Solution Manual for Intermediate Algebra, 6th Edition

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RESOURCEMANUALINTERMEDIATEALGEBRASIXTHEDITIONElayn Martin-GayUniversity of New Orleans

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Table of ContentsMini-Lectures (M)Chapter 1........................................................................................................................................... 1Chapter 2........................................................................................................................................... 9Chapter 3......................................................................................................................................... 17Chapter 4......................................................................................................................................... 25Chapter 5......................................................................................................................................... 31Chapter 6......................................................................................................................................... 39Chapter 7......................................................................................................................................... 45Chapter 8......................................................................................................................................... 53Chapter 9......................................................................................................................................... 59Chapter 10....................................................................................................................................... 67Answers........................................................................................................................................... 73Additional Exercises (E)Chapter 1........................................................................................................................................... 1Chapter 2......................................................................................................................................... 13Chapter 3......................................................................................................................................... 27Chapter 4......................................................................................................................................... 57Chapter 5......................................................................................................................................... 69Chapter 6......................................................................................................................................... 83Chapter 7......................................................................................................................................... 95Chapter 8....................................................................................................................................... 109Chapter 9....................................................................................................................................... 125Chapter 10..................................................................................................................................... 145Answers......................................................................................................................................... 161Group Activities (G)Chapter 1........................................................................................................................................... 1Chapter 2........................................................................................................................................... 3Chapter 3........................................................................................................................................... 5Chapter 4........................................................................................................................................... 7Chapter 5........................................................................................................................................... 9Chapter 6......................................................................................................................................... 11Chapter 7......................................................................................................................................... 13Chapter 8......................................................................................................................................... 15Chapter 9......................................................................................................................................... 17Chapter 10....................................................................................................................................... 19Answers........................................................................................................................................... 23Tests (T)Chapter 1........................................................................................................................................... 1Chapter 2......................................................................................................................................... 21Chapter 3......................................................................................................................................... 41Chapter 4......................................................................................................................................... 73Chapter 5....................................................................................................................................... 105Chapter 6....................................................................................................................................... 121Chapter 7....................................................................................................................................... 141Chapter 8....................................................................................................................................... 161Chapter 9....................................................................................................................................... 177Chapter 10..................................................................................................................................... 197Final Exam .................................................................................................................................... 217Test Answers................................................................................................................................. 239Final Exam Answers ..................................................................................................................... 269iii

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M-1Mini-Lecture 1.1Study Skill Tips for Success in MathematicsObjectives:A.Get ready for this course.B.Understand some general tips for success.C.Know how to use this text.D.Know how to use text resources.E.Get help as soon as you need it.F.Learn how to prepare for and take an exam.G.Develop good time management.Examples:1.Get ready for this course.a)Positive attitudeb)Be familiar with course structurec)Avoid schedule conflictsd)Allow adequate time for class arrivale)Bring all required materials2.Understand some general tips for success.a)Organize materialsb)Make contact with other studentsc)Choose to attend all classesd)Do your homeworke)Check your workf)Learn from mistakesg)Ask questionsh)Hand in assignments on time3.Know how to use this text.a)Each example in every section has a Practice exercise associated with it.b)At beginning of each section, a list of icons shows availability of support materials.c)Each chapter ends with Chapter Highlights, Reviews, and Practice Tests.4.Know how to use video and notebook organizer resources.a)Video resources include interactive lectures, test prep, and student success tips.b)Notebook organizer resources include video and student organizers5.Get help as soon as you need it.6.Learn how to prepare for and take an exam.a)Review previous homework assignments, class notes, quizzes, etc.b)Read Chapter Highlights to review concepts and definitions.c)Practice working out exercises in the end-of-the-chapter Review and Test.d)When taking a test, read directions and problems carefully.7.Develop good time management.a)Make a list of all weekly commitments with estimated time needed.b)Be sure to schedule study time. Don’t forget to eat, sleep, and relax!Teaching Notes:•Many developmental students are hesitant to ask questions and seek extra help.•Be sure to explain your expectations. Keep your expectations clear and concise.

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M-2Mini-Lecture 1.2Algebraic Expressions and Sets of NumbersObjectives:A.Identify natural numbers, whole numbers, integers, rational numbers, and irrational realnumbers.B.Write phrases as algebraic expressions.Key Vocabulary:variables, algebraic expression (expression), evaluating (an expression), value,number line, origin, unit distance, positive numbers, negative numbers, graphed, ellipsis, set,members (elements), roster, set builder notation, empty (null) set, subsetExamples:1.Define the number sets using set builder notation.a) natural numbersb) whole numbersc) integersd) rational numberse) irrational numbersf) real numbers2.Write each set in roster form.a) {x|xis an odd natural number}b) {x|xis an integer less than 2}3.List elements of the set1{5,0,3,49,,112}9−that are also elements of the given set.a) natural numbersb) whole numbersc) integersd) rational numberse) irrational numbersf) real numbers4.Place∈or∉in the space provided to make each statement true.a)9−{x|xis an integer}b)25{x|xis a rational number}c)3−{1, 3, 5, …}5.Write each phrase as an algebraic expression. Usexto represent each unknown number.a) three times a numberb) a number minus 2c) the quotient of a number and 5d) ten and one-tenth plus a numbere) five more than twelve times a numberf) four less than six times a numberTeaching Notes:•Remind students that “rational” starts with “ratio”, and any number that can be expressedas a ratio of integers is a rational number.•Remind students that irrational numbers have non-terminating, non-repeating decimals.•Some have difficulty writing phrases as algebraic expressions. Present several examples.•Refer toReal NumbersandSelected Key Words/Phrases and Their Translationscharts.Answers:1a) {1,2,3,…}, b) {0,1,2,3,…}, c) {…–3, –2, –1,0,1,2,3,…}, d){}|,a b a and b are integers and b0≠e) {x|x is a real number and x is not a rational number}, f) {x|x corresponds to a point on the number line};2a) {1,3,5,…}, b) {…–3, –2, –1,0,1}, 3a){ ,},549b){ , ,},5 049c){ , ,,},5 049112−d), ,,,,15 0491129−e){},3f), ,,,,,15 03491129−4a),∈b),∈c);∉5a) 3x, b) x–2, c),x5d),110x10+e) 12x+5, f) 6x–4

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M-3Mini-Lecture 1.3Equations, Inequalities, and Properties of Real NumbersObjectives:A.Write sentences as equations.B.Use inequality symbols.C.Find the opposite, or additive inverse, and the reciprocal, or multiplicative inverse, of anumber.D.Identify and use the commutative, associative, and distributive properties.Key Vocabulary:symbols(),,,,,,= ≠ < > ≤ ≥additive identity, multiplicative identity, opposite(additive inverse), reciprocal (multiplicative inverse), undefined, commutative properties,associative properties, distributivepropertyExamples:1.Write each sentence as an equation.a) The difference ofxand 4 amounts to 15.b) Five more than the product of 3 andbis 7.c) The quotient of 9 andyis 2 more thany.d) 3 added to one-halftis equal to 8 more thatt.2.Insert <, >, or = between each pair of numbers to form a true statement.a)20−b) 363696c)2.56.7−d) 395153.Write the opposite of each number. Then write the reciprocal of each number.a) 8b)23−c) 0d) 4574.Use a commutative property to write an equivalent expression.a)53xy+b)m n⋅c)3511x⋅5.Use an associative property to write an equivalent expression.a) 4 (15 )x⋅b) 9(3)pqr++c) (3.5 )xy⋅6.Use the distributive property to multiply.a) 3(5)x+b) 2(7)m−c) 3(5)y−d) 10(4)y z−e) 0.2(26)xy+f) 1 (95 )3xy−Teaching Notes:•In example 2, also discuss how the symbols,, and≤≥≠could be used.•Many students confuse the associative and commutative properties.•Students may have trouble using the distributive property when fractions are involved.Answers: 1a) x–4=15, b) 3b+5=7, c),9y2y=+d);1 t3t82+=+2a) <, b) <, c) >, d) =; 3a) -8,,18b),,2332−c) 0, undefined, d),;457745−4a) 3y+5x, b),n m⋅c);3x115⋅, 5a)() ,4 15 x⋅b) (9p+3q)+r, c). (),3 5 xy⋅6a) 3x+15,b) 2m–14, c) 15–3y, d) 10yz-40y, e) 0.4x+1.2y, f )53xy3−

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M-4Mini-Lecture 1.4Operations on Real NumbersObjectives:A.Find the absolute value of a number.B.Add and subtract real numbers.C.Multiply and divide real numbers.D.Simplify expressions containing exponents.E.Find roots of numbers.Key Vocabulary:absolute value, undefined, factor, base, exponent, nth power of a (a raised tothe nth power, an), square root, positive (principal) square root, cube rootExamples:1.Find each absolute value.a)6b)2−c)12−d)14− −2.Add, subtract, multiply, or divide as indicated.a)6( 3)−+ −b) 6( 3)+ −c)63−+d)531224−+e)25−f)2( 5)− −g)25−−h)9.7( 4.2)−− −i)4 5⋅j)4 5−⋅k) 0( 9)−l)29312−−m) 6( 2)÷ −n)124−−o)4.62.3−÷p)30−3.Evaluate each expression.a)25−b)2( 5)−c)312−d)413−e)25f)81g)1100h)384.Mixed practice. Evaluate each expression.a)6211−÷b)1257−−+c)3(4)( 7)−−d)43−Teaching Notes:•Some students try to distribute a negative sign through an absolute value symbol.•Students should master the integer examples before trying those with fractions/decimals.•Many students make sign errors when evaluating expressions with exponents.Answers: 1a) 6, b) 2, c) –12, d) –14; 2a) –9, b) 3, c) –3, d),724−e) –3, f) 7, g) –7, h) –5.5, i) 20, j) –20, k) 0, l),12m) –3, n) 3, 0) –2, p) undefined; 3a) –25, b) 25, c),18−d),181−e) 5, f) 9, g),110h) 2; 4a),311−b) –10, c) 84, d) –81

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M-5Mini-Lecture 1.5Order of Operations and Algebraic ExpressionsObjectives:A.Use the order of operations.B.Identify and evaluate algebraic expressions.C.Identify like terms and simplify algebraic expressions.Key Vocabulary:order of operations, value (of anexpression), evaluating an expression,simplified, terms, like terms, combining like termsExamples:1.Simplify each expression using order of operations.a)26(25)−b)23( 4)3−+c) 5[9(13)]−−d)3864−−−e)2( 85)( 2 )33−+−−−f)3(8)( 4)(16)( 2)−−−g)25(53.4)3−−−−h) |12 || 38 |12−−−−i)1285416164⋅−+⋅2.Evaluate each expression when5x=and3.y= −a)37xy−b)29yx−+c)644yxxy+++3.Simplify by distributing, if necessary, and combining like terms.a)45xx+b) 12yy−c)3912xx−−d) 2.58.63.412.3yy−+−e) 3(69)y+f) 2(54)kk−−g)(9)(36)tt−−+−h) 11(124)(30)26xxy−−−i)7.38.12(3.20.4)bb+−−4.IfCis degrees Celsius, the algebraic expression1.832C+represents the equivalenttemperature in degrees Fahrenheit. Calculate the degrees Fahrenheit for20, 0, 40.C= −As the temperature Celsius increases, does the temperature Fahrenheit increase/decrease?Teaching Notes:•If students have trouble using order of operations, encourage neatness and organization.•When collecting like terms, some students may assume2459.xxx+=•It may be helpful to write a “1” in front of the parenthesis in examples 3f) and 3g).Answers: 1a) 54, b) 43, c) 55, d) 0, e) –2, f) 0, g) 2.2, h),712−i);152a) 36, b) –76, c) –2; 3a) 9x, b) 11y, c) –9x–9,d) 5.9y–20.9, e) 18y+27, f) –3k+4, g) 4t–15, h),1xy26+−i) 0.9b+8.9; 4) –4°F, 32°F, 104°F, increase

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M-6Mini-Lecture 1.6Exponents and Scientific NotationObjectives:A.Use the product rule for exponents.B.Simplify expressions raised to the zero power.C.Use the quotient rule for exponents.D.Simplify expressions raised to negative powers.E.Simplify exponential expressions containing variables in the exponent.F.Convert between scientific notation and standard notation.Key Vocabulary:exponential expression, scientific notationExamples:1.Use the product rule or the quotient rule to simplify each expression.a)3422⋅b)97m mm⋅⋅c) ( 6)(6)xyy−d)323( 3)( 5)a ba b−−e)83xxf)117102yy−g)653159xyxyh)23129364a b cabc−2.Evaluate or simplify each expression. Write each answer using positive exponents only.a)02b)05−c)0( 10)−d)0(21)x+e)42−f)2( 3)−−g)24xxh)32a−3.Simplify and write each answer using positive exponents only.a)36yy−b)542xxx−−c)333124abab−−d)346yy−⋅ −e)002(2 )xx−f)3224−−−g)813202xyzxyz−−h)527(4)(3)( 2)a bba−4.Simplify. Assume that variables in the exponents represent nonzero integers,x,y,z0.≠a)27mmxx⋅b)322ppyy−c)57yyxx−⋅d)32xxxyyy−⋅5.Write each number in scientific notation or in standard notation.a) 645,000b) 0.005621c)43.610−×d)59.510×Teaching Notes:•Students need repetition and practice in order to master these objectives.•Students often move constants along with a variable that has a negative exponent.For example, in example 2h), a common (incorrect) answer is 2a-3= 1/(8a3).Answers: 1a) 128, b) m17, c) –36xy2, d) 15a6b3, e) x5, f) –5y4, g),525x y3h) –9ab2c3; 2a) 1, b) –1, c) 1, d) 1, e),116f),19g),21xh);32a3a),91yb) x, c),463abd) 24y4, e) 1, f),116g),91410x zh) -24a12b3; 4a) x9m, b) yp-2, c),2 y1xd) y3x-2; 5a).,56 4510×b).,35 62110−×c) 0.00036, d) 950,000

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M-7Mini-Lecture 1.7More Work with Exponents and Scientific NotationObjectives:A.Use the power rules for exponents.B.Use exponent rules and definitions to simplify exponential expressions.C.Simplify exponential expressions containing variables in the exponent.D.Use scientific notation to compute.Examples:1.Simplify using the product rules for exponents. Write answer using positive exponents.a)32()xb)232()xyc)223xyd)34()m−e)232(2)xyzf)5423xy−g)5303(4)xy z−−h)334( 2)y−−−−2.Simplify using exponent rules and definitions. Write answer using positive exponents.a)2349abc−−−−b)23( 4)x−c)5632nm−−d)2210347xyx y−−−e)023( 2)x y−−f)333()xx y−g)135227zyyz−−−−   h)42383(3)(2)xyx y−3.Simplify. Assume that variables in the exponents represent nonzero integers and that allother variables are not zero.a)352()bx+b)29yyxxx−+c)3621()aayy−d)4332124ababababxyxy−+−+4.Perform each indicated operation using the properties of exponents. Write each answer inscientific notation.a)97(4.910)(610 )−××b)65(410)−×c)841.210310−××Teaching Notes:•Some students are confused about when to add exponents or when to multiply exponents.•Encourage students to write exponent rules on a card to view while doing homework.Answers: 1a) x6, b) x4y6, c),46xyd),121me) 4x4y2z6, f) 243x20y10, g),159x64 yh) 4096y12; 2a),6818a bcb) –64x6,c),153032mnd),145y49xe),618 y−f),631x yg),452 y7 zh);43227 x y3a) x6b+10, b) x-y+8, c) y16a+1, d) 3x3a+2by2a-b;4a).,12 9410−×b).,271 02410−×c).114 010×

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M-9Mini-Lecture 2.1Linear Equations in One VariableObjectives:A.Decide whether a number is a solution of an equation.B.Solve linear equations using properties of equality.C.Solve linear equations that can be simplified by combining like terms.D.Solve linear equations containing fractions or decimals.E.Recognize identities and equations with no solution.Key Vocabulary:equation, solving the equation, linear equations, first-degree equations,linear equation in one variable, solution, solution set, equivalent equations, additionproperty of equality, multiplication property of equality, contradiction, identityExamples:1.Determine whether each number is a solution of the given equation.a) 2;35x+=b)6;39x−−=c)36;126x−=−2.Solve each equation. Check the answer.a)57x−=b)315x+=c)64x−=+d)210x=e)315x−=f)34x=g)4263xx−=+h)54103yy−=+i)9.342.3x−= −j)3(24)93xx+=−k)2(31)5(4)nnn−−−= −−3.Solve each equation. Check the answer.a)1324xx+=b) 2553xx−=c) 23510rr−=d) 2843xx−=e) 26125yy−=−f)3.4(25)0.2(25)xx+= −+4.Solve each equation.a) 2(6)122xx+=+b) 4(5)35(2)xxx++=+−Teaching Notes:•Encourage students to check their solutions.•Some students prefer to end up with the variable on the left, while others prefer to end upwith a positive coefficient in front of the variable.•Refer toAddition/Multiplication Property&Solving a Linear Equation in One Variable.Answers: 1a) yes, b) no, c) no; 2a) {12}, b) {12}, c) {–10}, d) {5}, e) {–5}, f) {12}, g) {8], h) {7}, i) {2.9}, j) {5},k) {–9}; 3a),310b) {75}, c) {10}, d) {4}, e),1112f) {–2.5}; 4a) {x|x is a real number}, b)∅

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M-10Mini-Lecture 2.2An Introduction to Problem SolvingObjectives:A.Write algebraic expressions that can be simplified.B.Apply the steps for problem solving.Key Vocabulary:understand, translate, solve, interpretExamples:1.Write each of the following as an algebraic expression. Then simplify.a)The sum of three consecutive integers if the first integer isxb)The perimeter of a rectangle with lengthxand widthx– 7c)The total amount of money (in cents) inxquarters, 5xdimes, and (3x– 1) nickels2.Solve using the General Strategy for Problem Solving.a)Number ProblemOne number is two times another number. The sum of thenumbers is 90. What are the two numbers?b)Number ProblemThree times the difference of a number and 5 is the same as1 increased by five times the number plus twice the number. Find the number.c)Age ProblemToday Henry is 7 years older than twice his age of 23 years ago.Find Henry’s age today.d)Car RentalA car rental agency advertised renting a luxury, full-size car for$49.95 per day and $0.69 per mile. If you rent this car for 5 days, how manywhole miles can you drive if you only have $500 to spend?e)CarpentryA 7-ft board is cut into 2 pieces so that one piece is 3 feet longer thanthree times the shorter piece. Find the length of each piece.f)Unknown SidesA triangle has sides measuring 2.5xcm, 3xcm, and (2x+ 3) cm.The perimeter measures 60 cm. Find the measures of the sides.g)Unknown AnglesTwo angles are complementary if their sum is 90°. The measureof one angle isx°, and the measure of the other angle is (3x– 2)°. Find the measure ofeach angle.h)LayoffsA major car manufacturer announced it would lay off 17,000 employeesworldwide. This is equivalent to 20% of its work force. Find the size of the workforce prior to lay-offs.Teaching Notes:•Many students have difficulty with word problems.•Encourage students to draw and label diagrams when appropriate.•Students may need to see several examples involving consecutive (or odd/even) integers.•Refer to theGeneral Strategy for Problem Solvingchart.Answers: 1a) x+x+1+x+2=3x+3, b) 4x–14, c) 90x–5; 2a) 30,60, b) –4, c) 39, d) 362 miles, e) 1 foot, 6 feet,f) 19 cm, 22.8 cm, 18.2 cm, g) 23°, 67°, h) 85,000 employees

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M-11Mini-Lecture 2.3Formulas and Problem SolvingObjectives:A.Solve a formula for a specified variable.B.Use formulas to solve problems.Key Vocabulary:formulaExamples:1.Solve each equation for the specified variable.a)Mkt=for tb)2Crπ=forrc)222abc+=fora2d)4516xy+=forye)22Plw=+forlf)5 (32)9CF=−forF2.Solve. Round all dollar amounts to two decimal places.a)VolumeFind the volume of a rectangular crate with dimensions 3 ft by 4 ft by 8 ft.b)DistanceSheranda drives at a constant rate of 65 miles per hour. How far will shetravel in 4 hours?c)Compound InterestEmmanuel puts $5010 at 9% compounded semiannually for 12years. What is the value of his account at the end of the 12 years?d)CircleCrystal is making a cover for a round table that has a diameter of 46 inches.How much fabric will she need if she wants the cover to fit exactly, with no extramaterial? (Use 3.14 forπand round to two decimal places.)e)Office RentalRent for a 17 foot by 20 foot office is $2040 per month. What is therental cost per square foot?f)TemperatureMichael’s cousin Luke was visiting from Montreal during the summer.On a news report, Luke heard that the temperature in Montreal that day was 98°F. Hewas used to hearing temperature in degrees Celsius. What is 98°F in degrees Celsius?g)TriangleA triangular piece of wood needs to be varnished. The base of the triangleis 3 meters and the height is 13 meters. How many cans of varnish will be needed ifeach can covers 10 square meters?Teaching Notes:•Students may have difficulty solving for a variable when other variables are present.•Many students benefit from seeing a parallel example with numbers instead of variables.For example, next to (1a) solve: 6 = 3t•Encourage students to draw and label diagrams when appropriate.•Refer to theFormulaandSolving an Equation for a Specified Variablecharts.Answers: 1a),Mtk=b),Cr2π=c)222,acb=−d),164xy5−=e),P2wl2−=f);9FC325=+2a) 96 cu. ft, b) 260 miles, c) $14,408.83, d) 1661.06 sq. in., e) $6.00 per sq. ft, f) 36.67°C, g) 2 cans

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M-12Mini-Lecture 2.4Linear Inequalities and Problem SolvingObjectives:A.Use interval notation.B.Solve linear inequalities using the addition property of inequality.C.Solve linear inequalities using the multiplication property of inequality.D.Solve linear inequalities using both properties of inequalityE.Solve problems that can be modeled by linear inequalities.Key Vocabulary:linear inequality, solution, solution set, interval notationExamples:1.Graph the solution set of each inequality on a number line and then write it in intervalnotation.a){|3}xx>b){|2}xx< −c){|4.2}xx−≥d){|30}xx−<≤2.Solve. Graph the solution set and write it in interval notation.a)26x+≤b)1093xx<+c)5545xx−≥−3.Solve. Graph the solution set and write it in interval notation.a)122x≥b)27.2x> −c)36x−≤4.Solve. Show your answer as an inequality.a)69x−< −b)72.8x−≤c)53643x−>d)3 (2)24xx+≥+e)0.3(61)1.4(3)0.1xx−<−−f)423153104xx+≥+Teaching Notes:•Students may have difficulty solving for a variable when other variables are present.•Remind students to reverse the direction of the inequality symbol when multiplying ordividing by a negative number.•Refer to theAddition/Multiplication Property of InequalityandSolving a LinearInequality in One Variablecharts.Answers: 1a)-3c) see graphing answers; 1a)( ,),3∞b)(,),2−∞ −c)(,. ],4 2−∞ −d)(,];3 0−2a)(,],4−∞b)(,),3−∞c)[ ,);0∞3a)[ ,),4∞b)(. ,),3 6−∞c)[,);2−∞4a),x3< −b). ,x0 4≥ −c),1x4<d),x2≤ −e),x10< −f)3x2≥ −

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M-13Mini-Lecture 2.5Sets and Compound InequalitiesObjectives:A.Find the intersection of two sets.B.Solve compound inequalities containing “and.”C.Find the union of two sets.D.Solve compound inequalities containing “or.”Key Vocabulary:compound inequalities, intersection (and), union (or)Examples:1.If{is an even integer},Ax x={is an odd integer},Bx x={1, 2,3, 4},C=and{3, 4,5,6},D=list the elements of each set.a)CD∩b)CD∪c)AD∪d)BC∩e)AB∩2.Solve each compound inequality by graphing the solution on a number line.a)1 and3xx≤≥ −b)1 and4xx<>c)3 and2xx≥ −>3.Solve each compound inequality. Write each solution in interval notation.a)34 and 528xx+≥−≥b)515 and1510xx−< −−< −c)412x−≤+≤ −d)23113x−<−<e)34115x−+−≤≤4.Solve each compound inequality by graphing the solution on a number line.a)3 or3xx≥ −≤b)1 or1xx< −<c)2 or3xx≥ −≤ −5.Solve each compound inequality. Write each solution in interval notation.a)1020 or 342xx−≤−≥b)81 or 515xx+< −> −c)6(2)12 or 410xx−≥ −−≤6.Solve each compound inequality. Write each solution in interval notation.a)2and13xx<<b)2or13xx<<c)1519x<−<d) 231 and3xx−≥−>e)21332x−−−<<f)6 or 4420xx−<+< −Teaching Notes:•Demonstrate how each inequality can be graphed individually. The graph of the solutionis the intersection (or union) of the individual graphs.Answers: 2a)-c), 4a)-c) see graphing answers; 1a) {3,4}, b) {1,2,3,4,5,6}, c) {x|x is an even integer, x=3, x=5},d) {1,3}, e);∅2a) [–3,1], b) no solution, c)( ,);2∞3a)[ ,),2∞b) (3,5), c) [–5, –3], d) (–3,3), e),;1 33−4a) all real numbers, b)(, ),1−∞c)(,][,);32−∞ −∪ −∞5a)[,),2−∞b)(,)(,),93−∞ −∪ −∞c)[,);6−∞6a),,23−∞b)(, ),1−∞c),,2 25d),∅e),,7522−f)(,)(,)66−∞ −∪ −∞

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