BASIC ALGEBRA - Edition 5 - Overview and Exercises

Oct 16, 2026

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BASIC ALGEBRA With Applications introduces core algebraic concepts and builds them through structured chapters covering expressions, relations, real number axioms, the number line, and properties of real numbers. The text progresses to order of operations, primes, fractions and rationals, translation between expressions and equations, then expands into linear equations with solving methods, percent applications, and linear inequalities. Subsequent chapters cover graphing, slope forms, functions, linear systems, and polynomial expressions with practice tests and homework exercises.

LanguageEnglish

CategoryExam

FormatPDF

Pages511

Reading Time21 h 28 min

AccessFree to download

Chapter 1 - Concepts

1. Expressions, Relations, and Substitution

2. Real Number Axioms

3. The Number Line and Sets of Numbers

4. Properties of Real Numbers

5. Order of Operations

6. Prime Numbers

7. Fractions and Rationals

9. Translation

Chapter 2 - Linear Equations

1. Properties of Equations

2. Solving Linear Equations

3. Linear Formulas

4. Percent

5. Applications

6. Linear Inequalities

Chapter 3 - Graphing

1. Reading and Constructing Graphs

2. Graphing Linear Equations

4. Slope

5. Slope-Intercept Form

6. Point-Slope Form

7. Function Notation

Chapter 4 - Linear Systems

1. Graphing Systems of Equations

2. Substitution

3. Elimination

4. Applications of Systems

5. Multivariate Linear Inequalities

Chapter 5 - Polynomial Expressions

1. Integer Exponent

2. Properties of Exponent

3. Introduction to Polynomials

4. Sums of Polynomials

BASIC ALGEBRA With Applications Ivan G. Zaigralin © 2017–2020 Ivan G. Zaigralin Cover design © 2018 Derrick Santiago This typeset version of the text is licensed under the Attribution-ShareAlike 4.0 International license, or, if a user so desires, any later version published by Creative Commons. A human-readable summary of (and not a substitute for) the license follows. YOU ARE FREE TO: SHARE: COPY AND REDISTRIBUTE THE MATERIAL IN ANY MEDIUM OR FORMAT ADAPT: REMIX, TRANSFORM, AND BUILD UPON THE MATERIAL FOR ANY PURPOSE, EVEN COMMERCIALLY. THIS LICENSE IS ACCEPTABLE FOR FREE CULTURAL WORKS. THE LICENSOR CANNOT REVOKE THESE FREEDOMS AS LONG AS YOU FOLLOW THE LICENSE TERMS. The source code for the text bears a different free copyleft license. Edition: 5th Publisher: Samizdat Contents Contents 5 Chapter 1 . Concepts 15 1. Expressions, Relations, and Substitution 15 1.1. Expressions versus Relations 15 1.2. Algebraic Substitution 17 1.3. Common Types of Expressions 18 Homework 1.1 21 Homework 1.1 Answers 22 2. Real Number Axioms 23 2.1. Axioms 23 2.2. Applying Axioms 27 2.3. Inverses, Subtraction, Division 28 2.4. Conclusion 30 Homework 1.2 32 Homework 1.2 Answers 33 3. The Number Line and Sets of Numbers 34 3.1. Roster 34 3.2. Integers 34 3.3. Set Builder 36 3.4. Rationals 37 3.5. Reals 38 3.6. Absolute Value 40 3.7. Inequality Relations 42 Homework 1.3 44 Homework 1.3 Answers 46 4. Properties of Real Numbers 47 4.1. Basic Properties 47 4.2. Positive Integer Exponent 50 Homework 1.4 52 Homework 1.4 Answers 53 5. Order of Operations 54 5.1. Evaluating Sums and Products 54 5.2. Like Terms 57 Homework 1.5 59 Homework 1.5 Answers 61 6. Prime Numbers 62 6.1. Integer Division and Prime Numbers 62 6.2. Fractions of Integers in Lowest Terms 64 Homework 1.6 67 Homework 1.6 Answers 69 7. Fractions and Rationals 70 7.1. Fraction Notation 70 7.2. Changing the Denominator 74 Homework 1.7 76 Homework 1.7 Answers 78 8. Fraction Addition 79 8.1. Adding Fractions with a Common Denominator 79 8.2. Least Common Multiple 80 8.3. Adding Fractions of Integers 81 8.4. Mixed Numbers 82 Homework 1.8 84 Homework 1.8 Answers 86 9. Translation 87 9.1. Expressions 87 9.2. Equations 87 9.3. Applications 90 Homework 1.9 91 Homework 1.9 Answers 92 Practice Test 1 93 Practice Test 1 Answers 94 Chapter 2 . Linear Equations 95 1. Properties of Equations 95 1.1. Equations and Solutions 95 1.2. Addition Property for Equations 97 1.3. Multiplication Property for Equations 98 1.4. Applications 99 Homework 2.1 101 Homework 2.1 Answers 103 2. Solving Linear Equations 104 2.1. Linear and Non-linear Equations 104 2.2. Isolating The Variable 105 2.3. Applications 110 Homework 2.2 114 Homework 2.2 Answers 116 3. Linear Formulas 117 3.1. Isolating a Variable 117 Homework 2.3 121 Homework 2.3 Answers 122 4. Percent 123 4.1. Percent Units and Notation 123 4.2. Percent Increase and Decrease 125 Homework 2.4 128 Homework 2.4 Answers 129 5. Applications 130 5.1. Distance and Work 130 5.2. Applications of w = r t 132 Homework 2.5 135 Homework 2.5 Answers 137 6. Linear Inequalities 138 6.1. Solution Sets 138 6.2. Interval Notation and Graphs 139 6.3. Addition and Multiplication Properties 141 Homework 2.6 144 Homework 2.6 Answers 145 Practice Test 2 146 Practice Test 2 Answers 147 Chapter 3 . Graphing 149 1. Reading and Constructing Graphs 149 1.1. Cartesian Plane 149 Homework 3.1 155 Homework 3.1 Answers 158 2. Graphing Linear Equations 159 2.1. Solution Sets 159 2.2. Graphing Solution Sets 160 2.3. Graphing Lines 162 Homework 3.2 165 Homework 3.2 Answers 166 3. Intercepts 168 3.1. x and y-intercepts 168 3.2. Finding Intercepts 168 Homework 3.3 171 Homework 3.3 Answers 172 4. Slope 174 4.1. Slope of a Line 174 4.2. Using Slo

FAQs

What topics are covered in Chapter 1?

Chapter 1 covers expressions and substitution, real number axioms, number line and number sets, properties of real numbers, order of operations, prime numbers, fractions and rationals, and translation of ideas into expressions and equations. It includes homework and answers.

How does the book teach solving linear equations?

It explains equation properties, then solving linear equations by isolating variables, including applications and practice. Homework and practice tests follow key subtopics.

Which later chapters focus on graphing and linear systems?

Chapter 3 focuses on reading and constructing graphs, graphing linear equations, intercepts, slope, slope-intercept and point-slope forms, and function notation. Chapter 4 covers graphing systems, substitution and elimination methods, and applications of systems, followed by practice tests.

Oct 16, 2026

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