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Front Matter
Colophon
Acknowledgements
To All
I
Linear Equations and Lines
1
Variables, Expressions, Equations, and Inequalities
1.1
Variables and Evaluating Expressions
1.1.1
Introduction to Variables
1.1.2
Algebraic Expressions
1.1.3
Evaluating Expressions with Exponents, Absolute Value, and Radicals
1.1.4
Evaluating Expressions with Negative Numbers
1.1.5
Reading Questions
1.1.6
Exercises
1.2
Combining Like Terms
1.2.1
Identifying Terms
1.2.2
Combining Like Terms
1.2.3
Applications
1.2.4
Reading Questions
1.2.5
Exercises
1.3
Comparison Symbols and Notation for Intervals
1.3.1
Comparison Symbols
1.3.2
Set-Builder and Interval Notation
1.3.3
Reading Questions
1.3.4
Exercises
1.4
Equations, Inequalities, and Solutions
1.4.1
Equations, Inequalities, and Solutions
1.4.2
Checking Possible Solutions
1.4.3
More Applications
1.4.4
Linear Equations
1.4.5
Reading Questions
1.4.6
Exercises
1.5
Solving One-Step Equations
1.5.1
Imagine Filling in the Blanks
1.5.2
The Basic Principle of Algebra
1.5.3
Solving One-Step Equations and Stating Solution Sets
1.5.4
Equations with Fractions
1.5.5
Reading Questions
1.5.6
Exercises
1.6
Solving One-Step Inequalities
1.6.1
Solving Linear Inequalities
1.6.2
Negation
1.6.3
Reading Questions
1.6.4
Exercises
1.7
Algebraic Properties and Simplifying Expressions
1.7.1
Identities and Inverses
1.7.2
Algebraic Properties
1.7.3
Applying the Commutative, Associative, and Distributive Properties
1.7.4
The Role of the Order of Operations
1.7.5
Reading Questions
1.7.6
Exercises
1.8
Modeling with Equations and Inequalities
1.8.1
Translating Phrases into Algebraic Expressions and Equations/Inequalities
1.8.2
Rate Models
1.8.3
Percent Applications
1.8.4
Inequalities in Modeling
1.8.5
Reading Questions
1.8.6
Exercises
1.9
Variables, Expressions, and Equations Chapter Review
1.9
Review Exercises for Chapter 1
2
Linear Equations and Inequalities
2.1
Solving Multistep Linear Equations
2.1.1
Solving Two-Step Equations
2.1.2
Solving Multistep Linear Equations
2.1.3
Revisiting Applications
2.1.4
Differentiating between Simplifying Expressions, Evaluating Expressions and Solving Equations
2.1.5
Reading Questions
2.1.6
Exercises
2.2
Solving Multistep Linear Inequalities
2.2.1
Solving Multistep Inequalities
2.2.2
Applications
2.2.3
Reading Questions
2.2.4
Exercises
2.3
Equations and Inequalities with Fractions
2.3.1
Eliminating Denominators
2.3.2
Proportional Equations
2.3.3
Solving Inequalities with Fractions
2.3.4
Reading Questions
2.3.5
Exercises
2.4
Special Solution Sets
2.4.1
Special Solution Sets
2.4.2
Further Examples
2.4.3
Reading Questions
2.4.4
Exercises
2.5
Isolating a Linear Variable
2.5.1
Solving for a Variable
2.5.2
Reading Questions
2.5.3
Exercises
2.6
Linear Equations and Inequalities Chapter Review
2.6
Review Exercises for Chapter 2
3
Graphing Lines
3.1
Cartesian Coordinates
3.1
Reading Questions
3.1
Exercises
3.2
Graphing Equations
3.2
Reading Questions
3.2
Exercises
3.3
Exploring Two-Variable Data and Rate of Change
3.3.1
Modeling data with two variables
3.3.2
Patterns in Tables
3.3.3
Rate of Change
3.3.4
Reading Questions
3.3.5
Exercises
3.4
Slope
3.4.1
What is slope?
3.4.2
Comparing Slopes
3.4.3
Finding Slope by Two Given Points
3.4.4
Reading Questions
3.4.5
Exercises
3.5
Slope-Intercept Form
3.5.1
Slope-Intercept Definition
3.5.2
Graphing Slope-Intercept Equations
3.5.3
Writing a Slope-Intercept Equation Given a Graph
3.5.4
Writing a Slope-Intercept Equation Given Two Points
3.5.5
Modeling with Slope-Intercept Form
3.5.6
Reading Questions
3.5.7
Exercises
3.6
Point-Slope Form
3.6.1
Point-Slope Motivation and Definition
3.6.2
Using Two Points to Build a Linear Equation
3.6.3
Recognizing Point-Slope Form
3.6.4
Reading Questions
3.6.5
Exercises
3.7
Standard Form
3.7.1
Standard Form Definition
3.7.2
The Importance of
x
- and
y
-Intercepts
3.7.3
Transforming between Standard Form and Slope-Intercept Form
3.7.4
Reading Questions
3.7.5
Exercises
3.8
Geometry of Lines
3.8.1
Horizontal Lines and Vertical Lines
3.8.2
Parallel Lines
3.8.3
Perpendicular Lines
3.8.4
Reading Questions
3.8.5
Exercises
3.9
Strategies for Graphing Lines
3.9.1
Graphing Lines in Slope-Intercept Form
3.9.2
Graphing Lines in Point-Slope Form
3.9.3
Graphing Lines in Standard Form
3.9.4
Graphing Horizontal and Vertical Lines
3.9.5
Exercises
3.10
Graphing Lines Chapter Review
3.10
Review Exercises for Chapter 3
4
Systems of Two Linear Equations
4.1
Solving a System by Graphing
4.1.1
Systems of Two Linear Equations in Two Variables
4.1.2
Solving a System of Equations by Graphing
4.1.3
Special Systems of Equations
4.1.4
Reading Questions
4.1.5
Exercises
4.2
Substitution
4.2.1
Substitution
4.2.2
Applications
4.2.3
Solving Special Systems of Equations with Substitution
4.2.4
Reading Questions
4.2.5
Exercises
4.3
Elimination
4.3.1
Solving Systems of Equations by Elimination
4.3.2
Solving Special Systems of Equations with Elimination
4.3.3
Substitution versus Elimination
4.3.4
Reading Questions
4.3.5
Exercises
4.4
Systems of Two Linear Equations Chapter Review
4.4
Review Exercises for Chapter 4
Appendices
A
Basic Math Review
A.1
Arithmetic with Negative Numbers
A.1.1
Signed Numbers
A.1.2
Adding
A.1.3
Subtracting
A.1.4
Multiplying
A.1.5
Powers
A.1.6
Summary
A.1.7
Exercises
A.2
Fractions and Fraction Arithmetic
A.2.1
Visualizing Fractions
A.2.2
Equivalent Fractions
A.2.3
Multiplying with Fractions
A.2.4
Division with Fractions
A.2.5
Adding and Subtracting Fractions
A.2.6
Mixed Numbers and Improper Fractions
A.2.7
Exercises
A.3
Absolute Value and Square Root
A.3.1
Introduction to Absolute Value
A.3.2
Square Root Facts
A.3.3
Calculating Square Roots with a Calculator
A.3.4
Square Roots of Fractions
A.3.5
Square Root of Negative Numbers
A.3.6
Exercises
A.4
Percentages
A.4.1
Converting Percents, Decimals, and English
A.4.2
Setting up and Solving Percent Equations
A.4.3
Exercises
A.5
Order of Operations
A.5.1
Grouping Symbols
A.5.2
Order of Operations
A.5.3
Absolute Value and Implied Grouping
A.5.4
Understanding
(
−
a
)
m
versus
−
a
m
A.5.5
Exercises
A.6
Set Notation and Types of Numbers
A.6.1
Set Notation
A.6.2
Different Number Sets
A.6.3
Converting Repeating Decimals to Fractions
A.6.4
Exercises
B
PCC Course Content and Outcome Guides
B.1
MTH 60
C
Answers to Exercises
Index
Chapter
3
Graphing Lines
3.1
Cartesian Coordinates
3.2
Graphing Equations
3.3
Exploring Two-Variable Data and Rate of Change
3.4
Slope
3.5
Slope-Intercept Form
3.6
Point-Slope Form
3.7
Standard Form
3.8
Geometry of Lines
3.9
Strategies for Graphing Lines
3.10
Graphing Lines Chapter Review
🔗
