Elementary & Intermediate Algebra:
ST
Functions and Authentic Applications –
3rd Edition
UV
INSTRUCTOR’S
IA
SOLUTIONS
_A
MANUAL
PP
RO
Jay Lehmann
VE
Comprehensive Solutions Manual for Instructors and
D?
Students
??
© Jay Lehmann
All rights reserved. Reproduction or distribution without permission is prohibited.
©STUDYSTREAM
, Contents
Chapter 1 Introduction to Modeling
ST
1.1 Variables and Constants 1
1.2 Scatterplots 3
1.3 Exact Linear Relationships 5
1.4 Approximate Linear Relationships 8
UV
Chapter 1 Review Exercises 12
Chapter 1 Test 15
Chapter 2 Operations and Expressions
2.1 Expressions 17
IA
2.2 Operations with Fractions 18
2.3 Absolute Value and Adding Real Numbers 21
2.4 Change in a Quantity and Subtracting Real Numbers 24
2.5 Ratios, Percents, and Multiplying and Dividing Real Numbers 27
_A
2.6 Exponents and Order of Operations 30
Chapter 2 Review Exercises 33
Chapter 2 Test 37
Cumulative Review of Chapters 1 and 2 39
PP
Chapter 3 Using Slope to Graph Linear Equations
3.1 Graphing Equations of the Forms y = mx + b and x = a 42
3.2 Graphing Linear Models; Unit Analysis 48
3.3 Slope of a Line 54
RO
3.4 Using Slope to Graph Linear Equations 56
3.5 Rate of Change 63
Chapter 3 Review Exercises 69
Chapter 3 Test 75
Chapter 4 Simplifying Expressions and Solving Equations
VE
4.1 Simplifying Expressions 79
4.2 Simplifying More Expressions 81
4.3 Solving Linear Equations in One Variable 83
4.4 Solving More Linear Equations in One Variable 88
D?
4.5 Comparing Expressions and Equations 96
4.6 Formulas 99
Chapter 4 Review Exercises 104
Chapter 4 Test 110
Cumulative Review of Chapters 1–4 113
??
i
, Chapter 5 Linear Equations in Two Variables and Linear Inequalities
in One Variable
ST
5.1 Graphing Linear Equations in Two Variables 118
5.2 Finding Equations of Lines 126
5.3 Finding Equations of Linear Models 133
5.4 Using Equations of Linear Models to Make Estimates and Predictions 139
5.5 Solving Linear Inequalities in One Variable 145
UV
Chapter 5 Review Exercises 150
Chapter 5 Test 162
Chapter 6 Systems of Linear Equations and Systems of Linear
Inequalities
IA
6.1 Using Graphs and Tables to Solve Systems 166
6.2 Using Substitution to Solve Systems 171
6.3 Using Elimination to Solve Systems 176
6.4 Using Systems to Model Data 185
_A
6.5 Perimeter, Value, Interest, and Mixture Problems 190
6.6 Linear Inequalities in Two Variables; Systems of Linear Inequalities in Two Variables 197
Chapter 6 Review Exercises 205
Chapter 6 Test 217
Cumulative Review of Chapters 1–6 223
PP
Chapter 7 Polynomials and Properties of Exponents
7.1 Graphing Quadratic Equations 232
7.2 Quadratic Models 236
RO
7.3 Adding and Subtracting Polynomials 239
7.4 Multiplying Polynomials 242
7.5 Powers of Polynomials; Product of Binomial Conjugates 246
7.6 Properties of Exponents 250
7.7 Negative-Integer Exponents 252
7.8 Dividing Polynomials 255
Chapter 7 Review Exercises 260
VE
Chapter 7 Test 266
Chapter 8 Factoring Polynomials and Solving Polynomial Equations
8.1 Factoring Trinomials of the Form x2 + bx + c and Differences of Two Squares 269
D?
8.2 Factoring Out the GCF; Factoring by Grouping 273
8.3 Factoring Trinomials of the Form ax2 + bx + c 276
8.4 Sums and Differences of Cubes; A Factoring Strategy 286
8.5 Using Factoring to Solve Polynomial Equations 290
8.6 Using Factoring to Make Predictions with Quadratic Models 295
??
Chapter 8 Review Exercises 299
Chapter 8 Test 305
Cumulative Review of Chapters 1–8 308
ii
, Chapter 9 Solving Quadratic Equations
9.1 Simplifying Radical Expressions 315
ST
9.2 Simplifying More Radical Expressions 317
9.3 Solving Quadratic Equations by the Square Root Property; The Pythagorean Theorem 319
9.4 Solving Quadratic Equations by Completing the Square 324
9.5 Solving Quadratic Equations by the Quadratic Formula 329
9.6 More Quadratic Models 336
UV
Chapter 9 Review Exercises 342
Chapter 9 Test 350
Chapter 10 Rational Expressions and Equations
10.1 Simplifying Rational Expressions 353
IA
10.2 Multiplying and Dividing Rational Expressions; Converting Units 357
10.3 Adding Rational Expressions 362
10.4 Subtracting Rational Expressions 368
10.5 Solving Rational Equations 375
_A
10.6 Proportions; Similar Triangles 387
10.7 Variation 389
10.8 Simplifying Complex Rational Expressions 393
Chapter 10 Review Exercises 397
Chapter 10 Test 407
PP
Chapter 11 More Radical Expressions and Equations
11.1 Adding and Subtracting Radical Expressions 412
11.2 Multiplying Radical Expressions 414
11.3 Solving Square Root Equations 416
RO
Chapter 11 Review Exercises 422
Chapter 11 Test 426
Cumulative Review of Chapters 1–11 428
VE
D?
??
iii
ST
Functions and Authentic Applications –
3rd Edition
UV
INSTRUCTOR’S
IA
SOLUTIONS
_A
MANUAL
PP
RO
Jay Lehmann
VE
Comprehensive Solutions Manual for Instructors and
D?
Students
??
© Jay Lehmann
All rights reserved. Reproduction or distribution without permission is prohibited.
©STUDYSTREAM
, Contents
Chapter 1 Introduction to Modeling
ST
1.1 Variables and Constants 1
1.2 Scatterplots 3
1.3 Exact Linear Relationships 5
1.4 Approximate Linear Relationships 8
UV
Chapter 1 Review Exercises 12
Chapter 1 Test 15
Chapter 2 Operations and Expressions
2.1 Expressions 17
IA
2.2 Operations with Fractions 18
2.3 Absolute Value and Adding Real Numbers 21
2.4 Change in a Quantity and Subtracting Real Numbers 24
2.5 Ratios, Percents, and Multiplying and Dividing Real Numbers 27
_A
2.6 Exponents and Order of Operations 30
Chapter 2 Review Exercises 33
Chapter 2 Test 37
Cumulative Review of Chapters 1 and 2 39
PP
Chapter 3 Using Slope to Graph Linear Equations
3.1 Graphing Equations of the Forms y = mx + b and x = a 42
3.2 Graphing Linear Models; Unit Analysis 48
3.3 Slope of a Line 54
RO
3.4 Using Slope to Graph Linear Equations 56
3.5 Rate of Change 63
Chapter 3 Review Exercises 69
Chapter 3 Test 75
Chapter 4 Simplifying Expressions and Solving Equations
VE
4.1 Simplifying Expressions 79
4.2 Simplifying More Expressions 81
4.3 Solving Linear Equations in One Variable 83
4.4 Solving More Linear Equations in One Variable 88
D?
4.5 Comparing Expressions and Equations 96
4.6 Formulas 99
Chapter 4 Review Exercises 104
Chapter 4 Test 110
Cumulative Review of Chapters 1–4 113
??
i
, Chapter 5 Linear Equations in Two Variables and Linear Inequalities
in One Variable
ST
5.1 Graphing Linear Equations in Two Variables 118
5.2 Finding Equations of Lines 126
5.3 Finding Equations of Linear Models 133
5.4 Using Equations of Linear Models to Make Estimates and Predictions 139
5.5 Solving Linear Inequalities in One Variable 145
UV
Chapter 5 Review Exercises 150
Chapter 5 Test 162
Chapter 6 Systems of Linear Equations and Systems of Linear
Inequalities
IA
6.1 Using Graphs and Tables to Solve Systems 166
6.2 Using Substitution to Solve Systems 171
6.3 Using Elimination to Solve Systems 176
6.4 Using Systems to Model Data 185
_A
6.5 Perimeter, Value, Interest, and Mixture Problems 190
6.6 Linear Inequalities in Two Variables; Systems of Linear Inequalities in Two Variables 197
Chapter 6 Review Exercises 205
Chapter 6 Test 217
Cumulative Review of Chapters 1–6 223
PP
Chapter 7 Polynomials and Properties of Exponents
7.1 Graphing Quadratic Equations 232
7.2 Quadratic Models 236
RO
7.3 Adding and Subtracting Polynomials 239
7.4 Multiplying Polynomials 242
7.5 Powers of Polynomials; Product of Binomial Conjugates 246
7.6 Properties of Exponents 250
7.7 Negative-Integer Exponents 252
7.8 Dividing Polynomials 255
Chapter 7 Review Exercises 260
VE
Chapter 7 Test 266
Chapter 8 Factoring Polynomials and Solving Polynomial Equations
8.1 Factoring Trinomials of the Form x2 + bx + c and Differences of Two Squares 269
D?
8.2 Factoring Out the GCF; Factoring by Grouping 273
8.3 Factoring Trinomials of the Form ax2 + bx + c 276
8.4 Sums and Differences of Cubes; A Factoring Strategy 286
8.5 Using Factoring to Solve Polynomial Equations 290
8.6 Using Factoring to Make Predictions with Quadratic Models 295
??
Chapter 8 Review Exercises 299
Chapter 8 Test 305
Cumulative Review of Chapters 1–8 308
ii
, Chapter 9 Solving Quadratic Equations
9.1 Simplifying Radical Expressions 315
ST
9.2 Simplifying More Radical Expressions 317
9.3 Solving Quadratic Equations by the Square Root Property; The Pythagorean Theorem 319
9.4 Solving Quadratic Equations by Completing the Square 324
9.5 Solving Quadratic Equations by the Quadratic Formula 329
9.6 More Quadratic Models 336
UV
Chapter 9 Review Exercises 342
Chapter 9 Test 350
Chapter 10 Rational Expressions and Equations
10.1 Simplifying Rational Expressions 353
IA
10.2 Multiplying and Dividing Rational Expressions; Converting Units 357
10.3 Adding Rational Expressions 362
10.4 Subtracting Rational Expressions 368
10.5 Solving Rational Equations 375
_A
10.6 Proportions; Similar Triangles 387
10.7 Variation 389
10.8 Simplifying Complex Rational Expressions 393
Chapter 10 Review Exercises 397
Chapter 10 Test 407
PP
Chapter 11 More Radical Expressions and Equations
11.1 Adding and Subtracting Radical Expressions 412
11.2 Multiplying Radical Expressions 414
11.3 Solving Square Root Equations 416
RO
Chapter 11 Review Exercises 422
Chapter 11 Test 426
Cumulative Review of Chapters 1–11 428
VE
D?
??
iii
