INSTRUCTOR’S SOLUTIONS
MANUAL
College Algebra | 6th edition
By Mark Dugopolski
TU
TO
R
G
U
R
U
,Table of Content
P. Prerequisites
P.1 Real Numbers and Their Properties
P.2 Integral Exponents and Scientific Notation
P.3 Rational Exponents and Radicals
P.4 Polynomials
P.5 Factoring Polynomials
P.6 Rational Expressions
P.7 Complex Numbers
1. Equations, Inequalities, and Modeling
1.1 Linear, Rational, and Absolute Value Equations
1.2 Constructing Models to Solve Problems
1.3 Equations and Graphs in Two Variables
TU
1.4 Linear Equations in Two Variables
1.5 Quadratic Equation
1.6 Miscellaneous Equations
1.7 Linear and Absolute Value Inequalities
2. Functions and Graphs
2.1 Functions
TO
2.2 Graphs of Relations and Functions
2.3 Families of Functions, Transformations, and Symmetry
2.4 Operations with Functions
2.5 Inverse Functions
2.6 Constructing Functions with Variation
3. Polynomial and Rational Functions
R
3.1 Quadratic Functions and Inequalities
3.2 Zeros of Polynomial Functions
3.3 The Theory of Equations
G
3.4 Graphs of Polynomial Functions
3.5 Rational Functions and Inequalities
4. Exponential and Logarithmic Functions
U
4.1 Exponential Functions and Their Applications
4.2 Logarithmic Functions and Their Applications
4.3 Rules of Logarithms
R
4.4 More Equations and Applications
5. Systems of Equations and Inequalities
5.1 Systems of Linear Equations in Two Variables
U
5.2 Systems of Linear Equations in Three Variables
5.3 Nonlinear Systems of Equations
5.4 Partial Fractions
5.5 Inequalities and Systems of Inequalities in Two Variables
5.6 The Linear Programming Model
6. Matrices and Determinants
6.1 Solving Linear Systems Using Matrices
6.2 Operations with Matrices
6.3 Multiplication of Matrices
6.4 Inverses of Matrices
6.5 Solution of Linear Systems in Two Variables Using Determinants
6.6 Solution of Linear Systems in Three Variables Using Determinants
7. The Conic Sections
,7.1 The Parabola
7.2 The Ellipse and the Circle
7.3 The Hyperbola
8. Sequences, Series, and Probability
8.1 Sequences and Arithmetic Sequences
8.2 Series and Arithmetic Series
8.3 Geometric Sequences and Series
8.4 Counting and Permutations
8.5 Combinations, Labeling, and the Binomial Theorem
8.6 Probability
8.7 Mathematical Induction
TU
TO
R
G
U
R
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, 34 Chapter 1 Equations, Inequalities, and Modeling
For Thought 1
17. Since 14x = 7, the solution set is .
2
1. True, since 5(1) = 6 − 1.
18. Since −2x = 2, the solution set is {−1}.
2. True, since x = 3 is the solution to both
equations. 19. Since 7 + 3x = 4x − 4, the solution set is {11}.
3. False, −2 20. Since −3x + 15 = 4 − 2x, the solution set
√ is not a solution of the first equation is {11}.
since −2 is not a real number.
4
4. True, since x − x = 0. 21. Since x = − · 18, the solution set is {−24}.
TU
3
5. False, x = 0 is the solution. 6. True 3
27
22. Since x = · (−9), the solution set is − .
7. False, since |x| = −8 has no solution. 2 2
x 23. Multiplying by 6 we get
8. False, is undefined at x = 5.
x−5
3x − 30 = −72 − 4x
TO
3
9. False, since we should multiply by − . 7x = −42.
2
10. False, 0 · x + 1 = 0 has no solution. The solution set is {−6}.
24. Multiplying by 4 we obtain
1.1 Exercises
R
x − 12 = 2x + 12
1. equation −24 = x.
2. linear
G
The solution set is {−24}.
3. equivalent
25. Multiply both sides of the equation by 12.
4. solution set
18x + 4 = 3x − 2
U
5. identity
15x = −6
6. inconsistent equation 2
x = − .
5
R
7. conditional equation
2
8. extraneous root The solution set is − .
5
U
9. No, since 2(3) − 4 = 2 6= 9. 10. Yes 26. Multiply both sides of the equation by 30.
11. Yes, since (−4)2 = 16.
15x + 6x = 5x − 10
√
12. No, since 16 6= −4. 16x = −10
5
x = − .
5
13. Since 3x = 5, the solution set is . 8
3
3 5
14. Since −2x = −3, the solution set is . The solution set is − .
2 8
15. Since −3x = 6, the solution set is {−2}. 27. Note, 3(x − 6) = 3x − 18 is true by the
distributive law. It is an identity and the
16. Since 5x = −10, the solution set is {−2}. solution set is R.
Copyright 2015 Pearson Education, Inc.
MANUAL
College Algebra | 6th edition
By Mark Dugopolski
TU
TO
R
G
U
R
U
,Table of Content
P. Prerequisites
P.1 Real Numbers and Their Properties
P.2 Integral Exponents and Scientific Notation
P.3 Rational Exponents and Radicals
P.4 Polynomials
P.5 Factoring Polynomials
P.6 Rational Expressions
P.7 Complex Numbers
1. Equations, Inequalities, and Modeling
1.1 Linear, Rational, and Absolute Value Equations
1.2 Constructing Models to Solve Problems
1.3 Equations and Graphs in Two Variables
TU
1.4 Linear Equations in Two Variables
1.5 Quadratic Equation
1.6 Miscellaneous Equations
1.7 Linear and Absolute Value Inequalities
2. Functions and Graphs
2.1 Functions
TO
2.2 Graphs of Relations and Functions
2.3 Families of Functions, Transformations, and Symmetry
2.4 Operations with Functions
2.5 Inverse Functions
2.6 Constructing Functions with Variation
3. Polynomial and Rational Functions
R
3.1 Quadratic Functions and Inequalities
3.2 Zeros of Polynomial Functions
3.3 The Theory of Equations
G
3.4 Graphs of Polynomial Functions
3.5 Rational Functions and Inequalities
4. Exponential and Logarithmic Functions
U
4.1 Exponential Functions and Their Applications
4.2 Logarithmic Functions and Their Applications
4.3 Rules of Logarithms
R
4.4 More Equations and Applications
5. Systems of Equations and Inequalities
5.1 Systems of Linear Equations in Two Variables
U
5.2 Systems of Linear Equations in Three Variables
5.3 Nonlinear Systems of Equations
5.4 Partial Fractions
5.5 Inequalities and Systems of Inequalities in Two Variables
5.6 The Linear Programming Model
6. Matrices and Determinants
6.1 Solving Linear Systems Using Matrices
6.2 Operations with Matrices
6.3 Multiplication of Matrices
6.4 Inverses of Matrices
6.5 Solution of Linear Systems in Two Variables Using Determinants
6.6 Solution of Linear Systems in Three Variables Using Determinants
7. The Conic Sections
,7.1 The Parabola
7.2 The Ellipse and the Circle
7.3 The Hyperbola
8. Sequences, Series, and Probability
8.1 Sequences and Arithmetic Sequences
8.2 Series and Arithmetic Series
8.3 Geometric Sequences and Series
8.4 Counting and Permutations
8.5 Combinations, Labeling, and the Binomial Theorem
8.6 Probability
8.7 Mathematical Induction
TU
TO
R
G
U
R
U
, 34 Chapter 1 Equations, Inequalities, and Modeling
For Thought 1
17. Since 14x = 7, the solution set is .
2
1. True, since 5(1) = 6 − 1.
18. Since −2x = 2, the solution set is {−1}.
2. True, since x = 3 is the solution to both
equations. 19. Since 7 + 3x = 4x − 4, the solution set is {11}.
3. False, −2 20. Since −3x + 15 = 4 − 2x, the solution set
√ is not a solution of the first equation is {11}.
since −2 is not a real number.
4
4. True, since x − x = 0. 21. Since x = − · 18, the solution set is {−24}.
TU
3
5. False, x = 0 is the solution. 6. True 3
27
22. Since x = · (−9), the solution set is − .
7. False, since |x| = −8 has no solution. 2 2
x 23. Multiplying by 6 we get
8. False, is undefined at x = 5.
x−5
3x − 30 = −72 − 4x
TO
3
9. False, since we should multiply by − . 7x = −42.
2
10. False, 0 · x + 1 = 0 has no solution. The solution set is {−6}.
24. Multiplying by 4 we obtain
1.1 Exercises
R
x − 12 = 2x + 12
1. equation −24 = x.
2. linear
G
The solution set is {−24}.
3. equivalent
25. Multiply both sides of the equation by 12.
4. solution set
18x + 4 = 3x − 2
U
5. identity
15x = −6
6. inconsistent equation 2
x = − .
5
R
7. conditional equation
2
8. extraneous root The solution set is − .
5
U
9. No, since 2(3) − 4 = 2 6= 9. 10. Yes 26. Multiply both sides of the equation by 30.
11. Yes, since (−4)2 = 16.
15x + 6x = 5x − 10
√
12. No, since 16 6= −4. 16x = −10
5
x = − .
5
13. Since 3x = 5, the solution set is . 8
3
3 5
14. Since −2x = −3, the solution set is . The solution set is − .
2 8
15. Since −3x = 6, the solution set is {−2}. 27. Note, 3(x − 6) = 3x − 18 is true by the
distributive law. It is an identity and the
16. Since 5x = −10, the solution set is {−2}. solution set is R.
Copyright 2015 Pearson Education, Inc.
