Elementary Algebra for College Students
ST
– 10th Edition
SOLUTIONS
UV
MANUAL
IA
_A
Allen R. Angel
Dennis C. Runde
PP
RO
Comprehensive Solutions Manual for Instructors
and Students
VE
© Allen R. Angel & Dennis C. Runde
D?
All rights reserved. Reproduction or distribution without permission is prohibited.
??
©STUDYSTREAM
, Elementary 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 .............................................................36
1.9 Exponents, Parentheses, and the Order of Operations .................................................42
IA
1.10 Properties of the Real Number System ......................................................................50
Review Exercises ...............................................................................................................52
Practice Test .......................................................................................................................57
2. Solving Linear Equations and Inequalities ...........................................................................59
2.1 Combining Like Terms ................................................................................................59
_A
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 ...............91
PP
2.6 Formulas ....................................................................................................................101
2.7 Ratios and Proportions ...............................................................................................112
2.8 Inequalities in One Variable ......................................................................................120
Review Exercises .............................................................................................................128
Practice Test .....................................................................................................................138
RO
Cumulative Review Test ..................................................................................................141
3. Applications of Algebra .........................................................................................................143
3.1 Changing Application Problems into Equations ........................................................143
3.2 Solving Application Problems ...................................................................................147
Mid-Chapter Test: Sections 3.1–3.2 ....................................................................154
VE
3.3 Geometric Problems...................................................................................................155
3.4 Motion, Money, and Mixture Problems .....................................................................159
Review Exercises .............................................................................................................170
Practice Test .....................................................................................................................175
Cumulative Review Test ..................................................................................................178
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4. Exponents and Polynomials ..................................................................................................180
4.1 Exponents ...................................................................................................................180
4.2 Negative Exponents ...................................................................................................187
4.3 Scientific Notation .....................................................................................................193
Mid-Chapter Test: Sections 4.1–4.3 ....................................................................199
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4.4 Addition and Subtraction of Polynomials ..................................................................200
4.5 Multiplication of Polynomials ...................................................................................205
4.6 Division of Polynomials ............................................................................................212
, Review Exercises .............................................................................................................219
Practice Test .....................................................................................................................225
Cumulative Review Test ..................................................................................................226
ST
5. Factoring .................................................................................................................................229
5.1 Factoring a Monomial from a Polynomial .................................................................229
5.2 Factoring by Grouping ...............................................................................................233
5.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1 ...............................................237
5.4 Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1 ...............................................240
UV
Mid-Chapter Test: Sections 5.1–5.4 ....................................................................243
5.5 Special Factoring Formulas and a General Review of Factoring ..............................244
5.6 Solving Quadratic Equations Using Factoring ..........................................................249
5.7 Applications of Quadratic Equations .........................................................................254
Review Exercises .............................................................................................................261
IA
Practice Test .....................................................................................................................267
Cumulative Review Test ..................................................................................................268
6. Rational Expressions and Equations....................................................................................271
6.1 Simplifying Rational Expressions..............................................................................271
6.2 Multiplication and Division of Rational Expressions ................................................276
_A
6.3 Addition and Subtraction of Rational Expressions with a Common Denominator and
Finding the Least Common Denominator........................................................................285
6.4 Addition and Subtraction of Rational Expressions ....................................................294
Mid-Chapter Test: Sections 6.1–6.4 ....................................................................305
6.5 Complex Fractions .....................................................................................................307
PP
6.6 Solving Rational Equations........................................................................................313
6.7 Rational Equations: Applications and Problem Solving ............................................337
6.8 Variation ....................................................................................................................345
Review Exercises .............................................................................................................350
Practice Test .....................................................................................................................358
RO
Cumulative Review Test ..................................................................................................360
7. Graphing Linear Equations ..................................................................................................363
7.1 The Cartesian Coordinate System and Linear Equations in Two Variables ..............363
7.2 Graphing Linear Equations ........................................................................................366
7.3 Slope of a Line ...........................................................................................................376
VE
Mid-Chapter Test: Sections 7.1–7.3 ....................................................................379
7.4 Slope-Intercept and Point-Slope Forms of a Linear Equation ...................................380
7.5 Graphing Linear Inequalities .....................................................................................387
7.6 Functions ....................................................................................................................391
Review Exercises .............................................................................................................395
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Practice Test .....................................................................................................................399
Cumulative Review Test ..................................................................................................401
8. Systems of Linear Equations ................................................................................................404
8.1 Solving Systems of Equations Graphically................................................................404
8.2 Solving Systems of Equations by Substitution ..........................................................412
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8.3 Solving Systems of Equations by the Addition Method ............................................421
Mid-Chapter Test: Sections 8.1–8.3 ....................................................................435
8.4 Systems of Equations: Applications and Problem Solving........................................438
, 8.5 Solving Systems of Linear Inequalities .....................................................................451
Review Exercises .............................................................................................................452
Practice Test .....................................................................................................................459
ST
Cumulative Review Test ..................................................................................................463
9. Roots and Radicals.................................................................................................................465
9.1 Evaluating Square Roots ............................................................................................465
9.2 Simplifying Square Roots ..........................................................................................468
9.3 Adding, Subtracting, and Multiplying Square Roots .................................................473
UV
9.4 Dividing Square Roots ...............................................................................................479
Mid-Chapter Test: Sections 9.1–9.4 ....................................................................488
9.5 Solving Radical Equations .........................................................................................489
9.6 Radicals: Applications and Problem Solving ............................................................499
9.7 Higher Roots and Rational Exponents .......................................................................503
IA
Review Exercises .............................................................................................................506
Practice Test .....................................................................................................................512
Cumulative Review Test ..................................................................................................514
10. Quadratic Equations............................................................................................................516
10.1 The Square Root Property ........................................................................................516
_A
10.2 Solving Quadratic Equations by Completing the Square ........................................522
10.3 Solving Quadratic Equations by the Quadratic Formula .........................................536
Mid-Chapter Test: Sections 10.1–10.3 ................................................................552
10.4 Graphing Quadratic Equations .................................................................................555
10.5 Complex Numbers ...................................................................................................575
PP
Review Exercises .............................................................................................................580
Practice Test .....................................................................................................................598
Cumulative Review Test ..................................................................................................602
RO
VE
D?
??
ST
– 10th Edition
SOLUTIONS
UV
MANUAL
IA
_A
Allen R. Angel
Dennis C. Runde
PP
RO
Comprehensive Solutions Manual for Instructors
and Students
VE
© Allen R. Angel & Dennis C. Runde
D?
All rights reserved. Reproduction or distribution without permission is prohibited.
??
©STUDYSTREAM
, Elementary 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 .............................................................36
1.9 Exponents, Parentheses, and the Order of Operations .................................................42
IA
1.10 Properties of the Real Number System ......................................................................50
Review Exercises ...............................................................................................................52
Practice Test .......................................................................................................................57
2. Solving Linear Equations and Inequalities ...........................................................................59
2.1 Combining Like Terms ................................................................................................59
_A
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 ...............91
PP
2.6 Formulas ....................................................................................................................101
2.7 Ratios and Proportions ...............................................................................................112
2.8 Inequalities in One Variable ......................................................................................120
Review Exercises .............................................................................................................128
Practice Test .....................................................................................................................138
RO
Cumulative Review Test ..................................................................................................141
3. Applications of Algebra .........................................................................................................143
3.1 Changing Application Problems into Equations ........................................................143
3.2 Solving Application Problems ...................................................................................147
Mid-Chapter Test: Sections 3.1–3.2 ....................................................................154
VE
3.3 Geometric Problems...................................................................................................155
3.4 Motion, Money, and Mixture Problems .....................................................................159
Review Exercises .............................................................................................................170
Practice Test .....................................................................................................................175
Cumulative Review Test ..................................................................................................178
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4. Exponents and Polynomials ..................................................................................................180
4.1 Exponents ...................................................................................................................180
4.2 Negative Exponents ...................................................................................................187
4.3 Scientific Notation .....................................................................................................193
Mid-Chapter Test: Sections 4.1–4.3 ....................................................................199
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4.4 Addition and Subtraction of Polynomials ..................................................................200
4.5 Multiplication of Polynomials ...................................................................................205
4.6 Division of Polynomials ............................................................................................212
, Review Exercises .............................................................................................................219
Practice Test .....................................................................................................................225
Cumulative Review Test ..................................................................................................226
ST
5. Factoring .................................................................................................................................229
5.1 Factoring a Monomial from a Polynomial .................................................................229
5.2 Factoring by Grouping ...............................................................................................233
5.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1 ...............................................237
5.4 Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1 ...............................................240
UV
Mid-Chapter Test: Sections 5.1–5.4 ....................................................................243
5.5 Special Factoring Formulas and a General Review of Factoring ..............................244
5.6 Solving Quadratic Equations Using Factoring ..........................................................249
5.7 Applications of Quadratic Equations .........................................................................254
Review Exercises .............................................................................................................261
IA
Practice Test .....................................................................................................................267
Cumulative Review Test ..................................................................................................268
6. Rational Expressions and Equations....................................................................................271
6.1 Simplifying Rational Expressions..............................................................................271
6.2 Multiplication and Division of Rational Expressions ................................................276
_A
6.3 Addition and Subtraction of Rational Expressions with a Common Denominator and
Finding the Least Common Denominator........................................................................285
6.4 Addition and Subtraction of Rational Expressions ....................................................294
Mid-Chapter Test: Sections 6.1–6.4 ....................................................................305
6.5 Complex Fractions .....................................................................................................307
PP
6.6 Solving Rational Equations........................................................................................313
6.7 Rational Equations: Applications and Problem Solving ............................................337
6.8 Variation ....................................................................................................................345
Review Exercises .............................................................................................................350
Practice Test .....................................................................................................................358
RO
Cumulative Review Test ..................................................................................................360
7. Graphing Linear Equations ..................................................................................................363
7.1 The Cartesian Coordinate System and Linear Equations in Two Variables ..............363
7.2 Graphing Linear Equations ........................................................................................366
7.3 Slope of a Line ...........................................................................................................376
VE
Mid-Chapter Test: Sections 7.1–7.3 ....................................................................379
7.4 Slope-Intercept and Point-Slope Forms of a Linear Equation ...................................380
7.5 Graphing Linear Inequalities .....................................................................................387
7.6 Functions ....................................................................................................................391
Review Exercises .............................................................................................................395
D?
Practice Test .....................................................................................................................399
Cumulative Review Test ..................................................................................................401
8. Systems of Linear Equations ................................................................................................404
8.1 Solving Systems of Equations Graphically................................................................404
8.2 Solving Systems of Equations by Substitution ..........................................................412
??
8.3 Solving Systems of Equations by the Addition Method ............................................421
Mid-Chapter Test: Sections 8.1–8.3 ....................................................................435
8.4 Systems of Equations: Applications and Problem Solving........................................438
, 8.5 Solving Systems of Linear Inequalities .....................................................................451
Review Exercises .............................................................................................................452
Practice Test .....................................................................................................................459
ST
Cumulative Review Test ..................................................................................................463
9. Roots and Radicals.................................................................................................................465
9.1 Evaluating Square Roots ............................................................................................465
9.2 Simplifying Square Roots ..........................................................................................468
9.3 Adding, Subtracting, and Multiplying Square Roots .................................................473
UV
9.4 Dividing Square Roots ...............................................................................................479
Mid-Chapter Test: Sections 9.1–9.4 ....................................................................488
9.5 Solving Radical Equations .........................................................................................489
9.6 Radicals: Applications and Problem Solving ............................................................499
9.7 Higher Roots and Rational Exponents .......................................................................503
IA
Review Exercises .............................................................................................................506
Practice Test .....................................................................................................................512
Cumulative Review Test ..................................................................................................514
10. Quadratic Equations............................................................................................................516
10.1 The Square Root Property ........................................................................................516
_A
10.2 Solving Quadratic Equations by Completing the Square ........................................522
10.3 Solving Quadratic Equations by the Quadratic Formula .........................................536
Mid-Chapter Test: Sections 10.1–10.3 ................................................................552
10.4 Graphing Quadratic Equations .................................................................................555
10.5 Complex Numbers ...................................................................................................575
PP
Review Exercises .............................................................................................................580
Practice Test .....................................................................................................................598
Cumulative Review Test ..................................................................................................602
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