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Tables of Contents for Introductory Algebra
Chapter/Section Title
Page #
Page Count
Preface
xi
To the Student
xix
Index of Applications
xxi
Real Numbers
1
50
Introduction to Integers
3
6
To use inequality symbols with integers
3
2
To use opposites and absolute value
5
4
Addition and Subtraction of Integers
9
8
To add integers
9
1
To subtract integers
10
2
To solve application problems
12
5
Multiplication and Division of Integers
17
6
To multiply integers
17
1
To divide integers
18
2
To solve application problems
20
3
Operations with Rational Numbers
23
14
To write a rational number in simplest form and as a decimal
23
2
To convert between percents, fractions, and decimals
25
1
To add or subtract rational numbers
26
2
To multiply or divide rational numbers
28
2
To solve application problems
30
7
Exponents and the Order of Operations Agreement
37
14
To evaluate exponential expressions
37
1
To use the Order of Operations Agreement to simplify expressions
38
5
Focus on Problem Solving: Inductive Reasoning
43
1
Projects and Group Activities: The +/- Key on a Calculator
44
1
Moving Averages
44
1
www.fedstats.gov
45
1
Chapter Summary
45
2
Chapter Review
47
2
Chapter Test
49
2
Variable Expressions
51
34
Evaluating Variable Expressions
53
4
To evaluate a variable expression
53
4
Simplifying Variable Expressions
57
10
To simplify a variable expression using the Properties of Addition
57
2
To simplify a variable expression using the Properties of Multiplication
59
1
To simplify a variable expression using the Distributive Property
60
2
To simplify variable expressions
62
5
Translating Verbal Expressions into Variable Expressions
67
18
To translate a verbal expression into a variable expression, given the variable
67
1
To translate a verbal expression into a variable expression and then simplify
68
2
To translate application problems
70
5
Focus on Problem Solving: From Concrete to Abstract
75
1
Projects and Group Activities: Prime and Composite Numbers
76
1
Investigation into Operations with Even and Odd Integers
77
1
Chapter Summary
78
1
Chapter Review
79
2
Chapter Test
81
2
Cumulative Review
83
2
Solving Equations
85
76
Introduction to Equations
87
12
To determine whether a given number is a solution of an equation
87
1
To solve an equation of the form x + a = b
88
1
To solve an equation of the form ax = b
89
2
To solve application problems using the basic percent equation
91
8
General Equations---Part I
99
10
To solve an equation of the form ax + b = c
99
1
To solve application problems using formulas
100
9
General Equations---Part II
109
8
To solve an equation of the form ax + b = cx + d
109
1
To solve an equation containing parentheses
110
2
To solve application problems using formulas
112
5
Translating Sentences into Equations
117
8
To solve integer problems
117
2
To translate a sentence into an equation and solve
119
6
Geometry Problem
125
14
To solve perimeter problems
125
2
To solve problems involving angles formed by intersecting lines
127
4
To solve problems involving the angles of a triangle
131
8
Mixture and Uniform Motion Problems
139
22
To solve value mixture problems
139
2
To solve percent mixture problems
141
2
To solve uniform motion problems
143
8
Focus on Problem Solving: Trial and Error Approach to Problem Solving
151
1
Projects and Group Activities: Nielsen Ratings
152
1
Chapter Summary
153
2
Chapter Review
155
2
Chapter Test
157
2
Cumulative Review
159
2
Polynomials
161
42
Addition and Subtraction of Polynomials
163
4
To add polynomials
163
1
To subtract polynomials
164
3
Multiplication of Monomials
167
4
To multiply monomials
167
1
To simplify powers of monomials
168
3
Multiplication of Polynomials
171
8
To multiply a polynomial by a monomial
171
1
To multiply two polynomials
171
1
To multiply two binomials
172
1
To multiply binomials that have special products
173
1
To solve application problems
174
5
Integer Exponents and Scientific Notation
179
10
To divide monomials
179
5
To write a number in scientific notation
184
5
Division of Polynomials
189
14
To divide a polynomial by a monomial
189
1
To divide polynomials
189
4
Focus on Problem Solving: Dimensional Analysis
193
2
Projects and Group Activities: Pascal's Triangle
195
1
Chapter Summary
195
2
Chapter Review
197
2
Chapter Test
199
2
Cumulative Review
201
2
Factoring
203
50
Common Factors
205
6
To factor a monomial from a polynomial
205
2
To factor by grouping
207
4
Factoring Polynomials of the Form x2 + bx + c
211
8
To factor a trinomial of the form x2 + bx + c
211
2
To factor completely
213
6
Factoring Polynomials of the Form ax2 + bx + c
219
8
To factor a trinomial of the form ax2 + bx + c by using trial factors
219
2
To factor a trinomial of the form ax2 + bx + c by grouping
221
6
Special Factoring
227
8
To factor the difference of two squares and perfect-square trinomials
227
2
To factor completely
229
6
Solving Equations
235
18
To solve equations by factoring
235
2
To solve application problems
237
6
Focus on Problem Solving: Making a Table
243
1
Projects and Group Activities: Evaluating Polynomials Using a Calculator
244
1
Search the World Wide Web
245
1
Chapter Summary
246
1
Chapter Review
247
2
Chapter Test
249
2
Cumulative Review
251
2
Rational Expressions
253
60
Multiplication and Division of Rational Expressions
255
8
To simplify a rational expression
255
1
To multiply rational expressions
256
2
To divide rational expressions
258
5
Expressing Fractions in Terms of the Least Common Multiple (LCM)
263
4
To find the least common multiple (LCM) of two or more polynomials
263
1
To express two fractions in terms of the LCM of their denominators
264
3
Addition and Subtraction of Rational Expressions
267
8
To add or subtract rational expressions with the same denominators
267
1
To add or subtract rational expressions with different denominators
268
7
Complex Fractions
275
4
To simplify a complex fraction
275
4
Solving Equations Containing Fractions
279
4
To solve an equation containing fractions
279
4
Ratio and Proportion
283
8
To solve a proportion
283
1
To solve application problems
284
1
To solve problems involving similar triangles
284
7
Literal Equations
291
4
To solve a literal equation for one of the variables
291
4
Application Problems
295
18
To solve work problems
295
2
To solve uniform motion problems
297
6
Focus on Problem Solving: Negations and If... then Sentences
303
1
Projects and Group Activities: Intensity of Illumination
304
2
Chapter Summary
306
1
Chapter Review
307
2
Chapter Test
309
2
Cumulative Review
311
2
Linear Equations in Two Variables
313
52
The Rectangular Coordinate System
315
12
To graph points in a rectangular coordinate system
315
2
To determine ordered-pair solutions of an equation in two variables
317
2
To determine whether a set of ordered pairs is a function
319
3
To evaluate a function written in functional notation
322
5
Linear Equation in Two Variables
327
10
To graph an equation of the form y = mx + b
327
2
To graph an equation of the form Ax + By = C
329
3
To solve application problems
332
5
Intercepts and Slopes of Straight Lines
337
10
To find the x- and y-intercepts of a straight line
337
1
To find the slope of a straight line
338
3
To graph a line using the slope and the y-intercept
341
6
Equations of Straight Lines
347
18
To find the equation of a line given a point and the slope
347
1
To find the equation of a line given two points
348
2
To solve application problems
350
5
Focus on Problem Solving: Counterexamples
355
1
Projects and Group Activities: Graphing Linear Equations with a Graphing Utility
356
1
Graphs of Motion
357
1
Chapter Summary
358
1
Chapter Review
359
2
Chapter Test
361
2
Cumulative Review
363
2
Systems of Linear Equations
365
42
Solving Systems of Linear Equations by Graphing
367
8
To solve a system of linear equations by graphing
367
8
Solving Systems of Linear Equations by the Substitution Method
375
10
To solve a system of linear equations by the substitution method
375
4
To solve investment problems
379
6
Solving Systems of Equations by the Addition Method
385
6
To solve a system of linear equations by the addition method
385
6
Application Problems in Two Variables
391
16
To solve rate-of-wind or-current problems
391
1
To solve application problems using two variables
392
5
Focus on Problem Solving: Using a Tale and Searching for a Pattern
397
1
Projects and Group Activities: Find a Pattern
398
1
Solving a System of Equations with a Scientific Calculator
398
1
Solving a System of Equations with a Graphing Calculator
399
1
Chapter Summary
400
1
Chapter Review
401
2
Chapter Test
403
2
Cumulative Review
405
2
Inequalities
407
34
Sets
409
6
To write a set using the roster method
409
1
To write a set using set-builder notation
410
1
To graph an inequality on the number line
411
4
The Addition and Multiplication Properties of Inequalities
415
8
To solve an inequality using the Addition Property of Inequalities
415
1
To solve an inequality using the Multiplication Property of Inequalities
416
2
To solve application problems
418
5
General Inequalities
423
4
To solve general inequalities
423
1
To solve application problems
424
3
Graphing Linear Inequalities
427
14
To graph an inequality in two variables
427
4
Focus on Problem Solving: Graphing Data
431
1
Projects and Group Activities: Mean and Standard Deviation
432
2
Chapter Summary
434
1
Chapter Review
435
2
Chapter Test
437
2
Cumulative Review
439
2
Radical Expressions
441
34
Introduction to Radical Expressions
443
6
To simplify numerical radical expressions
443
2
To simplify variable radical expressions
445
4
Addition and Subtraction of Radical Expressions
449
4
To add and subtract radical expressions
449
4
Multiplication and Division of Radical Expressions
453
6
To multiply radical expressions
453
1
To divide radical expressions
454
5
Solving Equations Containing Radical Expressions
459
16
To solve an equation containing a radical expression
459
2
To solve application problems
461
4
Focus on Problem Solving: Deductive Reasoning
465
1
Projects and Group Activities: Measurements as Approximations
466
1
Distance to the Horizon
467
1
Chapter Summary
468
1
Chapter Review
469
2
Chapter Test
471
2
Cumulative Review
473
2
Quadratic Equations
475
36
Solving Quadratic Equations by Factoring or by Taking Square Roots
477
6
To solve a quadratic equation by factoring
477
2
To solve a quadratic equation by taking square roots
479
4
Solving Quadratic Equations by Completing the Square
483
6
To solve a quadratic equation by completing the square
483
6
Solving Quadratic Equations by Using the Quadratic Formula
489
4
To solve a quadratic equation by using the quadratic formula
489
4
Graphing Quadratic Equations in Two Variables
493
4
To graph a quadratic equation of the form y = ax2 + bx + c
493
4
Application Problems
497
14
To solve application problems
497
4
Focus on Problem Solving: Algebraic Manipulation and Graphing Techniques
501
1
Projects and Group Activities: Graphical Solutions of Quadratic Equations
502
1
Properties of Polynomials
502
1
Iterative Calculations
503
1
Geometric Construction of Completing the Square
503
1
Chapter Summary
504
1
Chapter Review
505
2
Chapter Test
507
2
Cumulative Review
509
2
Final Exam
511
4
Appendix
Guidelines for Using Graphing Calculators
515
8
Table of Symbols and Table of Measurement Abbreviations
523
Solutions to ``You Try It''
S1
Answers to Odd-Numbered Exercises
A1
Glossary
G1
Index
I1