Unit 2. Solving Equations & Inequalities. Algebra I Honors. Mrs. Underwood s. Name: Date: Lesson 2-A. Lesson 2-B. Lesson 2-C.

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1 Mrs. Underwood s Algebra I Honors Lesson 2-A Lesson 2-B Lesson 2-C Lesson 2-D Unit 2 Study Guide Unit 2 Solving Equations Inequalities Solving One-Step Equations Inequalities Notes Practice 1 Practice 2 Solving Multi-Step Equations Inequalities Notes Practice 1 Practice 2 Solving Equations Inequalities with Variables on Both Sides Notes Practice Weighted Averages Notes Practice Name: Date:

2 Lesson 2-A Notes (2.1, 5.1) - Alg. I Honors Solving One-Step Equations Inequalities CCSS A-CED.1 Create equations that describe numbers or relationships. CCSS A-REI.1 Understand solving equations as a process of reasoning and explain the reasoning. CCSS A-REI. 3 Solve equations and inequalities in one variable. Past Target I translated sentences into expressions. Present Target I can solve one-step equations and inequalities in one variable. Name: Date: Future Target I will solve multi-step equations and inequalities. Tosolvean meanstofind thevalueofthevariablethatmakestheequation. Tosolvean meanstofindthe rangeofvaluesofthevariablethatmakethe inequality. When solving a 1-Step Equation: 1. Addorsubtracttheconstanttobothsides. OR Multiplyordividebythecoefficientonboth sides 2. Checkyourworkbysubstitutingthesolution intotheoriginalequation,andconfirmingthat itmakesatruestatementofequality. WHAT MAKES AN EQUATION IN ONE VARIABLE TRUE? 1SOLUTION Whengraphingthesolutionsettoaninequality YouNEEDtoknowthis: When solving a 1-Step Inequality: 1. FollowStep1ofSolvinganEquation then checkforanegativemultiplier.(seestep2) 2. IfyoumultiplyordividebyaNEGATIVEnumber, youmustchangethedirectionofyoursymbolto preservethebalanceoftheinequality. 3. Checkyourworkbysubstitutingavaluefrom withintherangeofsolutions,andconfirming thatitmakesatruestatementofinequality. <=Less$Thanwhile>=Greater$than.BotharegraphedwithanOPENcircle,thenshaded. =Less$Than$or$equal$towhile =Greater$than$or$equal$to. NOTE THE DIFFERENCE BothofthesearegraphedwithaCLOSEDcircleandthenshaded. WHAT MAKES AN INEQUALITY IN ONE VARIABLE TRUE? ARANGEOFSOLUTIONS(Many) (SOWEGRAPH ORWE DBEHERE FOREVERLISTINGTHESOLUTIONS If the solution is: x > 3 Set Builder Notation is: {x x > 3} Ex. 1 - Solve each equation/inequality. If it s an inequality, graph your solution and write it in set notation. Don t forget to check your solution. a. h 12 = 27 b > 12 c. 7 = 2 d n = 2 5 1

3 e < x + ( 2.78) f. 15b = 75 g. h. 4 = m 8 j k 2 3 k. 3 4 < n 12 Ex. 2 - Verbal Equations / Inequalities Write an equation/inequality for each sentence. Then solve it. (Do not graph) a.negativeninetimesa numberequalsnegativeone hundredseventeen. Ex. 3 - Real World Examples a. SHOPPING - $Shoe$Carnival$charges$$60$for$a$pair$of$tennis$ $$$$$shoes.$$this$is$four<fifths$of$the$price$for$the$$ $$$$$same$pair$of$tennis$shoes$at$rack$room. $$$$$Write$and$solve$an$equation$to$determine$the$$ $$$$$cost$of$the$shoes$at$rack$room.$ $ $ b.negativeoneeighthofa numberisatleastthree fourths. c.fivesixthsplusanumberis nomorethantwofifths. b. SALESW$ $$$$$Pet$Supplies$makes$a$profit$of$$5.50$per$bag$on$its$ $$$$$line$of$natural$dog$food.$$if$the$store$wants$to$ $$$$$make$a$profit$of$no$less$than$$5225$on$natural$$ $$$$$dog$food,$how$many$bags$of$dog$food$does$it$$ $$$$$need$to$sell?$$$ 2

4 Lesson 2-A Practice 1 (2.1, 5.1) Alg. I Honors Solving One-Step Equations Inequalities Name: Date: Directions: Solve each equation or inequality. If you need to graph, graph the solution and write it set notation. Don t forget to check your solution = = = h < = > = m = = = 3

5 = > 16. k = h > = < = = x = 4

6 Lesson 2-A Practice 2 (2.1, 5.1) Alg. I Honors Solving One-Step Equations Inequalities Section 1 PROVE IT Given >, $ > > Determine which quantity in each of the following is GREATER. Be ready to PROVE it through mathematical thinking a) b) + 2 Name: Date: c) d) Section 2 SOLVE IT Solve each equation and inequality. Make sure to represent the solution set appropriately for the problem (i.e. If it needs a graph and set notation, use it) a) 5 + = 10 b) 30 = 5 c) 30 5 d) > g) > e) 9 = 4 f)35 < 0.05h h) = 6 i) + 4 5

7 j) = k) 4.2 < 0.6 TRY IT = Section 3 TRANSLATE IT Translate each verbal expressions into an algebraic equation or inequality and solve. (Do not graph.) a)thesumoftwonumbersisatmost6,andone ofthenumbersis92. c)twelveisatmostanumberdecreasedbyseven. e)one9fifthlessthananumberisthree9fourths. Section 4 APPLY IT ATMOSPHERICSCIENCE ThetroposphereextendsfromtheEarth s surfacetoaheightof6912miles, dependingonthelocationandthe season.ifaplaneisflyingatanaltitudeof 5.8miles,andthetroposphereis8.6miles deepinthatarea,howmuchhighercan theplanegowithoutleavingthe troposphere? FUNDRAISING SarahissellingCandyBarstoraisemoney foraschooltriptonewyork.shewill makean30%profit(orcommission)on hertotalsalestoputtowardshertrip.if shesellseachcandybarfor$3.00,how manywillshehavetoselltomakeover $500? 6 b)fourtimesanumberisnomorethan108. d)twiceanumberisatleastsixteen. f)negativeone9sixthofanumberislessthan99. SUPREMECOURT ThefirstChiefJusticeoftheU.S.Supreme Court,JohnJay,served2079daysasChief Justice.Heserved10,463daysfewerthan JohnMarshall,whoservedasSupreme CourtChiefJusticeforthelongestperiod oftime.howmanydaysmustthecurrent SupremeCourtChiefJusticeJohnRoberts servetosurpassjohnmarshall srecordof service?

8 NAUTICAL Onthesea,distancesaremeasuredinnauticalmiles ratherthanmiles. 1nauticalmile 6080feet 1knot= 1nauticalmile hour FARMING Mr.Hill sfarmis126acres.mr.hill sfarm isonefourththesizeofmr.miller sfarm. HowmanyacresisMr.Miller sfarm? a.ifaboattravels16knotsin1hour,howfarwillithavetraveledinfeet?showhow youworkeditout. b.abouthowfastwastheboattravelinginmilesperhour?roundyouranswertothe nearesthundredth. Section 5 CHALLENGE ElevatorPuzzle Josegetsontheelevatorandrideswithoutpushinganybuttons.First,theelevatorgoesup4floorswhereBobgetson. Bobgoesdown6floorsandgetsoff.AtthatsamefloorFlorencegetsonandgoesuponefloorbeforegettingoff.The elevatorthenmovesdown8floorstopickuptheharttfamilywhoridedown3floorsandgetoff.thentheelevator goesuponefloor,picksupkris,andgoesdown6floorstothestreetlevelwherejoseexitstheelevator. 1.Supposexisyourstartingpoint.WriteanequationthatrepresentsJose selevatorride. 2.AtwhatfloordidJosegetontheelevator? 3. AtwhatfloordidBobgetontheelevator?AtwhatfloordidBobgetoff? 4. AtwhatfloordidFlorencegetontheelevator?AtwhatfloordidFlorencegetoff? 5. AtwhatfloordidtheHarttfamilygetontheelevator?AtwhatfloordidtheHarttfamilygetoff? 6.AtwhatfloordidKrisgetontheelevator?AtwhatfloordidKrisgetoff? 7

9 Lesson 2-B Notes (2.2, 5.3) Alg. I Honors Solving Multi-Step Equations Inequalities TNSS A-CED.1 Create equations that describe numbers or relationships. TNSS A-REI.1 Understand solving equations as a process of reasoning and explain the reasoning. TNSS A-REI. 3 Solve equations and inequalities in one variable. PastTarget Yousolvedone,stepequations inequalities. Ex. 1 Solve each equation or inequality. If it s an inequality, graph the solution set and write it in set builder notation. Don t forget to check your answer PresentTarget Solveequationsinequalitiesinvolving morethanoneoperation. Name: Date: FutureTarget Solveequationsandinequalitieswith variablesonbothsidesandwithgrouping symbols. Think BACKWARDS ORDER OF OPERATIONS You re trying to isolate the variable. 1. You usually add or subtract the constant to both sides first (zero pair) 2. THEN divide or multiply by the coefficient on both sides (to make it 1 - you want 1 of the variable). If it s an inequality and the coefficient is negative flip the symbol a = 27 c. 11 = 9 e.10 = 17 g. 1 4 f + 3 > 8 b.11d d. 14 > 5 x 8 f. 5 (2 + 3) 1 h.8 + = 32 8

10 Ex. 2 Write an equation and solve each problem. Ex. 3Real-World Examples i. 10 = k. 4 () a.threeisaddedtoa number,andthenthe sumismultipliedby4. Theresultis16. b.fivetimesanumber decreasedbyeightisat mosttenmorethan twicethenumber. a.shopping Susanhada$10couponforthepurchaseofanyitem. Sheboughtacoatthatwasonsaleforhalfofits originalprice.afterusingthecoupon,susanpaid $125.00forthecoatbeforetaxes.Whatwasthe originalpriceofthecoat?showhowyouarrivedat youranswer. j.16 = m. 4x What does CONSECUTIVE mean?? P c.findthreeconsecutive integerswithasum of 66 P d.findthreeconsecutive oddintegerswithasum of57. b.musicpractice Nancypracticestheviolinatleast12hoursper week.shepracticesforthreefourthsofanhour eachsession.ifnancyhasalreadypracticed3 hoursinoneweek,howmanysessionsremainto meetorexceedherweeklypracticegoal. 9

11 Lesson 2-B Practice 1 - Alg. I Honors Date: Solving Multi-Step Equations Inequalities Section 1 SOLVE IT Solve each equation and inequality. Make sure to represent the solution set appropriately for the problem (i.e. If it needs a graph and set notation, use it) a) = 1.8 b) 8 = 4 Name: c) 1 3 d) < 12 e) = 10 f) < 10 g) 8 = h) 1 8 = 7 8 i) 10 5 j) = 16 10

12 Section 2 TRANSLATE IT Translate each verbal expressions into an algebraic equation or inequality and solve. (Do not graph.) a) Two is subtracted from a number and the difference is multiplied by five. The result is 30. b) Negative three times a number increased by seven is less than negative eleven. c) Four times the sum of a number and two increased by three is at least twenty-seven. Section 3 APPLY IT GEOMETRY The area of a triangular garden can be no more than 120 square feet. The base of the triangle is 16 feet. What is the height of the triangle? SWIMMING POOL A rectangular swimming pool is surrounded by a concrete sidewalk that is 3 feet wide. The dimensions of the rectangle created by the sidewalk are 21 feet by 31 feet. a) Find the length and width of the pool. b) Find the area of the pool. c) Find the area of the sidewalk in square feet. TAXI FARE Jamal works in a city and sometimes takes a taxi to work. The taxicabs charge $1.50 for the first mile and $0.25 for each additional mile. Jamal has only $8.75 in his pocket. What is the maximum distance he can travel by cab if he intends to tip $1.00? Section 4 CHALLENGE a) The lesser of two consecutive even integers is 10 more than one-half the greater. Find the integers. b) The greater of two consecutive even integers is 6 less than three times the lesser. Find the integers. c) Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by ninety-one. d) Find a set of four consecutive positive integers such that the greatest integer in the set is twice the least integer in the set. Super Challenge 11

13 Lesson 2-B Practice 2 (2.2, 5.3) Algebra I Honors Solving Multi-Step Equations Inequalities Given in Word Problems Directions: For each situation: write an equation / inequality, and solve (showing ALL steps in correct form). Remember to answer the question that is being asked 1)331studentswentonafieldtrip.Sixbuseswerefilled and7studentstraveledincars.howmanystudents wereineachbus? 3)Thesumofthreeconsecutivenumbersis72. Whatisthesmallestofthesenumbers? 5)Stacyspenthalfofherallowanceplayingvideo games.toearnmoremoney,herparentsletherwash thecarfor$4.whatisherweeklyallowanceifshe endedupwith$12? 7)Ritaisorderingamoviefor$11.95,andafewCDs.She has$50.00tospend.shippingandsalestaxwillbe $10.00.IfeachCDcosts$9.99,what sthegreatest numberofcdsshecanbuy? 12 Name: Date: 2)Acarsalespersonispaidabasesalaryof$35,000a yearplus8%commission.whatarethesalesneeded tohaveanannualincomegreaterthan$65,000? 4)Benhas$6.00tospend.Asundaecosts$3.25plus $0.65pertopping.Howmanytoppingscanhehave? 6)Ralphhadsomecandytogivetohisfourfriends.He firsttook10piecesforhimselfandthenevenlydivided therestamonghisfriends.eachfriendgottwopieces. HowmanydidRalphstartoutwith? 8)Keith sdogweighs90pounds.ahealthyweightforhis dogwouldbelessthan75pounds.ifkeith sdogcan loseanaverageof1.25poundsperweekonacertain diet,howlonguntilthedogreachesahealthyweight?

14 9)Thepresidentofthemathclubwrote 400reducedby2 timesmyageis344 onhisdriver slicenseapplication. Howoldwashe? 10)Thesumofthreeconsecutiveevennumbersis66. Whatarethenumbers? 11)HomerrentedabikeatColliervilleRental.Theyrent bythehour(notpartialhours)atabasepriceof$17 plus$6anhour.ifhomerdoesn twanttospendmore than$30,howmanyhourscanherentthebike? 12)Arectanglehasaperimeterof50inches.Thewidthis 5incheslessthanthelength.Whatisthelengthof therectangle? 13)Ninahas6morevideogamesthanTracey.Together theyhave24games.howmanyvideogamedoesnina have? 14)Jamesreceived90votesforStudentCouncil President,whichwas50lessthantwicetheamount thattomgot.whowontherace,andbyhowmany votesdidhewin? 15)Lyndseywantstofenceinarectangularplayareaforherdog,Killer.Sheonlyhas82feetoffencingtouseand wantsthelengthoftheareatobeatleast9feetlongerthanthewidth.whatare2possibledimensionsofthe playarea? 13

15 Lesson 2-C Notes (2.4, 5.3) Algebra I Honors Solving Equations / Inequalities with Variables on Both Sides TNSS A-CED.1 Create equations that describe numbers or relationships. TNSS A-REI.1 Understand solving equations as a process of reasoning and explain the reasoning. TNSS A-REI. 3 Solve equations and inequalities in one variable. Ex 1: Solve equations / inequalities with variables on both sides a)6 = b) + 8 < + 2 c) Ex 2: Solve equations / inequalities with grouping symbols and variables on both sides a)6 + 7 = 4 12 Ex 3: Solve equations using ratios and proportions a) = Past Target I solved one-step and multi-step equations and inequalities. Present Target I can solve equations and inequalities with a variable on each side. I can solve equations and inequalities involving grouping symbols. Future Target I will solve equations involving only symbols. b) > 4(2 4) c) ( + 1) (3 5) 14 b) = Name: Date: GOAL 1. Move all the terms with variables to one side and the constants to the other. 2. Solve the resulting one-step equation Get rid of the parentheses first Then follow the steps above Make sure the (quantity) stays together

16 Ex. 4 - CHALLENGE In your groups, solve the following problems. Be prepared to share your answers and strategies a)3 8 = 3 b) 4 8 2( 2) c) = 3 2 WRITE: What may happen when solving equations / inequalities with variables on both sides? Ex. 5 Real World Examples wheredidthevariablesgo a) NUMBER THEORY Tripling the greater of two consecutive even integers gives the same results as subtracting 10 from the lesser even integer. What are the integers? b) GEOMETRY A rectangle has a perimeter of 26 inches. Find its dimensions in feet, if its length is 3 inches greater than its width. c) MODELS To make a model of the Tennessee River bed, Jimmy used ½ inch of clay for 5 miles of the river s actual length. His model river was 65 inches long. How long is the Tennessee River? d) WATER A dripping faucet wastes 3 cups of water every 8 hours. How many gallons are wasted in a week? e) GEOMETRY Find the value of h so that the figures have the same area. 15

17 Lesson 2-C Practice (2.4, 5.3) Alg. I Honors Solving Equations / Inequalities with Variables on Both Sides Name: Date: Directions: For each word problem, write an equation/inequality, and solve (showing all required steps). 1. The product of 3 and a number is more than twice that same number increased by An apple has 25 fewer calories than a pear. If six apples have the same calories as 4 pears, how many calories are in both kinds of fruit? 3. Tom and Harry are watching Netflix and eating MM s. Tom starts with 40 MM s and is steadily eating them at a rate of 6 per minute. Harry began with 60 MM s and is scarfing them down at a rate of 10 per minute. How many minutes before Tom and Harry both have the same amount left to eat? 4. Georgia is choosing between two cell phone plans that offer the same amount of free minutes. Cingular s plan charges $39.99 per month with additional minutes costing $0.45 each. Verizon s plan costs $44.99 with any additional minutes costing $0.40 each. How many minutes will she have to talk for both plans to cost the same? 5. You need to mail a package. UPS charges $7 for the first pound and $0.20 per each pound over. FedEx charges $5 for the first pound and $0.30 for each additional pound. How many pounds will result in both companies charging the same amount. When would you use UPS? FedEx? 6. Apartment hunting You have searched and searched and have decided on two final choices. Hickory Winds has a $1000 security deposit and costs $1200 each month. Pine Woods has a $1500 deposit and a rent of $1175. What information do you need to make a decision? Is there any solution that would make no difference on the decision? If there is, what is it? 7. A full 355 ml can of Coke is leaking at a rate of 5 ml per minute into an empty can. How long will it take for the two cans to have the same amount of Coke? 16

18 Solve each equation / inequality. (Do Not Graph.) ( 6) 9. < = (1 4) H.O.T Problems (Higher Order Thinking) 12. Explain how you could solve > 2 without multiplying or dividing each side by a negative number. 13. Create an equation with at least two grouping symbols for which there is no solution. 14. Find the value of for which each equation is an identity. What does that mean?? a. (3 2) = 4 6 b = If + < + has infinitely many solutions, what will be the solution of + > +? Explain how you know. 17

19 Lesson 2-D Notes (2.9) - Alg. 1 Honors Weighted Averages TNSSACED.1Createequationsthatdescribenumbersorrelationships. TNSSAREI.1Understandsolvingequationsasaprocessofreasoningandexplainthereasoning. Name: Date: PastTarget IsolvedoneOstepandmultiOstep equationsandinequalities. PresentTarget Icansolvemixtureproblems. Icansolveuniformmotionproblems. FutureTarget Iwillsolveequationsinvolvingonly symbols. MIXTURE PROBLEMS: Weighted averages can also be solved using Systems of Equations We will be practicing that skill next semester Ex.1:Abookstoresellspencilsfor$0.10eachanderasersfor$0.15each.OnMonday,thestoresold17more pencilsthanerasersforatotalof$23.45.howmanyofeachitemwassold? Amount Price Total Pencils Erasers Total Ex.2:Sallyhas$4.45inquartersandnickels.Sallyhas7morequartersthannickels.Howmanyofeachdoes Sallyhave? Amount Value Total Quarters Nickels Total Ex.3:AttheColliervilleMalcoCinema,ticketsforadultscost$5.50andticketsforchildrencost$3.50.How manyofeachkindofticketwaspurchasedif21ticketswereboughtfor$83.50? Amount Cost Total Adult Child Total 18

20 Ex.4:Acoffeeshopownerwantstocreateaspecialmixusing2coffees,onepricedat$6.40perpoundand the other prices at $7.28 per pound. How many pounds of the $7.28 coffee should she mix with 9 poundsofthe$6.40coffeetosellthemixturefor$6.95apound? Ex.5:Howmanyouncesofa6%iodinesolutionneedstobeaddedto12ouncesofa10%iodinesolutionto createa7%iodinesolution? UNIFORM MOTION PROBLEMS:$%'( = $ $ = Ex.6:TwotrainsleaveMemphisatthesametime,onegoingwestandtheothereast.Thewestboundtrain travelsat55mphandtheeastboundtraintravelsat45mph.inhowmanyhourswillthetrainsbe400 milesapart? Rate Time Distance ( = ) Train1 Train2 Ex.7:SupposeJohnandGinaleaveatthesametimetravelinginthesamedirection.Johndrivesatarateof 85km/handGinadrivesatarateof70km/h.Howlonguntiltheyare90kmapart? Rate Time Distance ( = ) John Gina 19

21 Ex. 8:At8:00AMFelicialeaveshomeonabusinesstripdriving35mph.Ahalfanhourlater,Jimdiscovers that she forgot her briefcase. He drives 50 miles per hour to catch up to her. If Jim is delayed 15minutesbyatrain,whenwillhecatchuptoFelicia? Rate Time Distance ( = ) Felicia Jose Ex. 9: Frank is driving 40 mph. After he has driven 30 miles, his brother Rico starts driving in the same direction.atwhatratemustricardodrivetocatchupwithpabloin5hours? Rate Time Distance ( = ) Frank Rico Ex.10:Anexpresstraintravels80kilometersperhourfromIrontontoWildwood.Alocaltrain,travelingat 48 kilometers per hour takes 2 hours longer for the same trip. How far apart are Ironton and Wildwood? 20

22 Lesson 2-D Practice (2.9) Alg. I Honors Weighted Averages Directions: Set up and solve each weighted average problem. Make sure you answer the question that is asked 1) TheColliervilleHighSchoolMarchingBandsoldgiftwraptoearnmoneyforabandtriptoOrlando.Thegiftwrap insolidcolorssoldfor$4.00perroll,andtheprintgiftwrapsoldfor$6.00perroll.theysold60morerollsofthe solidgiftwrapthantheprintgiftwrapforatotalof$2340.howmanyrollsofeachkindofgiftwrapweresold? 2) TheFordsaregoingtoSixFlags.Thetotalcostoftheticketsforafamilyof2adultsand3childrenis $79.50.Ifanadultticketcosts$6.00morethanachild sticket,findthecostofeach. 3) TheNutHousesellswalnutsfor$4.00apoundandcashewsfor$7.00apound.Howmanypoundsof cashewsshouldbemixedwith10poundsofwalnutstoobtainamixturethatsellsfor$ ) Joshuaisdoingachemistryexperimentthatcallsfora30%solutionofcoppersulfate.Hehas40mLof 25%solution.Howmanymillilitersof60%solutionshouldJoshuaaddtothe25%solutiontoobtainthe required30%solution? 5) PaulYuinvested$6,000intwoaccounts,partat4.5%andtheremainderat6%.Ifthetotalincomefrom bothinvestmentswas$279,howmuchdidpaulinvestateachrate? 21 Name: Date:

23 6) RyanandJessicaWilsonleavetheirhomeatthesametimetravelinginoppositedirections.Ryantravels at57mph,andjessicatravelsat65mph.inhowmanyhourswilltheybe366milesapart? 7) Twocyclistbegintravelinginthesamedirectiononthesamebikepath.Onetravelsat20mph,andthe otherat14mph.afterhowmanyhourswilltheybe15milesapart? 8) At7:00AMBrookleaveshometogoonabusinesstripdriving55mph.Fifteenminuteslater,Bart discoversthatbrookeforgothercomputer.hedrives70mphtocatchupwithher.ifbartisdelayed30 minutesbyaflattire,whenwillhecatchupwithbrooke? 9) Timisdriving55mph.Afterhehasdriven20miles,hisbrotherDylanstartsdrivinginthesame direction.atwhatratemustdylandrivetocatchupwithtimin2hours? 10) Anexpresstraintravels90kilometersperhourfromWheatontoWard.Alocaltrain,travelingat50 kilometersperhourtakes4hourslongerforthesametrip.howfarapartarewheatonandward? 22

24 Name Date Period Unit 2 Test Study Guide Algebra 1 Honors Solving Equations Inequalities Lesson 2-A Solving One-Step Equations Solve each equation/inequality. If it is an inequality, write the solution in set-builder notation and graph. Don t forget to check your solution. SHOW YOUR WORK 1) h 13 = 34 2) r + 7 > 5 3) 6f = 48 4) 3 > 5) r = 6) 58.5 = m ) 9 = 8) ) + 65 = 85 10) 5 11) = ) < 15 13) = 14) 15 > 60 15) = 16) ) > 23 Check it ** ** Did you remember to FLIP the symbol on inequalities when you multiplied or divided by a negative number?

25 Write an equation/inequality. Then solve it. (Do not graph.) SHOW YOUR WORK 18) Six times a number is ) Twelve is at most a number decreased by seven. 20) An electronics store sells a certain digital camera for $126. This is of the price that a photography store charges. What is the cost of the camera at the photography store? 21) Adult Nile crocodiles weigh up to 2200 pounds. If a young Nile crocodile weighs 1157 pounds, how many pounds might it be expected to gain in a lifetime? Lesson 2-B Solve each equation/inequality. If it is an inequality, write the solution in set-builder notation and graph. Don t forget to check your solution. SHOW YOUR WORK 22) 6 10 = 20 23) 5 < ) 3 = 9 25) 12 = 9 26) 5 27) 4h + 7 > 15 28) 32 6h 10 29) 9 > ) = 13 24

26 31) ) 15 = 8 33) + 5 < 3 Write an equation/inequality. Then solve it. (Do not graph.) SHOW YOUR WORK 34) Triple a number decreased by two is equal to ) One fifth of a number increased by twenty-one is greater than 4. 36) Kim bought a journal for $5 and 2 pens. She spent $ How much was each pen? 37) Sam needs to rent a pressure washer to clean his driveway. The rental company charges a one-time rental fee of $20 plus $3 per hour to rent a pressure washer. Sam has no more than $50 to spend. How many hours can Sam rent the pressure washer? 38) Find four consecutive integers with a sum of ) Find three consecutive even integers with a sum of -72. Lesson 2-C Solve each equation/inequality. If it is an inequality, write the solution in set-builder notation and graph. Don t forget to check your solution. SHOW YOUR WORK 40) = ) < ) =

27 43) h 8 < 2 h 1 44) = ) > ) = ) + 4 = ) ) ) = HEY A Don t Forget to review your Notes from each section Write an equation/inequality. Then solve it. (Do not graph.) SHOW YOUR WORK 51) Four times a number minus six is greater than eight plus two times the number. 52) One half the lesser of two consecutive even integers is three less than one-fourth times the greater even integer. What are the integers? Find the value of x so that the figures have the same area. 53) 6cm ( 1)cm cm 26 4cm

28 Lesson 2-D Solve each mixture / motion problem. 54)Rochellehas$2.55indimesandquarters.Shehas eightmoredimesthanquarters.howmany quartersdoesshehave? 55)TheCookieCrumblesCompanysellstwokindsof cookiesdaily:peanutbutterat$6.50perdozen andchocolatechipat$9.00perdozen.yesterday, theysold85dozenmorepeanutbutterthan chocolatechipcookies.thetotalsalesforboth were$ howmanydozensofeachwere sold? 56)Groundchucksellsfor$1.75perpound.How manypoundsofgroundroundsellingfor$2.45 perpoundshouldbemixedwith20poundsof groundchicktoobtainamixturethatsellsfor $2.05perpound? 57)Anadvertisementforanorangedrinkclaimsthat thedrinkcontains10%orangejuice.howmuch pureorangejuicewouldhavetobeaddedto5 quartsofthedrinktoobtainamixturecontaining 40%orangejuice? 58)Artleavesat10:00AM,travelingat50mph.At 11:30AM,Jenniferstartsinthesamedirectionat 45mph.Whenwilltheybe100milesapart? 59)The$Harvest$Moonleavesthepierat9:00AM travelingat8knots.ahalfhourlater,the$river$ $$$$$$$Steamerleavesthesamepierinthesame directiontravelingat10knots.atwhattimewith The$River$SteameroverstakeThe$Harvest$Moon? 27