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You have successfully signed out and will be required to sign back in should you need to download more resources. Intermediate Algebra, 11th Edition. Margaret L. Description For courses in Basic Mathematics. This package includes MyLab Math. The perfect combination to master concepts: student-friendly writing, well-crafted exercises, and superb support The Lial Series has helped thousands of students succeed in developmental mathematics by combining clear, concise writing and examples with carefully crafted exercises to support skill development and conceptual understanding.
Personalize learning with MyLab Math. Coverage of Guided Solution exercises has been increased in this revision. These exercises allow instructors to assess student understanding of the problem-solving process, rather than completing the steps by rote, and to also keep students on the right track as they work through the problem-solving steps. Relating Concepts exercises in the text help students make connections and problem-solve at a higher level.
These sets are assignable in MyLab Math, with expanded coverage in this revision. Workspace Assignments allow students to work through an exercise step-by-step, adjusting to the path each student takes and allowing them to show their mathematical reasoning as they progress, receiving feedback when and where they need it most. When accessed via a mobile device, Workspace exercises use handwriting recognition software that allows students to naturally write out their answers with their fingertip or stylus.
Premade sample assignments are available in the Assignment Manager, and include a pre-made pre- and post- test for every chapter, section-level homework with Guided Solutions exercises, and chapter review quiz linked to personalized homework. A variety of resources bring the hallmark Lial pedagogy and approach into the MyLab Math course.
The extensive Lial video program makes the MyLab Math course a true learning environment, and gives students support right when they need it, wherever they need it. The variety of videos give instructors flexibility - different types of videos allow for different learning environments, such as a flipped classroom or lab, and different assignment types. Many of the videos have been updated in this revision to more closely match the exercises from the text, in a more modern presentation format.
Videos available include the following, which all offer optional English and Spanish captioning: Solutions Clips for select exercises marked with a Play Button icon in the text and eText show an instructor working through the complete solution to that exact problem. Objective-level videos are short, bite-size chunks taken from the section lecture videos.
Students often will not watch a video longer than 5 minutes, so objective-level videos give just the right amount of content to keep their attention.
Section Lecture Videos are available for every section, and offer a navigation menu by example and objective. Quick Review Lectures provide a summary of key concepts for each chapter. They can also be accessed on YouTube. The Lial Video Workbook corresponds to the videos, and gives students a place to record the examples from the videos and try problems on their own. In addition to a library of premade developmental math questions in Learning Catalytics, the authors have included suggested Learning Catalytics questions , drawing on prerequisite skills, at the start of each section to check student preparedness for the new material.
In addition to assignable Study Skills and Reading Connection material, new Mindset material has been added to the course. This content encourages students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as a learning opportunity - so often a major hurdle for developmental math students. This latest course release is compatible with the JAWS screen reader, enabling print-disabled students to access and interact with numerous problems as noted by an icon within the assignment manager.
The course also works with the ZoomText enlarger, and includes an HTML eBook that is compatible with JAWS and other Windows screen readers, allowing all students to access the same text, at the same place, and at the same price.
Additionally, all videos include subtitles. About the Book Student-friendly features to make math accessible Margin Problems allow students to immediately practice the example material and check their answer at the bottom of the page in preparation for the exercise sets. Real-Life Applications with interesting data are used in many new or updated examples and exercises throughout the text.
Students are often asked to find data in a table, chart, graph, or advertisement. These applied problems provide an up-to-date flavor that will appeal to and motivate students.
Learning Objectives begin each section, and all material is keyed to these objectives to let students and instructors know exactly what will be covered. Pointers within examples, Cautions highlighted in yellow and Notes highlighted in blue provide students with important, on-the-spot reminders and warnings about common pitfalls.
A popular feature, Pointers have been increased in this edition. Study Skills activities provide students with proven strategies for learning math. Many of these now include a Now Try This section to increase student involvement and accountability for the study skills activities. See pages G-1 to G Over the years, we have come to rely on an extensive team of experienced professionals.
Abby Tanenbaum did a terrific job helping us revise real-data applications. Kathy Diamond provided expert guidance through all phases of production and rescued us from one snafu or another on multiple occasions.
Marilyn Dwyer and Nesbitt Graphics, Inc. It has indeed been a pleasure to work with such an outstanding group of professionals. As an author team, we are committed to providing the best possible text and supplements package to help instructors teach and students succeed.
As we continue to work toward this goal, we would welcome any comments or suggestions you might have via e-mail to [email protected] Margaret L. These are in Student Edition also. Cole, Anoka-Ramsey Community College N Provides complete answers to all text exercises, dents navigate the road to success N Available in MyMathLab with optional subtitles in English N Includes the following resources: Section Lecture Videos that offer a new navigation menu for easy focus on key examples and exercises needed for review in each section with optional subtitles in Spanish Solutions Clips that feature an instructor working through selected exercises marked in the text with a DVD icon Quick Review Lectures that provide a short summary lecture of each key concept from Quick Reviews at the end of every chapter in the text Chapter Test Prep Videos that include step-by-step solutions to all Chapter Test exercises and give guidance and support when needed most—the night before an exam.
MyMathLab gives instructors the tools they need to deliver all or a portion of their course online, whether their students are in a lab setting or working from home. N Interactive homework exercises, correlated to the textbook at the objective level, are algorithmically generated for unlimited practice and mastery. Most exercises are free-response and provide guided solutions, sample problems, and tutorial learning aids for extra help.
N Personalized homework assignments can be designed to meet the needs of the class. N Personalized Study Plan, generated when students complete a test or quiz or homework, indicates which topics have been mastered and links to tutorial exercises for topics students have not mastered.
Instructors can customize the Study Plan so that the topics available match their course content. N Multimedia learning aids, such as video lectures and podcasts, animations, and a complete multimedia textbook, help students independently improve their understanding and performance.
Instructors can assign these multimedia learning aids as homework to help their students grasp the concepts. N Homework and Test Manager lets instructors assign homework, quizzes, and tests that are automatically graded. They can also add offline paper-and-pencil grades to the gradebook.
Preface xvii N MathXL Exercise Builder allows instructors to create static and algorithmic exercises for their online assignments. They can use the library of sample exercises as an easy starting point, or they can edit any course-related exercise. N Pearson Tutor Center www.
The Tutor Center is staffed by qualified math instructors who provide textbook-specific tutoring for students via toll-free phone, fax, email, and interactive Web sessions. MyMathLab is available to qualified adopters. For more information, visit our website at www. Most exercises are free-response and provide guided solutions, sample problems, and learning aids for extra help. N Personalized homework assignments are designed by the instructor to meet the needs of the class, and then personalized for each student based on their test or quiz results.
As a result, each student receives a homework assignment that contains only the problems they still need to master. Instructors can customize the available topics in the study plan to match their course concepts. N Multimedia learning aids, such as video lectures and animations, help stu- dents independently improve their understanding and performance. These are assignable as homework, to further encourage their use. N MathXL Exercise Builder allows instructors to create static and algorithmic exercises for their online assignments.
They can use the library of sample exercises as an easy starting point or the Exercise Builder to edit any of the courserelated exercises. N Homework and Test Manager lets instructors create online homework, quizzes, and tests that are automatically graded. MathXL is available to qualified adopters. You will learn more if you fully make use of the features it offers.
Mark the chapters and sections you will cover, as noted on your course syllabus. N Answer Section Tab this section at the back of the book so you can refer to it frequently when doing homework.
Answers to odd-numbered section exercises are provided. Answers to ALL summary, chapter review, test, and cumulative review exercises are given.
N Glossary Find this feature after the answer section at the 2. His collection contai ns only dimes and nickels. How many of each type of coin does he have? How many of each quardenomination of coin did the cashier receive? Step 1 Read the probl em. The problem asks that we find the number of nicke the number of quarters the ls and cashier received.
Step 2 Assign a varia ble. Then organize the inform ation in a table. Nickels Number of Coins Step 4 Solve. Value 0. Denomination x 25 - x Step 3 Write an equat ion from helpful list of geometric formulas, along with review information on triangles and angles.
Use these for reference throughout the course. Distributive property Subtract Combine like terms. Divide by - Step 6 Check. Becau you are working probse you are dealing with a number of coins, the corre answer can be neither negat ct ive nor a fraction.
Once you finish a section, ask yourself if you have accomplished them. N Now Try Exercises These margin exercises allow you to immediately practice the material covered in the examples and prepare you for the exercises. Check your results using the answers at the bottom of the page. N Pointers These small shaded balloons provide on-the-spot warnings and reminders, point out key steps, and give other helpful tips. N Cautions These provide warnings about common errors that students often make or trouble spots to avoid.
N Notes These provide additional explanations or emphasize important ideas. N Problem-Solving Hints These green boxes give helpful tips or strategies to use Find an example of each of these features in your textbook. Equations Further Applications of Linear Equations back of the text. It provides an alphabetical list of the key terms found in the text, with definitions and section references. Over 71 million U. The fastest-growing segment of the pet industry is the high-end luxury area, which includes everything from gourmet pet foods, designer toys, and specialty furniture to groomers, dog walkers, boarding in posh pet hotels, and even pet therapists.
In Exercise of Section 1. Know the common sets of numbers. Use absolute value. Use inequality symbols. Graph sets of real numbers. A set is a collection of objects called the elements or members of the set.
In algebra, the elements of a set are usually numbers. For example, 2 is an element of the set 51, 2, Since we can count the number of elements in the set 51, 2, 36, it is a finite set. In our study of algebra, we refer to certain sets of numbers by name. The three dots ellipsis points show that the list continues in the same pattern indefinitely. We cannot list all of the elements of the set of natural numbers, so it is an infinite set.
Including 0 with the set of natural numbers gives the set of whole numbers. In algebra, letters called variables are often used to represent numbers or to define sets of numbers. The notation 5x x is a natural number between 3 and is an example of setbuilder notation.
This set is 51, 2, One way to describe the given set is 5x x is one of the first five odd natural numbers6. A good way to get a picture of a set of numbers is to use a number line. To draw a number line, choose any point on the line and label it 0. Then choose any point to the right of 0 and label it 1. Use the distance between 0 and 1 as the scale to locate, and then label, other points.
The number 0 is neither positive nor negative. A rational number can be expressed as the quotient of two integers, with denominator not 0. The set of all rational numbers is written as follows. A bar is written over the repeating digit s. Thus, terminating decimals, such as 0. Decimal numbers that neither terminate nor repeat, which include many square roots, are irrational numbers. Another irrational number is p, the ratio of the circumference of a circle to its diameter.
The rational numbers together with the irrational numbers make up the set of real numbers. Every point on a number line corresponds to a real number, and every real number corresponds to a point on the number line. Every real number is either rational or irrational.
Notice that the integers are elements of the set of rational numbers and that the whole numbers and natural numbers are elements of the set of integers. Real numbers Rational numbers 4 —1 9 4 —0. This number, part of the complex number system, is discussed in Chapter 8. If it is false, tell why. This is true. This statement is false. Although some rational numbers are integers, other rational numbers, such as 23 and - 14 , are not.
Look at For each positive number, there is a negative number on the opposite side of 0 that lies the same distance from 0. These pairs of numbers are called additive inverses, opposites, or negatives of each other. For example, 3 and - 3 are additive inverses. We change the sign of a number to find its additive inverse. As we shall see later, the sum of a number and its additive inverse is always 0.
The first indicates the additive inverse or opposite of - 5, and the second indicates a negative number, - 5. Number Additive Inverse 6 -6 -4 4 2 3 - 23 - 8. A positive number can be called a signed number even though the positive sign is usually left off. The table in the margin shows the additive inverses of several signed numbers. Geometrically, the absolute value of a number a, written a , is the distance on the number line from 0 to a. For example, the absolute value of 5 is the same as the absolute value of - 5 because each number lies five units from 0.
The formal definition of absolute value follows. If a is a negative number, then - a, the additive inverse or opposite of a, is a positive number. Thus, a is positive.
Finding Absolute Value Simplify by finding each absolute value. Then find the additive inverse. Of the security guards, file clerks, and customer service representatives, which occupation is expected to see the least change without regard to sign? What occupation in the table on the preceding page is expected to see the greatest change? The least change? We want the greatest change, without regard to whether the change is an increase or a decrease. Look for the number in the table with the greatest absolute value.
That number is for home health aides, since Similarly, the least change is for word processors and typists: - If two numbers are not equal, one must be less than the other. We know that 4 6 9. On the graph, 4 is to the left of 9. The lesser of two numbers is always to the left of the other on a number line. The empty set is a set A. A variable is A. The absolute value of a number is A. The reciprocal of a nonzero number a is A.
A factor is A. An exponential expression is A. A term is A. A numerical coefficient is A. C; Example: The set of whole numbers less than 0 is the empty set, written 0. A; Examples: a, b, c 3. B; Examples: 3 is the reciprocal of 31 ; - 52 is the reciprocal of - D; Example: 2 and 5 are factors of 10, since both divide evenly without remainder into B; Examples: 34 and x 10 7.
B; Examples: 6, 2x , - 4ab 2 8. A; Examples: The term 8z has numerical coefficient 8, and - 10x 3y has numerical coefficient - The sum has the same sign as the given numbers. The sum has the same sign as the number with the greater absolute value. Multiplication and Division Same Sign: The answer is positive when multiplying or dividing two numbers with the same sign. Different Signs: The answer is negative when multiplying or dividing two numbers with different signs.
The product of an odd number of negative factors is negative. Order of Operations 1. Work separately above and below any fraction bar. If parentheses, brackets, or absolute value bars are present, start with the innermost set and work outward. Evaluate all exponents, roots, and absolute values. Multiply or divide in order from left to right. Add or subtract in order from left to right. Simplify the elements of S as necessary, and then list those elements of S which belong to the specified set.
Whole numbers 7. Integers 8. Rational numbers 9. Real numbers Write each set by listing its elements. Use this graph to work Exercises 15— Which automaker had the greatest change in sales? What was that change? Which automaker had the least change in sales?
True or false: The absolute value of the percent change for Chrysler was greater than the absolute value of the percent change for Hyundai. True or false: The percent change for Subaru was more than twice the percent change for Chrysler.
Car Production, Write each set in interval notation and graph the interval. Telescope Peak, altitude 11, ft, is next to Death Valley, ft below sea level. Find the difference between these altitudes. Source: World Almanac and Book of Facts.
Concept Check 1. If it is not a real number, say so. The following expression for body mass index BMI can help determine ideal body weight. Source: The Washington Post. Source: www. Simplify each answer if possible. Year Exports Imports 10, 12, 11, Source: U. Census Bureau. Determine the absolute value of the difference between imports and exports for each year.
Is the balance of trade exports minus imports in each year positive or negative? This random ordering should help you prepare for the chapter test in yet another way. Graph e - 3, 0. Simplify the elements of A as necessary, and then list those elements of A which belong to the specified set. Whole numbers 3. Integers 4. Rational numbers 5. What is the difference between the height of Mt. Foraker and the depth of the Philippine Trench?
What is the difference between the height of Pikes Peak and the depth of the Java Trench? How much deeper is the Cayman Trench than the Java Trench? Find each square root. If the number is not real, say so. Concept Check the following?
Evaluate What is the simplified form? Answers may be used more than once. I II Distributive property Inverse property Identity property Associative property E. Commutative property F. You will learn more and be better prepared to work the exercises your instructor assigns. She previews the section before the lecture, so she knows generally what to expect. Student B learns best by reading on his own. He reads the section and works through the examples before coming to class. That way, he knows what the teacher is going to talk about and what questions he wants to ask.
Which reading approach works best for you—that of Student A or Student B? You will be able to concentrate more fully on what you are reading. N Read slowly. Read only one section—or even part of a section—at a sitting, with paper and pencil in hand. N Pay special attention to important information given in colored boxes or set in boldface type. N Study the examples carefully. Pay particular attention to the blue side comments and pointers.
N Do the Now Try exercises in the margin on separate paper as you go. These mirror the examples and prepare you for the exercise set. The answers are given at the bottom of the page. N Make study cards as you read. See page Make cards for new vocabulary, rules, procedures, formulas, and sample problems.
Follow up with your instructor, as needed. Select several reading tips to try this week. In , During the — season, favorite prime-time television programs were American Idol and Dancing with the Stars.
Source: Nielsen Media Research. In Section 2. Identify linear equations, and decide whether a number is a solution of a linear equation. Solve linear equations by using the addition and multiplication properties of equality. Solve linear equations by using the distributive property. Solve linear equations with fractions or decimals. Identify conditional equations, contradictions, and identities. In our work in Chapter 1, we reviewed algebraic expressions. Recall from Section 1.
An equation always contains an equals symbol, while an expression does not. In part b , there is no equals symbol, so it is an expression. See the diagram below. A linear equation in one variable involves only real numbers and one variable raised to the first power. A linear equation is a first-degree equation, since the greatest power on the variable is 1. Some equations that are not linear that is, nonlinear follow. An equation is solved by finding its solution set, the set of all solutions.
To solve an equation, we usually start with the given equation and replace it with a series of simpler equivalent equations. We use two important properties of equality to produce equivalent equations. That is, the same number may be added to each side of an equation without changing the solution set. That is, each side of an equation may be multiplied by the same nonzero number without changing the solution set. Because subtraction and division are defined in terms of addition and multiplication, respectively, the preceding properties can be extended.
The same number may be subtracted from each side of an equation, and each side of an equation may be divided by the same nonzero number, without changing the solution set. The goal is to isolate x on one side of the equation. Subtract 6x from each side. This is not the solution.
True The true statement indicates that 5- 36 is the solution set. Use only one equality symbol in a horizontal line of work when solving an equation. Eliminate fractions by multiplying each side by the least common denominator. Eliminate decimals by multiplying by a power of Step 2 Simplify each side separately. Use the distributive property to clear parentheses and combine like terms as needed.
Step 3 Isolate the variable terms on one side. Use the addition property to get all terms with variables on one side of the equation and all numbers on the other. Step 4 Isolate the variable. Use the multiplication property to get an equation with just the variable with coefficient 1 on one side. Step 5 Check. Substitute the proposed solution into the original equation. In Example 2, we did not use Step 1 or the distributive property in Step 2 as given in the box.
Many equations, however, will require one or both of these steps. Step 1 Since there are no fractions in this equation, Step 1 does not apply. Step 2 Use the distributive property to simplify and combine like terms on the left. Be sure to distribute over all terms within the parentheses. Step 3 Next, use the addition property of equality. Subtract x.
True The solution checks, so is the solution set. When fractions or decimals appear as coefficients in equations, our work can be made easier if we multiply each side of the equation by the least common denominator LCD of all the fractions.
This is an application of the multiplication property of equality. Multiply each side by the LCD, 6. Distributive property Multiply. Add Add and subtract in the numerators. Simplify each fraction. This allows us to obtain integer coefficients. Because each decimal number is given in hundredths, multiply each side of the equation by A number can be multiplied by by moving the decimal point two places to the right.
Multiply each term by Subtract Multiply and subtract. To be sure that your solution is correct, you should always check your work. In Examples 2—5, all of the equations had solution sets containing one element, such as in Example 5. Some equations, however, have no solutions, while others have an infinite number of solutions. The table on the next page gives the names of these types of equations. See Example 6 a. See Example 6 b. Decide whether it is a conditional equation, an identity, or a contradiction.
See Example 6 c. We could have identified the equation as an identity at that point. This equation has one solution, the number 0, so it is a conditional equation with solution set Concept Check Which equations are linear equations in x? Which of the equations in Exercise 1 are nonlinear equations in x? Explain why. If it is not a solution, explain why.
Decide whether each of the following is an expression or an equation. A loose-leaf, three-hole-punched version of the printed text. Privacy and Cookies We use cookies to give you the best experience on our website. Learn more Close this message and continue.
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