynomials 231
5.3 Multiplication of Binomials 238
5.4 Special Products 242
5.5 Division of Polynomials 247
5.6 Positive Integral Exponents 254
5.7 Negative Exponents and Scientific Notation 259
Collaborative Activities 268
Chapter Summary 269
Enriching Your Mathematical Word Power 271
Review Exercises 272
Chapter 5 Test 275
Making Connections Chapters 1–5 276
Chapter 6: Factoring 277
6.1 Factoring Out Common Factors 278
6.2 Factoring the Special Products and Factoring by Grouping 284
6.3 Factoring ax2 + bx + c with a equal to 1 290
6.4 Factoring ax2 + bx + c with a not equal to 1 296
6.5 The Factoring Strategy 302
6.6 Solving Quadratic Equations by Factoring 307
Collaborative Activities 316
Chapter Summary 316
Enriching Your Mathematical Word Power 318
Review Exercises 319
Chapter 6 Test 321
Making Connections Chapters 1–6 322
Chapter 7: Rational Expressions 323
7.1 Reducing Rational Expressions 324
7.2 Multiplication and Division 333
7.3 Finding the Least Common Denominator 340
7.4 Addition and Subtraction 346
7.5 Complex Fractions 354
7.6 Solving Equations with Rational Expressions 360
7.7 Applications of Ratios and Proportions 365
7.8 Applications of Rational Expressions 373
Collaborative Activities 380
Chapter Summary 381
Enriching Your Mathematical Word Power 382
Review Exercises 383
Chapter 7 Test 387
Making Connections Chapters 1–7 388Midtext Diagnostic Review 389
Chapter 8: Systems of Linear Equations and Inequalities 393
8.1 Solving Systems by Graphing and Substitution 394
8.2 The Addition Method 403
8.3 Systems of Linear Equations in Three Variables 411
8.4 Solving Linear Systems Using Matrices 418
8.5 Determinants and Cramer’s Rule 426
8.6 Graphing Linear Inequalities in Two Variables 436
8.7 Graphing Systems of Linear Inequalities 444
8.8 Linear Programming 451
Collaborative Activities 458
Chapter Summary 458
Enriching Your Mathematical Word Power 461
Review Exercises 462
Chapter 8 Test 465
Making Connections Chapters 1–8 466
Chapter 9: Radicals and Rational Exponents 467
9.1 Radicals 468
9.2 Rational Exponents 478
9.3 Operations with Radicals 487
9.4 More Operations with Radicals 493
9.5 Solving Equations with Radicals and Exponents 498
9.6 Complex Numbers 509
Collaborative Activities 517
Chapter Summary 517
Enriching Your Mathematical Word Power 520
Review Exercises 520
Chapter 9 Test 523
Making Connections Chapters 1–9 524
Chapter 10: Quadratic Equations, Functions, and Inequalities 525
10.1 Factoring and Completing the Square 526
10.2 The Quadratic Formula 535
10.3 Quadratic Functions and Their Graphs 543
10.4 More on Quadratic Equations 554
10.5 Quadratic and Rational Inequalities 562
Collaborative Activities 572
Chapter Summary 573
Enriching Your Mathematical Word Power 574
Review Exercises 575
Chapter 10 Test 579
Making Connections Chapters 1–10 580
Chapter 11: Functions 581
11.1 Graphs of Functions and Relations 582
11.2 Transformations of Graphs 592
11.3 Combining Functions 601
11.4 Inverse Functions 609
11.5 Variation 620
11.6 Synthetic Division and the Factor Theorem 628
Collaborative Activities 634
Chapter Summary 634
Enriching Your Mathematical Word Power 636
Review Exercises 637
Chapter 11 Test 641
Making Connections Chapters 1–11 643
Chapter 12: Exponential and Logarithmic Functions 645
12.1 Exponential Functions and Their Applications 646
12.2 Logarithmic Functions and Their Applications 657
12.3 Properties of Logarithms 665
12.4 Solving Equations and Applications 672
Collaborative Activities 680
Chapter Summary 681
Enriching Your Mathematical Word Power 682
Review Exercises 682
Chapter 12 Test 685
Making Connections Chapters 1–12 687
Chapter 13: Nonlinear Systems and the Conic Sections 689
13.1 Nonlinear Systems of Equations 690
13.2 The Parabola 698
13.3 The Circle 706
13.4 The Ellipse and Hyperbola 713
13.5 Second-Degree Inequalities 724
Collaborative Activities 730
Chapter Summary 730
Enriching Your Mathematical Word Power 733
Review Exercises 733
Chapter 13 Test 737
Making Connections Chapters 1–13 739
Chapter 14: Sequences and Series 741
14.1 Sequences 742
14.2 Series 748
14.3 Arithmetic Sequences and Series 752
14.4 Geometric Sequences and Series 757
14.5 Binomial Expansions 766
Collaborative Activities 772
Chapter Summary 772
Enriching Your Mathematical Word Power 774
Review Exercises 774
Chapter 14 Test 776
Making Connections Chapters 1–14 777
Appendix A-1
A Geometry Review A-1
B Table of Squares and Square Roots A-4
C Common Logarithms A-5 Answers A-7 Index I-1
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