SOLUTIONS MANUAL
For
A LGEBRA FOR COLLEGE
S TUDENTS
TENTH EDITION
By
Lial/Hornsby/McGinnis/Daniels
PART 1: SOLUTIONS MANUAL: Page 1-1137
PART 2: STUDENT SOLUTIONS MANUAL: Page 1138-1839
PART 3: INSTRUCTOR'S MANUAL: Page 1840-2372
, Table of Contents
R Review of the Real Number System....................................................................................................... 1
R.1 Fractions • .......................................................................................................................... 1
R.2 Decimals and Percents • .................................................................................................... 13
R.3 Basic Concepts from Algebra • ......................................................................................... 23
R.4 Operations on Real Numbers • .......................................................................................... 28
R.5 Exponents, Roots, and Order of Operations • .................................................................... 35
R.6 Properties of Real Numbers • ............................................................................................ 42
Chapter R Test • ................................................................................................................ 47
1 Linear Equations, Inequalities, and Applications ............................................................................. 49
1.1 Linear Equations in One Variable • ................................................................................... 49
1.2 Formulas and Percent • ...................................................................................................... 61
1.3 Applications of Linear Equations • .................................................................................... 72
1.4 Further Applications of Linear Equations • ....................................................................... 85
Summary Exercises Applying Problem-Solving Techniques • ........................................... 94
1.5 Linear Inequalities in One Variable • ................................................................................ 98
1.6 Set Operations and Compound Inequalities • .................................................................... 111
1.7 Absolute Value Equations and Inequalities •..................................................................... 120
Summary Exercises Solving Linear and Absolute Value Equations
and Inequalities • .................................................................................................... 135
Chapter 1 Review Exercises •............................................................................................ 138
Chapter 1 Mixed Review Exercises • ................................................................................ 145
Chapter 1 Test • ................................................................................................................. 147
Chapters R and 1 Cumulative Review Exercises• ............................................................. 151
2 Linear Equations, Graphs, and Functions ........................................................................................154
2.1 Linear Equations in Two Variables • ................................................................................. 154
2.2 The Slope of a Line • ......................................................................................................... 170
2.3 Writing Equations of Lines • ............................................................................................. 184
Summary Exercises Finding Slopes and Equations of Lines • ........................................... 197
2.4 Linear Inequalities in Two Variables • .............................................................................. 200
2.5 Introduction to Relations and Functions • ......................................................................... 210
2.6 Function Notation and Linear Functions • ......................................................................... 217
Chapter 2 Review Exercises •............................................................................................ 225
Chapter 2 Mixed Review Exercises • ................................................................................ 231
Chapter 2 Test • ................................................................................................................. 232
Chapters R2 Cumulative Review Exercises • .................................................................. 235
Copyright © 2025 Pearson Education, Inc.
,3 Systems of Linear Equations ..............................................................................................................238
3.1 Systems of Linear Equations in Two Variables • .............................................................. 238
3.2 Systems of Linear Equations in Three Variables • ............................................................ 259
3.3 Applications of Systems of Linear Equations • ................................................................. 279
Chapter 3 Review Exercises •............................................................................................ 299
Chapter 3 Mixed Review Exercises • ................................................................................ 305
Chapter 3 Test • ................................................................................................................. 308
Chapters R3 Cumulative Review Exercises • .................................................................. 312
4 Exponents, Polynomials, and Polynomial Functions........................................................................316
4.1 Integer Exponents • ........................................................................................................... 316
4.2 Scientific Notation • .......................................................................................................... 325
4.3 Adding and Subtracting Polynomials • .............................................................................. 330
4.4 Polynomial Functions, Graphs, and Composition • ........................................................... 336
4.5 Multiplying Polynomials • ................................................................................................. 350
4.6 Dividing Polynomials •...................................................................................................... 362
Chapter 4 Review Exercises •............................................................................................ 373
Chapter 4 Mixed Review Exercises • ................................................................................ 379
Chapter 4 Test • ................................................................................................................. 380
Chapters R4 Cumulative Review Exercises • .................................................................. 383
5 Factoring ..............................................................................................................................................388
5.1 Greatest Common Factors and Factoring by Grouping • .................................................... 388
5.2 Factoring Trinomials •......................................................................................................... 395
5.3 Special Factoring • .............................................................................................................. 403
5.4 A General Approach to Factoring • ..................................................................................... 411
5.5 Solving Equations by the Zero-Factor Property •................................................................ 419
Chapter 5 Review Exercises • ............................................................................................. 432
Chapter 5 Mixed Review Exercises • .................................................................................. 437
Chapter 5 Test • ................................................................................................................... 438
Chapters R5 Cumulative Review Exercises • ................................................................... 440
Copyright © 2025 Pearson Education, Inc.
, 6 Rational Expressions and Functions .................................................................................................444
6.1 Rational Expressions and Functions; Multiplying and Dividing • ...................................... 444
6.2 Adding and Subtracting Rational Expressions •.................................................................. 453
6.3 Complex Fractions • ............................................................................................................ 467
6.4 Equations with Rational Expressions and Graphs • ............................................................ 479
Summary Exercises Simplifying Rational Expressions vs. Solving
Rational Equations • ................................................................................................ 493
6.5 Applications of Rational Expressions • ............................................................................... 498
6.6 Variation • ........................................................................................................................... 514
Chapter 6 Review Exercises • ............................................................................................. 524
Chapter 6 Mixed Review Exercises • .................................................................................. 530
Chapter 6 Test • ................................................................................................................... 533
Chapters R6 Cumulative Review Exercises • ................................................................... 537
7 Roots, Radicals, and Root Functions .................................................................................................543
7.1 Radical Expressions and Graphs • ....................................................................................... 543
7.2 Rational Exponents • ........................................................................................................... 550
7.3 Simplifying Radicals, the Distance Formula, and Circles • ................................................ 558
7.4 Adding and Subtracting Radical Expressions • ................................................................... 571
7.5 Multiplying and Dividing Radical Expressions • ................................................................ 579
Summary Exercises Performing Operations with Radicals and
Rational Exponents • ................................................................................................ 591
7.6 Solving Equations with Radicals • ...................................................................................... 593
7.7 Complex Numbers • ............................................................................................................ 606
Chapter 7 Review Exercises • ............................................................................................. 614
Chapter 7 Mixed Review Exercises • .................................................................................. 621
Chapter 7 Test • ................................................................................................................... 623
Chapters R7 Cumulative Review Exercises • ................................................................... 626
Copyright © 2025 Pearson Education, Inc.
For
A LGEBRA FOR COLLEGE
S TUDENTS
TENTH EDITION
By
Lial/Hornsby/McGinnis/Daniels
PART 1: SOLUTIONS MANUAL: Page 1-1137
PART 2: STUDENT SOLUTIONS MANUAL: Page 1138-1839
PART 3: INSTRUCTOR'S MANUAL: Page 1840-2372
, Table of Contents
R Review of the Real Number System....................................................................................................... 1
R.1 Fractions • .......................................................................................................................... 1
R.2 Decimals and Percents • .................................................................................................... 13
R.3 Basic Concepts from Algebra • ......................................................................................... 23
R.4 Operations on Real Numbers • .......................................................................................... 28
R.5 Exponents, Roots, and Order of Operations • .................................................................... 35
R.6 Properties of Real Numbers • ............................................................................................ 42
Chapter R Test • ................................................................................................................ 47
1 Linear Equations, Inequalities, and Applications ............................................................................. 49
1.1 Linear Equations in One Variable • ................................................................................... 49
1.2 Formulas and Percent • ...................................................................................................... 61
1.3 Applications of Linear Equations • .................................................................................... 72
1.4 Further Applications of Linear Equations • ....................................................................... 85
Summary Exercises Applying Problem-Solving Techniques • ........................................... 94
1.5 Linear Inequalities in One Variable • ................................................................................ 98
1.6 Set Operations and Compound Inequalities • .................................................................... 111
1.7 Absolute Value Equations and Inequalities •..................................................................... 120
Summary Exercises Solving Linear and Absolute Value Equations
and Inequalities • .................................................................................................... 135
Chapter 1 Review Exercises •............................................................................................ 138
Chapter 1 Mixed Review Exercises • ................................................................................ 145
Chapter 1 Test • ................................................................................................................. 147
Chapters R and 1 Cumulative Review Exercises• ............................................................. 151
2 Linear Equations, Graphs, and Functions ........................................................................................154
2.1 Linear Equations in Two Variables • ................................................................................. 154
2.2 The Slope of a Line • ......................................................................................................... 170
2.3 Writing Equations of Lines • ............................................................................................. 184
Summary Exercises Finding Slopes and Equations of Lines • ........................................... 197
2.4 Linear Inequalities in Two Variables • .............................................................................. 200
2.5 Introduction to Relations and Functions • ......................................................................... 210
2.6 Function Notation and Linear Functions • ......................................................................... 217
Chapter 2 Review Exercises •............................................................................................ 225
Chapter 2 Mixed Review Exercises • ................................................................................ 231
Chapter 2 Test • ................................................................................................................. 232
Chapters R2 Cumulative Review Exercises • .................................................................. 235
Copyright © 2025 Pearson Education, Inc.
,3 Systems of Linear Equations ..............................................................................................................238
3.1 Systems of Linear Equations in Two Variables • .............................................................. 238
3.2 Systems of Linear Equations in Three Variables • ............................................................ 259
3.3 Applications of Systems of Linear Equations • ................................................................. 279
Chapter 3 Review Exercises •............................................................................................ 299
Chapter 3 Mixed Review Exercises • ................................................................................ 305
Chapter 3 Test • ................................................................................................................. 308
Chapters R3 Cumulative Review Exercises • .................................................................. 312
4 Exponents, Polynomials, and Polynomial Functions........................................................................316
4.1 Integer Exponents • ........................................................................................................... 316
4.2 Scientific Notation • .......................................................................................................... 325
4.3 Adding and Subtracting Polynomials • .............................................................................. 330
4.4 Polynomial Functions, Graphs, and Composition • ........................................................... 336
4.5 Multiplying Polynomials • ................................................................................................. 350
4.6 Dividing Polynomials •...................................................................................................... 362
Chapter 4 Review Exercises •............................................................................................ 373
Chapter 4 Mixed Review Exercises • ................................................................................ 379
Chapter 4 Test • ................................................................................................................. 380
Chapters R4 Cumulative Review Exercises • .................................................................. 383
5 Factoring ..............................................................................................................................................388
5.1 Greatest Common Factors and Factoring by Grouping • .................................................... 388
5.2 Factoring Trinomials •......................................................................................................... 395
5.3 Special Factoring • .............................................................................................................. 403
5.4 A General Approach to Factoring • ..................................................................................... 411
5.5 Solving Equations by the Zero-Factor Property •................................................................ 419
Chapter 5 Review Exercises • ............................................................................................. 432
Chapter 5 Mixed Review Exercises • .................................................................................. 437
Chapter 5 Test • ................................................................................................................... 438
Chapters R5 Cumulative Review Exercises • ................................................................... 440
Copyright © 2025 Pearson Education, Inc.
, 6 Rational Expressions and Functions .................................................................................................444
6.1 Rational Expressions and Functions; Multiplying and Dividing • ...................................... 444
6.2 Adding and Subtracting Rational Expressions •.................................................................. 453
6.3 Complex Fractions • ............................................................................................................ 467
6.4 Equations with Rational Expressions and Graphs • ............................................................ 479
Summary Exercises Simplifying Rational Expressions vs. Solving
Rational Equations • ................................................................................................ 493
6.5 Applications of Rational Expressions • ............................................................................... 498
6.6 Variation • ........................................................................................................................... 514
Chapter 6 Review Exercises • ............................................................................................. 524
Chapter 6 Mixed Review Exercises • .................................................................................. 530
Chapter 6 Test • ................................................................................................................... 533
Chapters R6 Cumulative Review Exercises • ................................................................... 537
7 Roots, Radicals, and Root Functions .................................................................................................543
7.1 Radical Expressions and Graphs • ....................................................................................... 543
7.2 Rational Exponents • ........................................................................................................... 550
7.3 Simplifying Radicals, the Distance Formula, and Circles • ................................................ 558
7.4 Adding and Subtracting Radical Expressions • ................................................................... 571
7.5 Multiplying and Dividing Radical Expressions • ................................................................ 579
Summary Exercises Performing Operations with Radicals and
Rational Exponents • ................................................................................................ 591
7.6 Solving Equations with Radicals • ...................................................................................... 593
7.7 Complex Numbers • ............................................................................................................ 606
Chapter 7 Review Exercises • ............................................................................................. 614
Chapter 7 Mixed Review Exercises • .................................................................................. 621
Chapter 7 Test • ................................................................................................................... 623
Chapters R7 Cumulative Review Exercises • ................................................................... 626
Copyright © 2025 Pearson Education, Inc.
