Elementary and Intermediate Algebra for
College Students – 5th Edition
ST
SOLUTIONS
UV
INSTRUCTOR’S
IA
_A
MANUAL
PP
Allen R. Angel
RO
Dennis C. Runde
VE
Comprehensive Solutions Manual for Instructors and
D?
Students
??
© Allen R. Angel & Dennis C. Runde
All rights reserved. Reproduction or distribution without permission is prohibited.
©STUDYSTREAM
, Elementary and Intermediate Algebra For College Students
Table of Contents
1. Real Numbers ............................................................................................................................ 1
ST
1.1 Study Skills for Success in Mathematics ...................................................................... 1
1.2 Problem Solving ........................................................................................................... 1
1.3 Fractions........................................................................................................................ 6
1.4 The Real Number System ........................................................................................... 15
1.5 Inequalities and Absolute Value ................................................................................. 17
UV
Mid-Chapter Test: Sections 1.1–1.5 ..................................................................... 21
1.6 Addition of Real Numbers .......................................................................................... 22
1.7 Subtraction of Real Numbers ...................................................................................... 29
1.8 Multiplication and Division of Real Numbers ............................................................ 35
1.9 Exponents, Parentheses, and the Order of Operations ................................................ 41
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1.10 Properties of the Real Number System ..................................................................... 50
Review Exercises ............................................................................................................. 52
Practice Test ...................................................................................................................... 57
2. Solving Linear Equations ....................................................................................................... 59
_A
2.1 Combining Like Terms ............................................................................................... 59
2.2 The Addition Property of Equality ............................................................................. 64
2.3 The Multiplication Property of Equality ..................................................................... 71
2.4 Solving Linear Equations with a Variable on Only One Side of the Equation........... 79
Mid-Chapter Test: Sections 2.1–2.4 ..................................................................... 89
2.5 Solving Linear Equations with the Variable on Both Sides of the Equation .............. 90
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2.6 Formulas ................................................................................................................... 101
2.7 Ratios and Proportions .............................................................................................. 112
Review Exercises ............................................................................................................ 119
Practice Test .................................................................................................................... 128
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Cumulative Review Test ................................................................................................. 130
3. Applications of Algebra ........................................................................................................ 132
3.1 Changing Application Problems into Equations ....................................................... 132
3.2 Solving Application Problems .................................................................................. 136
Mid-Chapter Test: Sections 3.1–3.2 ................................................................... 143
3.3 Geometric Problems.................................................................................................. 144
VE
3.4 Motion, Money, and Mixture Problems.................................................................... 148
Review Exercises ............................................................................................................ 158
Practice Test .................................................................................................................... 163
Cumulative Review Test ................................................................................................. 165
4. Graphing Linear Equations ................................................................................................. 168
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4.1 The Cartesian Coordinate System and Linear Equations in Two Variables ............. 168
4.2 Graphing Linear Equations ....................................................................................... 171
4.3 Slope of a Line .......................................................................................................... 180
Mid-Chapter Test: Sections 4.1–4.3 ................................................................... 183
4.4 Slope-Intercept and Point-Slope Forms of a Linear Equation .................................. 185
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Review Exercises ............................................................................................................ 191
Practice Test .................................................................................................................... 194
Cumulative Review Test ................................................................................................. 196
, 5. Exponents and Polynomials ................................................................................................. 198
5.1 Exponents.................................................................................................................. 198
5.2 Negative Exponents .................................................................................................. 204
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5.3 Scientific Notation .................................................................................................... 211
Mid-Chapter Test: Sections 5.1–5.3 ................................................................... 217
5.4 Addition and Subtraction of Polynomials ................................................................. 217
5.5 Multiplication of Polynomials .................................................................................. 223
5.6 Division of Polynomials ........................................................................................... 230
UV
Review Exercises ............................................................................................................ 237
Practice Test .................................................................................................................... 243
Cumulative Review Test ................................................................................................. 245
6. Factoring ................................................................................................................................ 247
6.1 Factoring a Monomial from a Polynomial ................................................................ 247
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6.2 Factoring by Grouping .............................................................................................. 251
6.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1 .............................................. 255
6.4 Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1 .............................................. 258
Mid-Chapter Test: Sections 6.1–6.4 ................................................................... 261
_A
6.5 Special Factoring Formulas and a General Review of Factoring ............................. 262
6.6 Solving Quadratic Equations Using Factoring ......................................................... 267
6.7 Applications of Quadratic Equations ........................................................................ 272
Review Exercises ............................................................................................................ 278
Practice Test .................................................................................................................... 284
Cumulative Review Test ................................................................................................. 285
PP
7. Rational Expressions and Equations................................................................................... 288
7.1 Simplifying Rational Expressions............................................................................. 288
7.2 Multiplication and Division of Rational Expressions ............................................... 293
7.3 Addition and Subtraction of Rational Expressions with a Common
RO
Denominator and Determining the Least Common Denominator ............................ 301
7.4 Addition and Subtraction of Rational Expressions ................................................... 310
Mid-Chapter Test: Sections 7.1–7.4 ................................................................... 322
7.5 Complex Fractions .................................................................................................... 324
7.6 Solving Rational Equations....................................................................................... 330
7.7 Rational Equations: Applications and Problem Solving........................................... 352
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7.8 Variation ................................................................................................................... 360
Review Exercises ............................................................................................................ 368
Practice Test .................................................................................................................... 377
Cumulative Review Test ................................................................................................. 379
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, 8. Functions and Their Graphs ................................................................................................ 382
8.1 More on Graphs ........................................................................................................ 382
8.2 Functions ................................................................................................................... 389
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8.3 Linear Functions ....................................................................................................... 395
Mid-Chapter Test: Sections 8.1–8.3 ................................................................... 406
8.4 Slope, Modeling, and Linear Relationships .............................................................. 408
8.5 The Algebra of Functions ......................................................................................... 421
Review Exercises ............................................................................................................ 427
UV
Practice Test .................................................................................................................... 435
Cumulative Review Test ................................................................................................. 437
9. Systems of Linear Equations ............................................................................................... 440
9.1 Solving Systems of Equations Graphically............................................................... 440
9.2 Solving Systems of Equations by Substitution ......................................................... 448
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9.3 Solving Systems of Equations by the Addition Method ........................................... 457
9.4 Solving Systems of Linear Equations in Three Variables ........................................ 469
Mid-Chapter Test: Sections 9.1–9.4 ................................................................... 487
9.5 Systems of Linear Equations: Applications and Problem Solving ........................... 490
_A
9.6 Solving Systems of Equations Using Matrices ......................................................... 507
9.7 Solving Systems of Equations Using Determinants and Cramer’s Rule .................. 521
Review Exercises ............................................................................................................ 539
Practice Test .................................................................................................................... 551
Cumulative Review Test ................................................................................................. 556
10. Inequalities in One and Two Variables............................................................................. 560
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10.1 Solving Linear Inequalities in One Variable .......................................................... 560
10.2 Solving Equations and Inequalities Containing Absolute Values .......................... 571
Mid-Chapter Test: Sections 10.1–10.2 ............................................................... 584
10.3 Graphing Linear Inequalities in Two Variables and Systems
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of Linear Inequalities .............................................................................................. 586
Review Exercises ............................................................................................................ 604
Practice Test .................................................................................................................... 611
Cumulative Review Test ................................................................................................. 613
11. Roots, Radicals, and Complex Numbers........................................................................... 616
11.1 Roots and Radicals.................................................................................................. 616
VE
11.2 Rational Exponents ................................................................................................. 622
11.3 Simplifying Radicals............................................................................................... 629
11.4 Adding, Subtracting, and Multiplying Radicals ..................................................... 634
Mid-Chapter Test: Sections 11.1–11.4 ............................................................... 643
11.5 Dividing Radicals.................................................................................................... 644
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11.6 Solving Radical Equations ...................................................................................... 658
11.7 Complex Numbers .................................................................................................. 680
Review Exercises ............................................................................................................ 693
Practice Test .................................................................................................................... 706
Cumulative Review Test ................................................................................................. 708
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College Students – 5th Edition
ST
SOLUTIONS
UV
INSTRUCTOR’S
IA
_A
MANUAL
PP
Allen R. Angel
RO
Dennis C. Runde
VE
Comprehensive Solutions Manual for Instructors and
D?
Students
??
© Allen R. Angel & Dennis C. Runde
All rights reserved. Reproduction or distribution without permission is prohibited.
©STUDYSTREAM
, Elementary and Intermediate Algebra For College Students
Table of Contents
1. Real Numbers ............................................................................................................................ 1
ST
1.1 Study Skills for Success in Mathematics ...................................................................... 1
1.2 Problem Solving ........................................................................................................... 1
1.3 Fractions........................................................................................................................ 6
1.4 The Real Number System ........................................................................................... 15
1.5 Inequalities and Absolute Value ................................................................................. 17
UV
Mid-Chapter Test: Sections 1.1–1.5 ..................................................................... 21
1.6 Addition of Real Numbers .......................................................................................... 22
1.7 Subtraction of Real Numbers ...................................................................................... 29
1.8 Multiplication and Division of Real Numbers ............................................................ 35
1.9 Exponents, Parentheses, and the Order of Operations ................................................ 41
IA
1.10 Properties of the Real Number System ..................................................................... 50
Review Exercises ............................................................................................................. 52
Practice Test ...................................................................................................................... 57
2. Solving Linear Equations ....................................................................................................... 59
_A
2.1 Combining Like Terms ............................................................................................... 59
2.2 The Addition Property of Equality ............................................................................. 64
2.3 The Multiplication Property of Equality ..................................................................... 71
2.4 Solving Linear Equations with a Variable on Only One Side of the Equation........... 79
Mid-Chapter Test: Sections 2.1–2.4 ..................................................................... 89
2.5 Solving Linear Equations with the Variable on Both Sides of the Equation .............. 90
PP
2.6 Formulas ................................................................................................................... 101
2.7 Ratios and Proportions .............................................................................................. 112
Review Exercises ............................................................................................................ 119
Practice Test .................................................................................................................... 128
RO
Cumulative Review Test ................................................................................................. 130
3. Applications of Algebra ........................................................................................................ 132
3.1 Changing Application Problems into Equations ....................................................... 132
3.2 Solving Application Problems .................................................................................. 136
Mid-Chapter Test: Sections 3.1–3.2 ................................................................... 143
3.3 Geometric Problems.................................................................................................. 144
VE
3.4 Motion, Money, and Mixture Problems.................................................................... 148
Review Exercises ............................................................................................................ 158
Practice Test .................................................................................................................... 163
Cumulative Review Test ................................................................................................. 165
4. Graphing Linear Equations ................................................................................................. 168
D?
4.1 The Cartesian Coordinate System and Linear Equations in Two Variables ............. 168
4.2 Graphing Linear Equations ....................................................................................... 171
4.3 Slope of a Line .......................................................................................................... 180
Mid-Chapter Test: Sections 4.1–4.3 ................................................................... 183
4.4 Slope-Intercept and Point-Slope Forms of a Linear Equation .................................. 185
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Review Exercises ............................................................................................................ 191
Practice Test .................................................................................................................... 194
Cumulative Review Test ................................................................................................. 196
, 5. Exponents and Polynomials ................................................................................................. 198
5.1 Exponents.................................................................................................................. 198
5.2 Negative Exponents .................................................................................................. 204
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5.3 Scientific Notation .................................................................................................... 211
Mid-Chapter Test: Sections 5.1–5.3 ................................................................... 217
5.4 Addition and Subtraction of Polynomials ................................................................. 217
5.5 Multiplication of Polynomials .................................................................................. 223
5.6 Division of Polynomials ........................................................................................... 230
UV
Review Exercises ............................................................................................................ 237
Practice Test .................................................................................................................... 243
Cumulative Review Test ................................................................................................. 245
6. Factoring ................................................................................................................................ 247
6.1 Factoring a Monomial from a Polynomial ................................................................ 247
IA
6.2 Factoring by Grouping .............................................................................................. 251
6.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1 .............................................. 255
6.4 Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1 .............................................. 258
Mid-Chapter Test: Sections 6.1–6.4 ................................................................... 261
_A
6.5 Special Factoring Formulas and a General Review of Factoring ............................. 262
6.6 Solving Quadratic Equations Using Factoring ......................................................... 267
6.7 Applications of Quadratic Equations ........................................................................ 272
Review Exercises ............................................................................................................ 278
Practice Test .................................................................................................................... 284
Cumulative Review Test ................................................................................................. 285
PP
7. Rational Expressions and Equations................................................................................... 288
7.1 Simplifying Rational Expressions............................................................................. 288
7.2 Multiplication and Division of Rational Expressions ............................................... 293
7.3 Addition and Subtraction of Rational Expressions with a Common
RO
Denominator and Determining the Least Common Denominator ............................ 301
7.4 Addition and Subtraction of Rational Expressions ................................................... 310
Mid-Chapter Test: Sections 7.1–7.4 ................................................................... 322
7.5 Complex Fractions .................................................................................................... 324
7.6 Solving Rational Equations....................................................................................... 330
7.7 Rational Equations: Applications and Problem Solving........................................... 352
VE
7.8 Variation ................................................................................................................... 360
Review Exercises ............................................................................................................ 368
Practice Test .................................................................................................................... 377
Cumulative Review Test ................................................................................................. 379
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, 8. Functions and Their Graphs ................................................................................................ 382
8.1 More on Graphs ........................................................................................................ 382
8.2 Functions ................................................................................................................... 389
ST
8.3 Linear Functions ....................................................................................................... 395
Mid-Chapter Test: Sections 8.1–8.3 ................................................................... 406
8.4 Slope, Modeling, and Linear Relationships .............................................................. 408
8.5 The Algebra of Functions ......................................................................................... 421
Review Exercises ............................................................................................................ 427
UV
Practice Test .................................................................................................................... 435
Cumulative Review Test ................................................................................................. 437
9. Systems of Linear Equations ............................................................................................... 440
9.1 Solving Systems of Equations Graphically............................................................... 440
9.2 Solving Systems of Equations by Substitution ......................................................... 448
IA
9.3 Solving Systems of Equations by the Addition Method ........................................... 457
9.4 Solving Systems of Linear Equations in Three Variables ........................................ 469
Mid-Chapter Test: Sections 9.1–9.4 ................................................................... 487
9.5 Systems of Linear Equations: Applications and Problem Solving ........................... 490
_A
9.6 Solving Systems of Equations Using Matrices ......................................................... 507
9.7 Solving Systems of Equations Using Determinants and Cramer’s Rule .................. 521
Review Exercises ............................................................................................................ 539
Practice Test .................................................................................................................... 551
Cumulative Review Test ................................................................................................. 556
10. Inequalities in One and Two Variables............................................................................. 560
PP
10.1 Solving Linear Inequalities in One Variable .......................................................... 560
10.2 Solving Equations and Inequalities Containing Absolute Values .......................... 571
Mid-Chapter Test: Sections 10.1–10.2 ............................................................... 584
10.3 Graphing Linear Inequalities in Two Variables and Systems
RO
of Linear Inequalities .............................................................................................. 586
Review Exercises ............................................................................................................ 604
Practice Test .................................................................................................................... 611
Cumulative Review Test ................................................................................................. 613
11. Roots, Radicals, and Complex Numbers........................................................................... 616
11.1 Roots and Radicals.................................................................................................. 616
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11.2 Rational Exponents ................................................................................................. 622
11.3 Simplifying Radicals............................................................................................... 629
11.4 Adding, Subtracting, and Multiplying Radicals ..................................................... 634
Mid-Chapter Test: Sections 11.1–11.4 ............................................................... 643
11.5 Dividing Radicals.................................................................................................... 644
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11.6 Solving Radical Equations ...................................................................................... 658
11.7 Complex Numbers .................................................................................................. 680
Review Exercises ............................................................................................................ 693
Practice Test .................................................................................................................... 706
Cumulative Review Test ................................................................................................. 708
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