Solution Manual for Beginning and Intermediate Algebra, 7th Edition

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RESOURCEMANUALWITHTESTSDAVIDATWOODRochester Community and Technical CollegeBEGINNING ANDINTERMEDIATEALGEBRASEVENTHEDITIONMargaret L. LialAmerican River CollegeJohn HornsbyUniversity of New OrleansTerry McGinnis

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Contents____________________________iii__________________________________Mini-Lectures by Section………………………………………………….......................3Mini-Lecture Graph Answers …………………………………………..………105Chapter Test FormsPreTest…………………………………………………………………………..119Chapter 1…..…………………………………………………...……………….133Chapter 2………………………………………………………………………..157Chapter 3………………………………………………………………………..177Chapter 4………………………………………………………………………..203Chapter 5………………………………………………………………………..225Chapter 6………………………………………………………………………..245Chapter 7………………………………………………………………………..267Chapter 8………………………………………………………………………..293Chapter 9………………………………………………………………………..313Chapter 10………………………………………………………………………331Chapter 11………………………………………………………………………357Chapter 12………………………………………………………………………387Chapter 13………………………………………………………………………415Chapter 14………………………………………………………………………443Final …………………………………………………………………………….463Answers to Test FormsPreTest – Final Exam...………………………………………………..………..481

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BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture R.13FractionsLearning Objectives:1.Write numbers in factored form2.Write fractions in lowest terms.3.Convert between improper fractions and mixed numbers.4.Multiply and divide fractions.5.Add and subtract fractions.6.Solve applied problems that involve fractions.7.Interpret data in a circle graph.Examples:1.Identify each number asprimeorcomposite.If the number is composite, write it in factored form.a)31b)65c)97d)2162.Simplify each fraction.a)510b)1664c)4277d)88903.Change each improper fraction to a mixed number or a whole number, or change each mixed number to animproper fraction.a)85b)344c)32 4d)26 94.Find each product and write in lowest terms.a)539 15b)5962c)4 189d)1131245.Find each quotient and write in lowest terms.a)53915b)5962c)5362424d)538346.Find each sum or difference and write in lowest terms.a)341414b)2133c)2148d)5768e)791230f)2213246g)31811010h)311210847.Rachel is jogging for exercise. This week, she ran121miles on Monday,142miles on Tuesday, and onThursday she ran122times the distance that she ran on Monday. How many miles did she run this week?

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4BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture R.18.In a recent survey 1000 people were asked about their favorite breed of dog. The circle graph below shows theapproximate fractions of their responses.a)Which breed of dog was most popular? What was the fractional value for the most popular breed of dog?b)How many people chose the Yorkshire Terrier as their favorite breed of dog?c)How many people did not choose the Pug as their favorite breed of dog?Teaching Notes:Encourage students to simplify fractions by dividing numerator and denominator by the same number andby factoring into primes and dividing out common factors.Some students try to multiply/divide whole number parts together, and then multiply/divide fractional partstogether when working with mixed numbers.Some students add/subtract the denominators when adding/subtracting fractions.Answers: 1a) prime, b) composite,5 13, c) prime, d) composite,2 2 2 3 3 3; 2a)12, b)14, c)611, d)4445; 3a)351, b)128, c)114, d)569; 4a)19, b)154or343, c) 8, d)358or384; 5a)259or792, b)527, c)536, d)421; 6a)12,b)13, c)58, d)4124or17241, e)5360, f)1112, g)259, h)182; 7)127miles ; 8a) Labrador Retriever, 91/200, b) 200, c) 925

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BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture R.25Decimals and PercentsLearning Objectives:1.Write decimals as fractions.2.Add and subtract decimals.3.Multiply and divide decimals.4.Write fractions as decimals.5.Write percents as decimals and decimals as percents.6.Write percents as fractions and fractions as percents.7.Solve applied problems that involve percent.Examples:1.Write the following decimal numbers as fractions. Do not write in lowest terms.a)0.42b)1.285c)0.93752.Add or subtract as indicated..a)50.586b)45.333.306c)4.11.032.123.Multiply or divide as indicated.a)5.8643.2b)1687.1423.4c)7.863752.25d)57.410004.Write each fraction as a decimal.a)245b)79c)385.Write each percent as a decimal.a)53%b)255%c)34%46.Write each decimal as a percent.a)0.428b)3.21c)0.3057.Write each percent as a fraction. Give answers in lowest terms.a)7%b)185%c)12.4%8.Write each fraction as a percent.a)35b)13c)929.a)A refrigerator with a regular price of $2100 is on sale this week at 25% off. Find the amount of thediscount and the sale price of the refrigerator.b)Mark took an algebra test that was worth 150 points. If he earned 120 points on the test, what percent didhe score?

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6BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture R.2Teaching Notes:Many students are confused by percents that are less than 1%. It may be helpful to have the studentsdistinguish between 0.2 and 0.2%.Many students are confused by percents that are greater than 100%. It may be helpful to show that100% =1Mention to students that another way to convert a fraction to a percent is to first convert the fraction to adecimal and then convert the decimal to a percent.Answers: 1a)42100, b)12851000, c)937510, 000; 2a) 4.414, b) 11.994, c) 5.19, 3a) 1.8325, b) 72.1, c)3.495, d) 0.0574;4a) 4.8, b)0.7, c) 0.375; 5a) 0.53, b) 2.55, c) 0.475; 6a) 42.8%, b) 321%, c) 30.5%; 7a)7100, b)171 20, c)31250,8a) 60%, b)33.3%, c) 450%; 9a) $525, $1575, b) 80%

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BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.17Exponents, Order of Operations, and InequalityLearning Objectives:1.Use exponents.2.Use the rules for order of operations.3.Use more than one grouping symbol.4.Use inequality symbols in statements.5.Translate word statements to symbols.6.Write statements that change the direction of inequality symbols.Examples:1.Find the value of each exponential expression.a)26b)43c)4342.Find the value of each expression.a)482b)2233c)21032d)316322e)21646222f)2324596g)2 313 424 h)124 3¸⋅3.Using inequality symbols:a)Determine whether the statement is true or false:165b)Write the statement in symbols:Seven is not equal to 5.c)Write the statement with the inequality symbol reversed:138d)Write the statement in words:51e)Write the statement 0.5 < 2.5 as another true statement with the inequality symbol reversed.Teaching Notes:Some students do not know how to say23, or32, or45, etc., in words and need to see the words written.Students will often compute42as2 4. Illustrate the difference between the expressions with examples.Students should be reminded to work from inside out when evaluating expressions with grouping symbols.Students should be reminded thatimplies that either thepartorthe = part can be true to satisfy theinequality (similarly for).One way to remember the meaning ofandis that the symbol always points to the lesser number.Refer students to the order of operations chart in the text. It can also be helpful to use PEMDAS or PleaseExcuse My Dear Aunt Sally as a memory device for order of operations. Emphasize that multiplicationand division are done left to right as is addition and subtraction.Answers: 1a) 36, b) 81, c)81256; 2a) 0, b) 9, c) 3, d) 12, e) 6, f) 13, g) 18, h) 9; 3a) false, b)75, c)813,d) Five is greater than one. , e) 2.5 > 0.5

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8BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.2Variables, Expressions, and EquationsLearning Objectives:1.Evaluate algebraic expressions, given values for the variables.2.Translate word phrases to algebraic expressions.3.Identify solutions of equations.4.Identify solutions of equations from a set of numbers.5.Distinguish between equations and expressions.Examples:1.Evaluate the expressions when2a,3b, and6c.a)34abb)51abcc)536abcbd)314abc2.Write each word phrase as an algebraic expression, usingxas the variable.a)The quotient of 6 less than a number and 3b)Seventy more than a numberc)The product of 8 and the total of a number and 53.Decide whether the given number is a solution of the equation.a)Is 0 a solution of6365xx?b)Is 5 a solution of410x?c)Is 9 a solution of123x?4.Write each word statement as an equation. Usexas the variable. Find all solutions from the set1,3,5, 7,9.a)A number plus 4 equals 7.b)Two less than three times a number is thirteen.c)Four times a number added to three is equal to six more than the number.d)A number divided by fourteen is one-half.5.Decide whether each of the following is an equation or expression.a)348xy+=b)348xy+-c)2223xy-Teaching Notes:When a numerical coefficient is 1, the 1 is usually not written (e.g.,1xis usually written asx). Studentsoften ignore a term when they do not see a coefficient or think the coefficient is 0.Remind students that an exponent refers only to the variable just before it(e.g.,25xmeans25x, not55xx).When translating“the difference between a and b”,the order is kept the same:ab.When determining the difference between an expression and an equation ask “Is there an equality symbol?”If the answer to the question is no, then we have an expression. If the answer to the question is yes, then wehave an equation.Answers: 1a) 30, b) 4, c) 59, d) 1; 2a)x63, b)x70, c)8 x5; 3a) yes, b) no, c) yes; 4a) 3, b) 5, c) 1,d) 7; 5a) equation, b) expression, c) expression

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BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.39Real Numbers and the Number LineLearning Objectives:1.Classify numbers and graph them on number lines.2.Use inequality symbols with real numbers.3.Find the additive inverse of a real number.4.Find the absolute value of a real number.5.Interpret meanings of real numbers from a table of data.Examples:1.List all numbers from the set310,5,2, 0,5, 104that are:a)natural numbersb)whole numbersc)integersd)rational numberse)irrational numbersf)real numbers2.Graph each of the numbers on a number line:112, 5,4, 132.3.Select the lesser number in each pair.a)–3, 8b)41,53c)10, –12d)–15, –204.Find the additive inverse of each number.a)6b)–5c)565.Simplify.a)3b)6 c)13166.Decide whether the statement is true or false.a)102b)35 c)71 7.The table shows the percent change in real median income for selected age groups from 2015 to 2016 and 2017to 2018. Use the table to answer the questions below.Age GroupsPercent Change from 2015 to 2016Percent Change from 2017 to 201825-34 years–1.9–0.935-44 years–0.70.745-54 years–4.31.955-64 years–2.32.7a)Which age group in which year represents the greatest percent decrease?b)Which age group in which year represents the greatest percent increase?c)Which age group in which year represents the smallest percent decrease?

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10BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.3Teaching Notes:Some students find it helpful to see each type of number in examples 2 and 3 on a number line.Remind students that integers are rational numbers; any integer can be written as the ratio of itself and 1.Decimal numbers that terminate or repeat in a fixed block are rational numbers – ask students to giveexamples of both.The decimal form of an irrational number neither terminates nor repeats.The number line is a good way to illustrate that opposite numbers are equidistant from 0 but on oppositesides of 0.Some students have never seen absolute value before and will need examples.Answers: 1a) 10, b) 0, 10, c) –10, –5, 0, 10, d) –10, –5,32 4, 0, 10, e)5, f) –10, –5,32 4, 0,5, 10;2); 3a) –3, b)45, c) –12, d)–20; 4a) –6, b) 5, c)56; 5a) 3, b) –6, c) 3;6a) true, b) true, c) false; 7a) 45-54 years from 2015-2016, b) 55-64 years from 2017-2018, c) 35-44 years from2015-2016

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BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.411Adding and Subtracting Real NumbersLearning Objectives:1.Add two numbers with the same sign.2.Add two numbers with different signs.3.Use the definition of subtraction.4.Use the rules for order of operations when adding or subtracting signed numbers.5.Translate words and phrases involving addition and subtraction.6.Use signed numbers to interpret data.Examples:1.Find each sum or difference.a)912b)1610 c)1426 d)6.35.2e)12617 f)1426 g)2617  h)72105i)1113242.Write a numerical expression for each phrase, and simplify the expression.a)The sum of –6 and 3 and –1b)The sum of –10 and –15, increased by 12c)0.29 more than the sum of 3.56 and –2.41Solve each problem.3.A scuba diver is at a depth of 16 feet below the surface. She descends another 8 feet. What is her new depth?4.On January 14, in New Market, Indiana, the temperature rose 17º F in three hours. If the starting temperaturewas –5º F, what was the temperature three hours later?5.The bar graph gives the sales of a large company (in millions of dollars) for over a five year period.a)Use a signed number to represent the change in sales from year 2 to 3.b)Use a signed number to represent the change in sales from year 3 to 4.

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12BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.4Teaching Notes:Some students need to see addition problems done on a number line first.Caution students about the difference between the subtraction key and the change-of-sign key on acalculator.Have students read problems carefully to ensure their understanding of the symbols.Emphasize the uses of the – symbol with students.Answers: 1a) 21, b) 6, c) –40, d) –1.1, e) –1, f) 12, g) 10, h)310, i)512; 2a);6314 , b);10151213  , c)...;.3 562 410 29 1 44  ; 3) –24 feet; 4) 12ºF; 5a)-$5, b) $7

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BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.513Multiplying and Dividing Real NumbersLearning Objectives:1.Find the product of a positive number and a negative number.2.Find the product of two negative numbers.3.Identify factors of integers.4.Use the reciprocal of a number to apply the definition of division.5.Use the rules for order of operations when multiplying and dividing signed numbers.6.Evaluate algebraic expressions given values for the variables.7.Translate words and phrases involving multiplication and division.8.Translate simple sentences into equations.Examples:1.Find each product. Be sure to write your answer in simplest form.a)2 0b)415c)305d)2.23.3e)3849   2.Find all of the integer factors of each number.a)12b)32c)9d)113.Find each quotient.a)168b)93c)4.60d)315520e)044.Perform each indicated operation.a)4728b)9851121c)22642 51 5.Evaluate each expression if2x ,4y,1a , and3b.a)24ybxb)22yxbya6.Write each sentence as an expression or equation, usingxas a variable. Simplify each expression.a)The product of –5 and the difference between 4 and –9.b)The quotient of –18 and the sum of –7 and –2.c)Seven times a number is –35.d)7 less than a number is 6.

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14BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.5Teaching Notes:Refer students to the rules for multiplying and dividing signed numbers.Give examples to show why division by zero is undefined but zero can be divided by any number exceptzero.,,xxyyandy xwhere0y, all indicate division.Answers: 1a) 0, b) –60, c) 150, d) –7.26, e)23; 2a) 1 and 12, 2 and 6,3 and 4, –1 and –12, –2 and –6,–3 and –4, b) 1 and 32, 2 and 16, 4 and 8, –1 and –32, –2 and –16, –4 and –8,c) –1 and 9, 1 and –9, –3 and 3;d) –1 and –11, 1 and 11, 3a) –2, b) 3, c) undefined, d)45, e) 0; 4a) 1, b) –7, c)53; 5a) 57, b)–8;6a)5 49;65 , b)18; 272 , c)735x , d)76x

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BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.615Properties of Real NumbersLearning Objectives:1.Use the commutative properties.2.Use the associative properties.3.Use the identity properties.4.Use the inverse properties.5.Use the distributive property.Examples:1.Name the property (commutative, associative, identity property, inverse property, or distributive property)illustrated by each statement.a)3773 b)23132   c)362362     d)11055e)555cdcd f)57101057 g)337777h)56 156 2.Use the distributive property to rewrite each expression. Simplify if possible.a)36kb)52hc)33yzd)2 52abce)2 723 Teaching Notes:Remind students that the commutative property deals with the order of addition (or multiplication), whereasthe associative property deals with grouping.Students often confuse the additive identity (zero) and the multiplicative identity (one).The generalized distributive property covers multiplication over addition and/or subtraction.Have students provide examples to show whether or not the commutative / associative properties hold forsubtraction and division.Answers: 1a) commutative, b) inverse, c) associative, d) inverse, e) distributive, f) commutative, g) commutative,h) identity; 2a)3k18, b)5h10, c)3 yz, d)10a4b2c, e);2 7320

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