Elementary algebra

OpenStax

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0.1 Pedagogical features

0.3 Arithmetic review

0.4 Basic properties of real numbers

0.5 Basic operations with real numbers

0.6 Algebraic expressions and equations

0.7 Solving linear equations and inequalities

0.8 Factoring polynomials

0.9 Graphing linear equations and inequalities in one and two variables

0.10 Rational expressions

0.11 Roots, radicals, and square root equations

0.12 Quadratic equations

0.13 Systems of linear equations

1 Acknowledgments

Arithmetic review

1 Factors, products, and exponents

2 Prime factorization

3 The least common multiple

4 Equivalent fractions

4.2 Equivalent fractions

4.3 Reducing fractions to lowest terms

4.4 Sample set a

4.5 Raising a fraction to higher terms

4.6 Sample set b

5 Operations with fractions

6 Decimal fractions

6.2 Decimal fractions

6.3 Sample set a

6.4 Adding and subtracting decimal fractions

6.5 Sample set b

6.6 Multiplying decimal fractions

6.7 Sample set c

6.8 Dividing decimal fractions

6.9 Sample set d

6.10 Converting decimal fractions to fractions

6.11 Sample set e

6.12 Converting fractions to decimal fractions

6.13 Sample set f

Basic properties of real numbers

1 Symbols and notations

2 The real number line and the real numbers

3 Properties of the real numbers

3.2 The closure properties

3.3 The commutative properties

3.4 Sample set a

3.5 Practice set a

3.6 The associative properties

3.7 Sample set b

3.8 Practice set b

3.9 Sample set c

3.10 Practice set c

3.11 The distributive properties

3.12 Sample set d

3.13 Practice set d

3.14 The identity properties

3.15 The inverse properties

3.17 Exercises for review

4.2 Exponential notation

4.3 Sample set a

4.4 Practice set a

4.5 Sample set b

4.6 Practice set b

4.7 Sample set c

4.8 Practice set c

4.9 Reading exponential notation

4.10 The order of operations

4.11 Sample set d

4.12 Practice set d

4.14 Exercises for review

5 Rules of exponents

6 The power rules for exponents

7 Summary of key concepts

8 Exercise supplement

9 Proficiency exam

Basic operations with real numbers

1 Signed numbers

2 Absolute value

3 Addition of signed numbers

3.2 Addition of numbers with like signs

3.3 Sample set a

3.4 Practice set a

3.5 Addition with zero

3.6 Addition of numbers with unlike signs

3.7 Sample set b

3.8 Practice set b

3.10 Exercises for review

4 Subtraction of signed numbers

4.2 Definition of subtraction

4.3 Subtraction of signed numbers

4.4 Sample set a

4.5 Practice set a

4.7 Exercises for review

5 Multiplication and division of signed numbers

5.2 Multiplication of signed numbers

5.3 Sample set a

5.4 Practice set a

5.5 Division of signed numbers

5.6 Sample set b

5.7 Practice set b

5.8 Sample set c

5.9 Practice set c

5.11 Exercises for review

6 Negative exponents

6.2 Reciprocals

6.3 Negative exponents

6.4 Sample set a

6.5 Practice set a

6.6 Working with negative exponents

6.7 Sample set b

6.8 Practice set b

6.9 Sample set c

6.10 Practice set c

6.12 Exercises for review

7 Scientific notation

8 Summary of key concepts

8.1 Summary of key concepts

9 Exercise supplement

10 Proficiency exam

Algebraic expressions and equations

1 Algebraic expressions

3 Classification of expressions and equations

3.2 Polynomials

3.3 Classification of polynomials

3.4 Classification of polynomial equations

3.5 Sample set a

3.6 Practice set a

3.8 Exercises for review

4 Combining polynomials using addition and subtraction

5 Combining polynomials using multiplication

6 Special binomial products

6.2 Expanding ( a + b ) 2 And ( a − b ) 2

6.3 Expanding ( a + b ) ( a − b )

6.4 Sample set a

6.5 Practice set a

6.7 Exercises for review

7 Terminology associated with equations

8 Summary of key concepts

9 Exercise supplement

10 Proficiency exam

Solving linear equations and inequalities

1 Solving equations

2 Solving equations of the form ax=b and x/a=b

2.2 Equality property of division and multiplication

2.3 Solving a x = b And x a = b For x

2.4 Sample set a

2.5 Practice set a

2.7 Exercises for review

3 Further techniques in equation solving

4 Application i - translating from verbal to mathetical expressions

5 Application ii - solving problems

6 Linear inequalities in one variable

6.2 Inequalities

6.3 Linear inequalities

6.4 Sample set a

6.5 Practice set a

6.6 The algebra of linear inequalities

6.7 Sample set b

6.8 Practice set b

6.9 Compound inequalities

6.10 Sample set c

6.11 Practice set c

6.13 Exercises for review

7 Linear equations in two variables

8 Summary of key concepts

9 Exercise supplement

10 Proficiency exam

Factoring polynomials

1 Finding the factors of a monomial

1.2 Products of polynomials

1.4 Sample set a

1.5 Practice set a

1.7 Exercises for review

2 Factoring a monomial from a polynomial

3 The greatest common factor

3.2 Factoring method

3.3 Greatest common factor

3.4 Sample set a

3.5 Practice set a

3.6 Sample set b

3.7 Practice set b

3.9 Exercises for review

4 Factoring by grouping

5 Factoring two special products

6 Factoring trinomials with leading coefficient 1

7 Factoring trinomials with leading coefficient other than 1

8 Summary of key concepts

9 Exercise supplement

10 Proficiency exam

Graphing linear equations and inequalities in one and two variables

1 Graphing linear equations and inequalities in one variable

2 Plotting points in the plane

2.3 Coordinates of a point

2.4 Plotting points

2.5 Sample set a

2.6 Practice set a

2.8 Exercises for review

3 Graphing linear equations in two variables

4 The slope-intercept form of a line

4.2 The general form of a line

4.3 The slope-intercept form of a line

4.4 Sample set a

4.5 Practice set a

4.6 Slope and intercept

4.7 Sample set b

4.8 Practice set b

4.9 Sample set c

4.10 Practice set c

4.11 The formula for the slope of a line

4.12 Sample set d

4.13 Practice set d

4.15 Calculator problems

4.16 Exercises for review

5 Graphing equations in slope-intercept form

6 Finding the equation of a line

7 Graphing linear inequalities in two variables

8 Summary of key concepts

9 Exercise supplement

10 Proficiency exam

Rational expressions

1 Rational expressions

1.2 Rational expressions

1.3 Zero-factor property

1.4 Sample set a

1.5 Practice set a

1.6 The equality property of fractions

1.7 The negative property of fractions

1.8 Sample set b

1.9 Practice set b

1.11 Exercises for review

2 Reducing rational expressions

2.2 The logic behind the process

2.4 The process

2.5 Sample set a

2.6 Practice set a

2.8 Excercises for review

3 Multiplying and dividing rational expressions

3.2 Multiplication of rational expressions

3.3 Sample set a

3.4 Practice set a

3.5 Division of rational expressions

3.6 Sample set b

3.7 Practice set b

3.9 Exercises for review

4 Building rational expressions and the lcd

4.2 The process

4.3 Sample set a

4.4 Practice set a

4.5 The reason for building rational expressions

4.6 The least common denominator (lcd)

4.7 Sample set b

4.8 Practice set b

4.9 Sample set c

4.10 Practice set c

4.12 Excercises for review

5 Adding and subtracting rational expressions

5.3 Fractions with the same denominator

5.4 Sample set a

5.5 Practice set a

5.6 Fractions with different denominators

5.7 Sample set b

5.8 Practice set b

5.9 Sample set c

5.10 Practice set c

5.12 Exercises for review

6 Rational equations

6.2 Rational equations

6.3 Rational equations

6.4 The logic behind the process

6.5 The process

6.6 Extraneous solutions

6.7 Sample set a

6.8 Practice set a

6.9 Sample set b

6.10 Practice set b

6.11 Section 7.6 exercises

6.12 Exercises for review

8 Complex rational expressions

8.2 Simple and complex fractions

8.3 The combine-divide method

8.4 Sample set a

8.5 Practice set a

8.6 The lcd-multiply-divide method

8.7 Sample set b

8.8 Practice set b

8.10 Exercises for review

9 Dividing polynomials

9.2 Dividing a polynomial by a monomial

9.3 Sample set a

9.4 Practice set a

9.5 The process of division

9.6 Review of subtraction of polynomials

9.7 Dividing a polynomial by a polynomial

9.8 Sample set b

9.9 Practice set b

9.10 Sample set c

9.11 Practice set c

9.13 Exercises for review

10 Summary of key concepts

11 Exercise supplement

12 Proficiency exam

Roots, radicals, and square root equations

1 Square root expressions

1.2 Square roots

1.3 Sample set a

1.4 Practice set a

1.5 Principal and secondary square roots

1.6 Sample set b

1.7 Practice set b

1.8 Meaningful expressions

1.9 Sample set c

1.10 Practice set c

1.11 Simplifying square roots

1.12 Sample set d

1.13 Practice set d

1.15 Exercised for review

2 Simplifying square root expressions

3 Multiplication of square root expressions

4 Division of square root expressions

5 Addition and subtraction of square root expressions

5.2 The logic behind the process

5.3 The process

5.4 Sample set a

5.5 Practice set a

5.6 Sample set b

5.7 Practice set b

5.9 Exercises for review

6 Square root equations with applications

7 Summary of key concepts

8 Exercise supplement

9 Proficiency exam

Quadratic equations

1 Solving quadratic equations

1.2 Standard form of a quadratic equation

1.3 Sample set a

1.4 Practice set a

1.5 Zero-factor property

1.6 Sample set b

1.7 Practice set b

1.9 Exercises for review

2 Solving quadratic equations by factoring

3 Solving quadratic equations using the method of extraction of roots

4 Solving quadratic equations using the method of completing the square

5 Solving quadratic equations using the quadratic formula

5.2 Standard form of a quadratic equation

5.3 Sample set a

5.4 Practice set a

5.5 The quadratic formula

5.6 Derivation of the quadratic formula

5.7 Sample set b

5.8 Practice set b

5.10 Exercises for review

6.2 The five-step method

6.3 Sample set a

6.4 Practice set a

6.5 Sample set b

6.6 Practice set b

6.7 Sample set c

6.8 Practice set c

6.9 Sample set d

6.10 Practice set d

6.11 Sample set e

6.12 Practice set e

6.13 Sample set f

6.14 Practice set f

6.16 Sample set a—type problems

6.17 Sample set b—type problems

6.18 Sample set c—type problems

6.19 Sample set d—type problems

6.20 Sample set e—type problems

6.21 Sample set f—type problems

6.22 Astrophysical problem

6.23 Exercises for review

7 Graphing quadratic solutions

8 Summary of key concepts

9 Exercise supplement

10 Proficiency exam

Systems of linear equations

1 Solutions by graphing

1.2 Systems of equations

1.3 Solution to a system of equations

1.4 Graphs of systems of equations

1.5 Independent, inconsistent, and dependent systems

1.6 The method of solving a system graphically

1.7 Sample set a

1.8 Practice set a

1.10 Exercises for review

2 Elimination by substitution

2.2 When substitution works best

2.3 The substitution method

2.4 Sample set a

2.5 Practice set a

2.6 Substitution and parallel lines

2.7 Sample set b

2.8 Practice set b

2.9 Substitution and coincident lines

2.10 Sample set c

2.11 Practice set c

2.12 Sample set d

2.13 Practice set d

2.15 Exercises for review

3 Elimination by addition

3.2 The properties used in the addition method

3.3 The addition method

3.4 Sample set a

3.5 Practice set a

3.6 Sample set b

3.7 Practice set b

3.8 Addition and parallel or coincident lines

3.9 Sample set c

3.10 Practice set c

3.12 Exercises for review

4.2 The five-step method

4.3 Sample set a (number problems)

4.4 Practice set a

4.5 Sample set b (coin problems)

4.6 Practice set b

4.7 Sample set c (mixture problems)

4.8 Practice set c

4.10 Exercises for review

5 Summary of key concepts

6 Exercise supplement

7 Proficiency exam

Table of symbols

1 Properties of real numbers

2 Important and useful rules/formulas

3 The 5-step method of solving applied problems

Source: OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3

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