Beginning Algebra, 13th Edition By Margaret Lial, John Hornsby, Terry McGinnis (eBook PDF)

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Get the Most Out of MyLab Math Beginning Algebra Contents Preface Welcome to the 13th Edition What’s New in this Edition? Content Changes Lial Developmental Hallmark Features Resources for S... uccess Photo Credits Study Skills Chapter R Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Study Skills Study Skill 1 Using Your Math Text Study Skill 2 Reading Your Math Text Approaches to Reading Your Math Text Tips for Reading Your Math Text Study Skill 3 Taking Lecture Notes Study Skill 4 Completing Your Homework Homework Tips Study Skill 5 Using Study Cards Vocabulary Cards Procedure (“Steps”) Cards Practice Problem Cards Study Skill 6 Managing Your Time Time Management Tips Study Skill 7 Reviewing a Chapter Techniques for Reviewing a Chapter Study Skill 8 Taking Math Tests Study Skill 9 Analyzing Your Test Results Typical Reasons for Errors on Math Tests Study Skill 10 Preparing for Your Math Final Exam Final Exam Preparation Suggestions Chapter R Prealgebra Review Chapter Contents R.1 Fractions Objectives Objective 1 Write numbers in factored form Objective 2 Write fractions in lowest terms Objective 3 Convert between improper fractions and mixed numbers Objective 4 Multiply and divide fractions Objective 5 Add and subtract fractions Objective 6 Solve applied problems that involve fractions Objective 7 Interpret data in a circle graph R.1 Exercises R.2 Decimals and Percents Objectives Objective 1 Write decimals as fractions Objective 2 Add and subtract decimals Objective 3 Multiply and divide decimals Objective 4 Write fractions as decimals Objective 5 Write percents as decimals and decimals as percents Objective 6 Write percents as fractions and fractions as percents Objective 7 Solve applied problems that involve percents R.2 Exercises Chapter 1 The Real Number System Chapter Contents 1.1 Exponents, Order of Operations, and Inequality Objectives Objective 1 Use exponents Objective 2 Use the rules for order of operations Objective 3 Use more than one grouping symbol Objective 4 Use inequality symbols in statements Objective 5 Translate word statements to symbols Objective 6 Write statements that change the direction of inequality symbols 1.1 Exercises 1.2 Variables, Expressions, and Equations Objectives Objective 1 Evaluate algebraic expressions, given values for the variables Objective 2 Translate word phrases to algebraic expressions Objective 3 Identify solutions of equations Objective 4 Identify solutions of equations from a set of numbers Objective 5 Distinguish between expressions and equations 1.2 Exercises 1.3 Real Numbers and the Number Line Objectives Objective 1 Classify numbers and graph them on number lines Objective 2 Use inequality symbols with real numbers Objective 3 Find the additive inverse of a real number Objective 4 Find the absolute value of a real number Objective 5 Interpret meanings of real numbers from a table of data 1.3 Exercises 1.4 Adding and Subtracting Real Numbers Objectives Objective 1 Add two numbers with the same sign Objective 2 Add two numbers with different signs Objective 3 Use the definition of subtraction Objective 4 Use the rules for order of operations when adding and subtracting signed numbers Objective 5 Translate words and phrases involving addition and subtraction Objective 6 Use signed numbers to interpret data 1.4 Exercises 1.5 Multiplying and Dividing Real Numbers Objectives Objective 1 Find the product of a positive number and a negative number Objective 2: Find the product of two negative numbers Objective 3 Identify factors of integers Objective 4 Use the reciprocal of a number to apply the definition of division Objective 5 Use the rules for order of operations when multiplying and dividing signed numbers Objective 6 Evaluate algebraic expressions given values for the variables Objective 7 Translate words and phrases involving multiplication and division Objective 8 Translate simple sentences into equations 1.5 Exercises Summary Exercises: Performing Operations with Real Numbers 1.6 Properties of Real Numbers Objectives Objective 1 Use the commutative properties Objective 2 Use the associative properties Objective 3 Use the identity properties Objective 4 Use the inverse properties Objective 5 Use the distributive property 1.6 Exercises 1.7 Simplifying Expressions Objectives Objective 1 Simplify expressions Objective 2 Identify terms and numerical coefficients Objective 3 Identify like terms Objective 4 Combine like terms Objective 5 Simplify expressions from word phrases 1.7 Exercises Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Mixed Review Exercises Chapter 1 Test Chapters R and 1 Cumulative Review Exercises Chapter 2 Linear Equations and Inequalities in One Variable Chapter Contents 2.1 The Addition Property of Equality Objectives Objective 1 Identify linear equations. Objective 2 Use the addition property of equality. Objective 3 Simplify, and then use the addition property of equality. 2.1 Exercises 2.2 The Multiplication Property of Equality Objectives Objective 1 Use the multiplication property of equality. Objective 2 Simplify, and then use the multiplication property of equality. 2.2 Exercises 2.3 Solving Linear Equations Using Both Properties of Equality Objectives Objective 1 Use the four steps for solving a linear equation. Objective 2 Solve equations with no solution or infinitely many solutions. Objective 3 Write expressions for two related unknown quantities. 2.3 Exercises 2.4 Clearing Fractions and Decimals When Solving Linear Equations Objectives Objective 1 Solve equations with fractions as coefficients. Objective 2 Solve equations with decimals as coefficients. 2.4 Exercises Summary Exercises: Applying Methods for Solving Linear Equations 2.5 Applications of Linear Equations Objectives Objective 1 Learn the six steps for solving applied problems. Objective 2 Solve problems involving unknown numbers. Objective 3 Solve problems involving sums of quantities. Objective 4 Solve problems involving consecutive integers. Objective 5 Solve problems involving complementary and supplementary angles. 2.5 Exercises 2.6 Formulas and Additional Applications from Geometry Objectives Objective 1 Solve a formula for one variable, given values of the other variables. Objective 2 Use a formula to solve an applied problem. Objective 3 Solve problems involving vertical angles and straight angles. Objective 4 Solve a formula for a specified variable. 2.6 Exercises 2.7 Ratio, Proportion, and Percent Objectives Objective 1 Write ratios. Objective 2 Solve proportions. Objective 3 Solve applied problems using proportions. Objective 4 Find percents and percentages. 2.7 Exercises 2.8 Further Applications of Linear Equations Objectives Objective 1 Solve percent problems involving rates. Objective 2 Solve problems involving mixtures. Objective 3 Solve problems involving simple interest. Objective 4 Solve problems involving denominations of money. Objective 5 Solve problems involving distance, rate, and time. 2.8 Exercises 2.9 Solving Linear Inequalities Objectives Objective 1 Graph intervals on a number line. Objective 2 Use the addition property of inequality. Objective 3 Use the multiplication property of inequality. Objective 4 Solve linear inequalities using both properties of inequality. Objective 5 Solve applied problems using inequalities. Objective 6 Solve linear inequalities with three parts. 2.9 Exercises Chapter 2 Summary Key Terms 2.1 2.3 2.5 2.6 2.7 2.9 New Symbols Test Your Word Power ANSWERS Chapter 2 Review Exercises Chapter 2 Mixed Review Exercises Chapter 2 Test Chapters R–2 Cumulative Review Exercises Chapter 3 Linear Equations and Inequalities in Two Variables; Functions Chapter Contents 3.1 Linear Equations and Rectangular Coordinates Objectives Objective 1 Interpret line graphs. Objective 2 Write a solution as an ordered pair. Objective 3 Determine whether a given ordered pair is a solution of a given equation. Objective 4 Complete ordered pairs for a given equation. Objective 5 Complete a table of values. Objective 6 Plot ordered pairs. 3.1 Exercises 3.2 Graphing Linear Equations in Two Variables Objectives Objective 1 Graph linear equations by plotting ordered pairs. Objective 2 Find intercepts. Objective 3 Graph linear equations of the form Ax+By=0. Objective 4 Objective 5 Use a linear equation to model data. 3.2 Exercises 3.3 The Slope of a Line Objectives Objective 1 Find the slope of a line given two points. Objective 2 Find the slope from the equation of a line. Objective 3 Use slopes to determine whether two lines are parallel, perpendicular, or neither. 3.3 Exercises 3.4 Slope-Intercept Form of a Linear Equation Objectives Objective 1 Use slope-intercept form of the equation of a line. Objective 2 Graph a line using its slope and a point on the line. Objective 3 Write an equation of a line using its slope and any point on the line. Objective 4 Graph and write equations of horizontal and vertical lines. 3.4 Exercises 3.5 Point-Slope Form of a Linear Equation and Modeling Objectives Objective 1 Use point-slope form to write an equation of a line. Objective 2 Write an equation of a line using two points on the line. Objective 3 Write an equation of a line that fits a data set. 3.5 Exercises Summary Exercises: Applying Graphing and Equation-Writing Techniques for Lines 3.6 Graphing Linear Inequalities in Two Variables Objectives Objective 1 Graph linear inequalities in two variables. Objective 2 Graph an inequality with a boundary line through the origin. 3.6 Exercises 3.7 Introduction to Functions Objectives Objective 1 Define a relation. Objective 2 Define a function. Objective 3 Determine whether a graph or an equation represents a function. Objective 4 Find domains and ranges. Objective 5 Use function notation. Objective 6 Apply the function concept in an application. 3.7 Exercises Chapter 3 Summary Key Terms 3.1 3.2 3.3 3.6 3.7 New Symbols Test Your Word Power ANSWERS Chapter 3 Review Exercises Chapter 3 Mixed Review Exercises Chapter 3 Test Chapters R–3 Cumulative Review Exercises Chapter 4 Systems of Linear Equations and Inequalities Chapter Contents 4.1 Solving Systems of Linear Equations by Graphing Objectives Objective 1 Determine whether a given ordered pair is a solution of a system Objective 2 Solve linear systems by graphing Objective 3 Solve special systems by graphing Objective 4 Identify special systems without graphing 4.1 Exercises 4.2 Solving Systems of Linear Equations by Substitution Objectives Objective 1 Solve linear systems by substitution Objective 2 Solve special systems by substitution Objective 3 Solve linear systems with fractions and decimals 4.2 Exercises 4.3 Solving Systems of Linear Equations by Elimination Objectives Objective 1 Solve linear systems by elimination Objective 2 Multiply when using the elimination method Objective 3 Use an alternative method to find the second value in a solution Objective 4 Solve special systems by elimination 4.3 Exercises Summary Exercises: Applying Techniques for Solving Systems of Linear Equations 4.4 Applications of Linear Systems Objectives Objective 1 Solve problems about unknown numbers Objective 2 Solve problems about quantities and their costs Objective 3 Solve problems about mixtures Objective 4 Solve problems about distance, rate (or speed), and time 4.4 Exercises 4.5 Solving Systems of Linear Inequalities Objective Objective 1 Solve systems of linear inequalities by graphing 4.5 Exercises Chapter 4 Summary Key Terms 4.1 4.5 Test Your Word Power ANSWERS Chapter 4 Review Exercises Chapter 4 Mixed Review Exercises Chapter 4 Test Chapters R–4 Cumulative Review Exercises Chapter 5 Exponents and Polynomials Chapter Contents 5.1 The Product Rule and Power Rules for Exponents Objectives Objective 1 Use exponents Objective 2 Use the product rule for exponents Objective 3 Use the rule (am)n=amn. Objective 4 Use the rule (ab)m=ambm. Objective 5 Use the rule (ab)m=ambm . Objective 6 Use combinations of the rules for exponents Objective 7 Apply the rules for exponents in a geometry application 5.1 Exercises 5.2 Integer Exponents and the Quotient Rule Objectives Objective 1 Use 0 as an exponent Objective 2 Use negative numbers as exponents Objective 3 Use the quotient rule for exponents Objective 4 Use combinations of the rules for exponents 5.2 Exercises Summary Exercises: Applying the Rules for Exponents 5.3 Scientific Notation Objectives Objective 1 Express numbers in scientific notation Objective 2 Convert numbers in scientific notation to standard notation Objective 3 Use scientific notation in calculations 5.3 Exercises 5.4 Adding, Subtracting, and Graphing Polynomials Objectives Objective 1 Identify terms and coefficients Objective 2 Combine like terms Objective 3 Describe polynomials using appropriate vocabulary Objective 4 Evaluate polynomials Objective 5 Add and subtract polynomials Objective 6 Graph equations defined by polynomials of degree 2 5.4 Exercises 5.5 Multiplying Polynomials Objectives Objective 1 Multiply monomials Objective 2 Multiply a monomial and a polynomial Objective 3 Multiply two polynomials Objective 4 Multiply binomials using the FOIL method 5.5 Exercises 5.6 Special Products Objectives Objective 1 Square binomials Objective 2 Find the product of the sum and difference of two terms Objective 3 Find greater powers of binomials 5.6 Exercises 5.7 Dividing Polynomials Objectives Objective 1 Divide a polynomial by a monomial Objective 2 Divide a polynomial by a polynomial Objective 3 Apply polynomial division in a geometry problem 5.7 Exercises Chapter 5 Summary Key Terms 5.1 5.3 5.4 5.5 5.6 New Symbols Test Your Word Power ANSWERS Chapter 5 Review Exercises Chapter 5 Mixed Review Exercises Chapter 5 Test Chapters R–5 Cumulative Review Exercises Chapter 6 Factoring and Applications Chapter Contents 6.1 Greatest Common Factors; Factoring by Grouping Objectives Objective 1 Find the greatest common factor of a list of numbers Objective 2 Find the greatest common factor of a list of variable terms Objective 3 Factor out the greatest common factor Objective 4 Factor by grouping 6.1 Exercises 6.2 Factoring Trinomials Objectives Objective 1 Factor trinomials with coefficient 1 for the second-degree term Objective 2 Factor out the greatest common factor first 6.2 Exercises 6.3 More on Factoring Trinomials Objectives Objective 1 Factor trinomials by grouping when the coefficient of the second- degree term is not 1 Objective 2 Factor trinomials using the FOIL method 6.3 Exercises 6.4 Special Factoring Techniques Objectives Objective 1 Factor a difference of squares Objective 2 Factor a perfect square trinomial Objective 3 Factor a difference of cubes Objective 4 Factor a sum of cubes 6.4 Exercises Summary Exercises: Recognizing and Applying Factoring Strategies 6.5 Solving Quadratic Equations Using the Zero-Factor Property Objectives Objective 1 Solve quadratic equations using the zero-factor property Objective 2 Solve other equations using the zero-factor property 6.5 Exercises 6.6 Applications of Quadratic Equations Objectives Objective 1 Solve problems involving geometric figures Objective 2 Solve problems involving consecutive integers Objective 3 Solve problems by applying the Pythagorean theorem Objective 4 Solve problems using given quadratic models 6.6 Exercises Chapter 6 Summary Key Terms 6.1 6.2 6.4 6.5 6.6 Test Your Word Power Answers Chapter 6 Review Exercises Chapter 6 Mixed Review Exercises Chapter 6 Test Chapters R–6 Cumulative Review Exercises Chapter 7 Rational Expressions and Applications Chapter Contents 7.1 The Fundamental Property of Rational Expressions Objectives Objective 1 Find the numerical value of a rational expression Objective 2 Find the values of the variable for which a rational expression is undefined Objective 3 Write rational expressions in lowest terms Objective 4 Recognize equivalent forms of rational expressions 7.1 Exercises 7.2 Multiplying and Dividing Rational Expressions Objectives Objective 1 Multiply rational expressions Objective 2 Find reciprocals of rational expressions Objective 3 Divide rational expressions 7.2 Exercises 7.3 Least Common Denominators Objectives Objective 1 Find the least common denominator for a list of fractions Objective 2 Write equivalent rational expressions 7.3 Exercises 7.4 Adding and Subtracting Rational Expressions Objectives Objective 1 Add rational expressions having the same denominator Objective 2 Add rational expressions having different denominators Objective 3 Subtract rational expressions 7.4 Exercises 7.5 Complex Fractions Objectives Objective 1 Define and recognize a complex fraction Objective 2 Simplify a complex fraction by writing it as a division problem (Method 1) Objective 3 Simplify a complex fraction by multiplying numerator and denominator by the LCD (Method 2) 7.5 Exercises 7.6 Solving Equations with Rational Expressions Objectives Objective 1 Distinguish between operations with rational expressions and equations with terms that are rational expressions. Objective 2 Solve equations with rational expressions. Objective 3 Solve a formula for a specified variable. 7.6 Exercises Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations 7.7 Applications of Rational Expressions Objectives Objective 1 Solve problems about numbers. Objective 2 Solve problems about distance, rate, and time. Objective 3 Solve problems about work. 7.7 Exercises 7.8 Variation Objectives Objective 1 Solve direct variation problems. Objective 2 Solve inverse variation problems. 7.8 Exercises Chapter 7 Summary Key Terms 7.1 7.2 7.3 7.5 7.6 7.8 Test Your Word Power ANSWERS Chapter 7 Review Exercises Chapter 7 Mixed Review Exercises Chapter 7 Test Chapters R–7 Cumulative Review Exercises Chapter 8 Roots and Radicals Chapter Contents 8.1 Evaluating Roots Objectives Objective 1 Find square roots. Objective 2 Determine whether a given root is rational, irrational, or not a real number. Objective 3 Find decimal approximations for irrational square roots. Objective 4 Use the Pythagorean theorem. Objective 5 Use the distance formula. Objective 6 Find cube, fourth, and other roots. 8.1 Exercises 8.2 Multiplying, Dividing, and Simplifying Radicals Objectives Objective 1 Multiply square root radicals. Objective 2 Simplify radicals using the product rule. Objective 3 Simplify radicals using the quotient rule. Objective 4 Simplify radicals involving variables. Objective 5 Simplify other roots. 8.2 Exercises 8.3 Adding and Subtracting Radicals Objectives Objective 1 Add and subtract radicals. Objective 2 Simplify radical sums and differences. Objective 3 Simplify more complicated radical expressions. 8.3 Exercises 8.4 Rationalizing the Denominator Objectives Objective 1 Rationalize denominators with square roots. Objective 2 Write radicals in simplified form. Objective 3 Rationalize denominators with cube roots. 8.4 Exercises 8.5 More Simplifying and Operations with Radicals Objectives Objective 1 Simplify products of radical expressions. Objective 2 Use conjugates to rationalize denominators of radical expressions. Objective 3 Write radical expressions with quotients in lowest terms. 8.5 Exercises Summary Exercises: Applying Operations with Radicals 8.6 Solving Equations with Radicals Objectives Objective 1 Solve radical equations having square root radicals. Objective 2 Identify equations with no solutions. Objective 3 Solve equations by squaring a binomial. Objective 4 Solve radical equations having cube root radicals. 8.6 Exercises Chapter 8 Summary Key Terms 8.1 8.3 8.5 8.6 New Symbols Test Your Word Power ANSWERS Chapter 8 Review Exercises Chapter 8 Mixed Review Exercises Chapter 8 Test Chapters R–8 Cumulative Review Exercises Chapter 9 Quadratic Equations Chapter Contents 9.1 Solving Quadratic Equations by the Square Root Property Objectives Objective 1 Solve quadratic equations using the zero-factor property. (Review) Objective 2 Solve equations of the form x2=k, where k>0. Objective 3 Solve equations of the form (ax+b)2=k, where k>0. Objective 4 Use formulas involving second-degree variables 9.1 Exercises 9.2 Solving Quadratic Equations by Completing the Square Objectives Objective 1 Solve quadratic equations by completing the square when the coefficient of the second-degree term is 1 Objective 2 Solve quadratic equations by completing the square when the coefficient of the second-degree term is not 1 Objective 3 Simplify the terms of an equation before solving Objective 4 Solve applied problems that require quadratic equations 9.2 Exercises 9.3 Solving Quadratic Equations by the Quadratic Formula Objectives Objective 1 Identify the values of a, b, and c in a quadratic equation Objective 2 Use the quadratic formula to solve quadratic equations Objective 3 Solve quadratic equations with a double solution Objective 4 Solve quadratic equations with fractional coefficients 9.3 Exercises Summary Exercises: Applying Methods for Solving Quadratic Equations 9.4 Graphing Quadratic Equations Objectives Objective 1 Graph quadratic equations Objective 2 Find the vertex and intercepts of a parabola 9.4 Exercises Chapter 9 Summary Key Terms 9.1 9.3 9.4 New Symbol Test Your Word Power ANSWERS Chapter 9 Review Exercises Chapter 9 Mixed Review Exercises Chapter 9 Test Chapters R–9 Cumulative Review Exercises Answers to Selected Exercises R Prealgebra Review Section R.1 Section R.2 1 The Real Number System Section 1.1 Section 1.2 Section 1.3 Section 1.4 Section 1.5 Section 1.6 Section 1.7 Chapter 1 Review Exercises Chapter 1 Mixed Review Exercises Chapter 1 Test Chapters R and 1 Cumulative Review Exercises 2 Linear Equations and Inequalities in One Variable Section 2.1 Section 2.2 Section 2.3 Section 2.4 Section 2.5 Section 2.6 Section 2.7 Section 2.8 Section 2.9 Chapter 2 Review Exercises Chapter 2 Mixed Review Exercises Chapter 2 Test Chapters R–2 Cumulative Review Exercises 3 Linear Equations and Inequalities in Two Variables; Functions Section 3.1 Section 3.2 Section 3.3 Section 3.4 Section 3.5 Summary Exercises: Applying Graphing and Equation-Writing Techniques for Lines Section 3.6 Section 3.7 Chapter 3 Review Exercises Chapter 3 Mixed Review Exercises Chapter 3 Test Chapters R–3 Cumulative Review Exercises 4 Systems of Linear Equations and Inequalities Section 4.1 Section 4.2 Section 4.3 Summary Exercises: Applying Techniques for Solving Systems of Linear Equations Section 4.4 Section 4.5 Chapter 4 Review Exercises Chapter 4 Mixed Review Exercises Chapter 4 Test Chapters R– 4 Cumulative Review Exercises 5 Exponents and Polynomials Section 5.1 Section 5.2 Summary Exercises: Applying the Rules for Exponents Section 5.3 Section 5.4 Section 5.5 Section 5.6 Section 5.7 Chapter 5 Review Exercises Chapter 5 Mixed Review Exercises Chapter 5 Test Chapters R–5 Cumulative Review Exercises 6 Factoring and Applications Section 6.1 Section 6.2 Section 6.3 Section 6.4 Summary Exercises: Recognizing and Applying Factoring Strategies Section 6.5 Section 6.6 Chapter 6 Review Exercises Chapter 6 Mixed Review Exercises Chapter 6 Test Chapters R–6 Cumulative Review Exercises 7 Rational Expressions and Applications Section 7.1 Section 7.2 Section 7.3 Section 7.4 Section 7.5 Section 7.6 Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations Section 7.7 Section 7.8 Chapter 7 Review Exercises Chapter 7 Mixed Review Exercises Chapter 7 Test Chapters R–7 Cumulative Review Exercises 8 Roots and Radicals Section 8.1 Section 8.2 Section 8.3 Section 8.4 Section 8.5 Summary Exercises Applying Operations with Radicals Section 8.6 Chapter 8 Review Exercises Chapter 8 Mixed Review Exercises Chapter 8 Test Chapters R–8 Cumulative Review Exercises 9 Quadratic Equations Section 9.1 Section 9.2 Section 9.3 Summary Exercises: Applying Methods for Solving Quadratic Equations Section 9.4 Chapter 9 Review Exercises Chapter 9 Mixed Review Exercises Chapter 9 Test Chapters R–9 Cumulative Review Exercises [Show More]

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