Skip to main content
Elementary Algebra
Katherine Yoshiwara
Contents
Index
Search Book
close
Search Results:
No results.
Calc
Dark Mode
Prev
Up
Next
\(\require{cancel}\newcommand{\alert}[1]{\boldsymbol{\color{magenta}{#1}}} \newcommand{\blert}[1]{\boldsymbol{\color{blue}{#1}}} \newcommand{\bluetext}[1]{\color{skyblue}{#1}} \delimitershortfall-1sp \newcommand\abs[1]{\left|#1\right|} \newcommand\degree[0]{^{\circ}} \newcommand\Ccancel[2][black]{\renewcommand\CancelColor{\color{#1}}\cancel{#2}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \newcommand{\fillinmath}[1]{\mathchoice{\boxed{\displaystyle \phantom{\,#1\,}}}{\boxed{\textstyle \phantom{\,#1\,}}}{\boxed{\scriptstyle \phantom{\,#1\,}}}{\boxed{\scriptscriptstyle\phantom{\,#1\,}}}} \)
Front Matter
Colophon
Preface
1
Variables
1.1
Variables
What is a Variable?
Using Letters to Represent Variables
Connections Between Variables
Lesson
Wrap-Up
Homework 1.1
1.2
Algebraic Expressions
Writing an Algebraic Expression
Sums
Products
Differences
Quotients
Evaluating an Algebraic Expression
Some Useful Algebraic Formulas
Lesson
Wrap-Up
Homework 1.2
1.3
Equations and Graphs
Anatomy of a Graph
Graphing an Equation
Choosing Scales for the Axes
Solving Equations with Graphs
Lesson
Wrap-Up
Homework 1.3
1.4
Solving Equations
What is an Equation?
Trial and Error
Inverse Operations
Solving Equations
Problem Solving with Equations
Lesson
Wrap-Up
Homework 1.4
1.5
Order of Operations
Addition and Multiplication
Subtraction and Division
Combined Operations
Parentheses
Fraction Bars
Summary
Algebraic Expressions
Lesson
Wrap-Up
Homework 1.5
1.6
Chapter 1 Summary and Review
Lesson 1.1 Variables
Lesson 1.2 Algebraic Expressions
Lesson 1.3 Equations and Graphs
Lesson 1.4 Solving Equations
Lesson 1.5 Order of Operations
Review Questions
Review Problems
Exercises
2
Linear Equations
2.1
Signed Numbers
Types of Numbers
Adding Two Numbers with the Same Sign
Adding Two Numbers with Opposite Signs
Subtracting a Positive Number
Subtracting a Negative Number
Multiplying Signed Numbers
The product of numbers with opposite signs
The product of numbers with the same sign
Dividing Signed Numbers
Fractions
Quotients Involving Zero
Lesson
Wrap-Up
Homework 2.1
2.2
Expressions and Equations
Writing Algebraic Expressions
Evaluating Algebraic Expressions
Negative Numbers
Lesson
Wrap-Up
Homework 2.2
2.3
Graphs of Linear Equations
Graphing Equations
Cartesian Coordinate System
Lesson
Wrap-Up
Homework 2.3
2.4
Linear Equations and Inequalities
Solving Equations
Applied Problems
Solving Inequalities
Compound Inequalities
Lesson
Wrap-Up
Homework 2.4
2.5
Like Terms
Equivalent Expressions
Like Terms
Adding and Subtracting Like Terms
Removing Parentheses
Solving Equations and Inequalities
Lesson
Wrap-Up
Homework 2.5
2.6
Chapter 2 Summary and Review
Lesson 2.1 Signed Numbers
Section 2.2 Expressions and Equations
Section 2.3 Graphs of Linear Equations
Section 2.4 Linear Equations and Inequalities
Section 2.5 Like Terms
Review Questions
Review Problems
Exercises
3
Graphs of Linear Equations
3.1
Intercepts
Intercepts of a Line
The Intercept Method of Graphing
Interpreting the Intercepts
Lesson
Wrap-Up
Homework 3.1
3.2
Ratio and Proportion
Ratios
Rates
Proportions
Proportional Variables
Lesson
Wrap-Up
Homework 3.2
3.3
Slope
Rate of Change
Slope
Meaning of Slope
Geometrical Meaning of Slope
Lesson
Wrap-Up
Homework 3.3
3.4
Slope-Intercept Form
Writing a Linear Equation
Slope-Intercept Method of Graphing
Finding the Slope-Intercept Form
Lesson
Wrap-Up
Homework 3.4
3.5
Properties of Lines
Parallel and Perpendicular Lines
Equations for Horizontal and Vertical Lines
Distance Between Points
Subscript Notation
A New Formula for Slope
Lesson
Wrap-Up
Homework 3.5
3.6
Chapter 3 Summary and Review
Lesson 3.1 Intercepts
Lesson 3.2 Ratio and Proportion
Lesson 3.3 Slope
Lesson 3.4 Slope-Intercept Form
Lesson 3.5 Properties of Lines
Review Questions
Review Problems
Exercises
4
Applications of Linear Equations
4.1
The Distributive Law
Products
The Distributive Law
Solving Equations and Inequalities
Algebraic Expressions
Lesson
Wrap-Up
Homework 4.1
4.2
Systems of Linear Equations
What is a System of Equations?
Solving a System of Equations by Graphing
Inconsistent and Dependent Systems
Problem Solving with Systems
Lesson
Wrap-Up
Homework 4.2
4.3
Algebraic Solution of Systems
Substitution Method
Elimination Method
Inconsistent and Dependent Systems
Lesson
Wrap-Up
Homework 4.3
4.4
Problem Solving with Systems
Interest
Mixtures
Motion
Lesson
Wrap-Up
Homework 4.4
4.5
Point-Slope Formula
Finding an Equation for a Line
The Line Through Two Points
Applications
Lesson
Wrap-Up
Homework 4.5
4.6
Chapter 4 Summary and Review
Lesson 4.1 The Distributive Law
Lesson 4.2 Systems of Linear Equations
Lesson 4.3 Algebraic Solution of Systems
Lesson 4.4 Applications of Systems
Lesson 4.5 Point-Slope Form
Review Questions
Review Problems
Exercises
5
Exponents and Roots
5.1
Exponents
What is an Exponent?
Powers of Negative Numbers
Using a Calculator
Powers of Variables
Order of Operations
Like Terms
Lesson
Wrap-Up
Homework 5.1
5.2
Square Roots and Cube Roots
What is a Square Root?
Radicals
Rational and Irrational Numbers
Order of Operations
Cube Roots
Lesson
Wrap-Up
Homework 5.2
5.3
Using Formulas
Volume and Surface Area
Solving Equations with
\(x^2\)
Pythagorean Theorem
Solving for One Variable
Lesson
Wrap-Up
Homework 5.3
5.4
Products of Binomials
Products of Variables
Using the Distributive Law
Multiplying Binomials
The Four Terms in a Binomial Product
Lesson
Wrap-Up
Homework 5.4
5.5
Chapter 5 Summary and Review
Lesson 5.1 Exponents
Lesson 5.2 Square Roots and Cube Roots
Lesson 5.3 Using Formulas
Lesson 5.4 Products of Binomials
Review Questions
Review Problems
Exercises
6
Quadratic Equations
6.1
Extracting Roots
Quadratic Equations
Graphs of Quadratic Equations
Solving Quadratic Equations
Extraction of Roots
Solving Formulas
Lesson
Wrap-Up
Homework 6.1
6.2
Some Quadratic Models
Revenue
The Zero-Factor Principle
Factoring
Solving Quadratic Equations by Factoring
Lesson
Wrap-Up
Homework 6.2
6.3
Solving Quadratic Equations by Factoring
The Zero-Factor Principle
Factoring Quadratic Trinomials
Solving a Quadratic Equation
Application
Lesson
Wrap-Up
Homework 6.3
6.4
Graphing Quadratic Equations
\(x\)
-Intercepts of a Parabola
The Vertex
Graphing Parabolas
Lesson
Wrap-Up
Homework 6.4
6.5
The Quadratic Formula
Using the Quadratic Formula
Non-Real Solutions
Lesson
Wrap-Up
Homework 6.5
6.6
Chapter 6 Summary and Review
Lesson 6.1 Extracting Roots
Lesson 6.2 Some Quadratic Models
Lesson 6.3 Solving Quadratic Equations by Factoring
Lesson 6.4 Graphing Quadratic Equations
Lesson 6.5 The Quadratic Formula
Review Questions
Review Problems
Exercises
7
Polynomials
7.1
Polynomials
What is a Polynomial?
Degree
Evaluating Polynomials
Like Terms
Adding Polynomials
Subtracting Polynomials
Application
Lesson
Wrap-Up
Homework 7.1
7.2
Products of Polynomials
Products of Powers
Products of Monomials
Multiplying by a Monomial
Products of Polynomials
Lesson
Wrap-Up
Homework 7.2
7.3
More About Factoring
Quotients of Powers
Quotients of Monomials
Greatest Common Factors
Factoring Quadratic Trinomials by Guess-and-Check
Quadratic Trinomials in Two Variables
Combining Factoring Techniques
\(\blert{\text{Optional Extension: The Box Method}}\)
Factoring Quadratic Trinomials by the Box Method
Lesson
Wrap-Up
Homework 7.3
7.4
Special Products and Factors
Squares of Monomials
Squares of Binomials
Difference of Two Squares
Factoring Special Products
Lesson
Wrap-Up
Homework 7.4
7.5
Chapter 7 Summary and Review
Lesson 7.1 Polynomials
Lesson 7.2 Products of Polynomials
Lesson 7.3 More About Factoring
Lesson 7.4 Special Products and Factors
Review Questions
Review Problems
Exercises
8
Algebraic Fractions
8.1
Algebraic Fractions
What is an Algebraic Fraction?
Applications of Algebraic Fractions
Reducing Fractions
Negative of a Binomial
Lesson
Wrap-Up
Homework 8.1
8.2
Operations on Fractions
Products of Fractions
Quotients of Fractions
Adding Like Fractions
Subtracting Like Fractions
Polynomial Division
Lesson
Wrap-Up
Homework 8.2
8.3
Lowest Common Denominator
Building Fractions
Adding and Subtracting Unlike Fractions
Finding the Lowest Common Denominator
Lesson
Wrap-Up
Homework 8.3
8.4
Equations with Fractions
"Clearing" Fractions
Using an LCD to Clear Fractions
Variables in the Denominator
Extraneous Solutions
Formulas
Applications
Lesson
Homework 8.4
8.5
Chapter 8 Summary and Review
Lesson 8.1 Algebraic Fractions
Lesson 8.2 Operations on Algebraic Fractions
Lesson 8.3 Lowest Common Denominator
Lesson 8.4 Equations with Fractions
Review Questions
Review Problems
Exercises
9
More About Exponents and Roots
9.1
Laws of Exponents
Products and Quotients
Power of a Power
Power of a Product
Power of a Quotient
Using the Laws of Exponents
Lesson
Wrap-Up
Homework 9.1
9.2
Negative Exponents and Scientific Notation
Zero as an Exponent
Negative Exponents
Laws of Exponents
Powers of Ten
Scientific Notation
Calculators and Scientific Notation
Mental Calculation with Scientific Notation
Lesson
Wrap-Up
Homework 9.2
9.3
Properties of Radicals
Product and Quotient Rules
Simplifying Square Roots
Square Root of a Variable Expression
Sums and Differences
Lesson
Wrap-Up
Homework 9.3
9.4
Operations on Radicals
Products
Quotients
Fractions
Rationalizing the Denominator
Lesson
Wrap-Up
Homework 9.4
9.5
Equations with Radicals
Radical Equations
Extraneous Solutions
Equations with Cube Roots
Extraction of Roots
Lesson
Wrap-Up
Homework 9.5
9.6
Chapter 9 Summary and Review
Lesson 9.1 Laws of Exponents
Lesson 9.2 Negative Exponents and Scientific Notation
Lesson 9.3 Properties of Radicals
Lesson 9.4 Operations on Radicals
Lesson 9.5 Equations with Radicals
Review Questions
Review Problems
Exercises
Appendices
A
Answers to Selected Exercises and Homework Problems
B
GNU Free Documentation License
Index
Colophon
Colophon
This book was authored in PreTeXt.