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1 Chapter(1:(Equations(and(Inequalities( ClassNotesandHomeworkWorksheets

2 Chapter(1:(Equations(and(Inequalities( Assignment(Sheet( Date( Topic( Assignment( Completed( ( Course(Introduction( 1)(Sign(class(syllabus,(both( ( student(and(parent( 2)(Get(supplies(by(Monday( 3)(Download(suggested(iPad( apps( ( 1.1:(Real(Numbers( and(operations( Homework(1.1( ( ( 1.2:(Algebraic( Expressions(and( Models/(1.3:(Solving( Linear(Equations( ( 1.2:(Algebraic( Expressions(and( Models/(1.3:(Solving( Linear(Equations( ( 1.4:(Rewriting( Equations(and( Formulas( ( 1.4:(Rewriting( Equations(and( Formulas( Begin(Homework(1.2Q1.3( ( Complete(Homework(1.2Q1.3( ( Homework(1.4( ( Homework(1.4(Day(2( ( ( 1.1Q1.4(Review( 1)(Chapter(Review(pg.(58(1Q25( ( odd( 2)(Chapter(Test(pg.(60(1Q25( odd( ( QUIZ(1.1Q1.4( NO(HOMEWORK( ( ( 1.6:(Solving(Linear( Inequalities( ( 1.7:(Solving(Absolute( Value(Equations(and( Inequalities( ( 1.7:(Solving(Absolute( Value(Equations(and( Inequalities( Homework(1.6( ( Homework(1.7( ( 1)(Chapter(Review(pg.(58(2Q26( even( 2)(Chapter(Review(pg.(60((27Q 40( ( 1.1Q1.7(Review( ( ( ( Chapter(1(EXAM( NO(HOMEWORK( ( (

3 1.1RealNumbersandNumberOperations TheRealNumberSystem CreateaVennDiagramthatrepresentstherealnumbersystem,besuretoincludethe followingtypesofnumbers:real,irrational,rational,integers,wholes,and natural/counting. PropertiesofRealNumbers Leta,bandcberealnumbers. Property Addition Multiplication Commutative a+b=b+a a b=b a Associative (a+b)+c=a+(b+c) (ab) c=a (bc) Identity a+0=a;0+a=a a 1=a,1 a=a Inverse a+(-a)=0 a 1 a DistributiveProperty a(b+c)=ab+ac Identifythepropertyillustrated. a.)14+7=7+14 b.)5 1 5 = 1 c.)(5+3)+2=5+(3+2) d.)5(x+2)=5x+10 e.) = 0 f.)1 5=5 = 1 ; (a 0)

4 UnitAnalysis ConversionReferenceTable EnglishUnits MetricUnits English/MetricUnits 1ft=12in 1m=100cm 1in=2.54cm 1yd=3ft 1cm=10mm 1mi=1.61km 1mi=5280ft 1kg=1000g 10km=6.2mi 1lb=16oz 1L=1000mL lb=454g 1gal=4qt 1L=1.057qt Trythefollowingconversions. 1.)2.45mi= ft 2.)36g= kg 3.)470mi= km 4.)200mi/hr= ft/sec 5.)526yds/sec= mi/hr 6.)75.0kg= lbs. 7.)10gal= ml 8.)1.43kg/L= g/ml

5 1.1 Real Numbers and Number Operations Homework 1. Giveanexampleofanumberthatisbotharationalnumberandawholenumber. 2. Giveanexampleofanumberthatisbothanintegerandanaturalnumber (countingnumber). 3. Giveanexampleofanumberthatisarationalnumber,butNOTaninteger. 4. Namethepropertyillustratedineachexamplebelow: a) 5(x + 7) = 5x + 35 b) (59 + 7) + 62 = 59 + (7 + 62) c) 10 i 1 10 = 1 d) = e) 387+0=387 f) 4(3)=3(4) g) 0=5+(\5) 5. Performthefollowingconversionsusingconversionfactors.Showyoursetup. 86inches= ft5.17lb/gal= lb/qt 2.4g/mL= lb/gal3.4km/hr= mi/hr

6 Usewhatyouhavelearnedaboutconversionfactorstosolvethefollowingapplication problems. 6. TheelevatorintheWashingtonMonumenttakes75secondstotravel500ftto thetopfloor.whatisthespeedoftheelevatorinmilesperhour? 7. WhenyoudriveacrosstheborderintoQuebec,Canada,allthespeedlimitsigns areinkm/hour.howmightyougetaquick,reasonableapproximationofthe equivalentspeedinmi/hour? 8. Asanurse,youmustdeterminetheproperdoseofamedicationforyourpatient whoweighs160pounds.theamountofmedicationis20mg/kg.(mgofmedication perthepatient sweightinkilograms)howmanymilligramsofmedicationwould beaproperdoseforyourpatient? 9. Ablooddonorgives1pintofbloodeachtimehedonates.Helearnsfromthe AmericanRedCrossthathewillbehonoredataspecialdinnerforoutstanding donorsforhislifetimedonationof6gallonsofblood.howmanytimeshashe donatedblood?(thereare2pintsper1quartofanyliquid.)

7 1.2AlgebraicExpressionsandModels&1.3SolvingLinear Equations OrderofOperationsKPEMDAS 1.)Undogroupingsymbols parentheses,absolutevalue,braces,brackets 2.)Evaluateanyexponents/powers 3.)Domultiplicationanddivisionastheyappearlefttoright 4.)Doadditionandsubtractionastheyappearlefttoright Evaluate 1. \8+5(1 (\3)) 3 2. ( 3) Evaluate 1. 3x 2 5x + 7 when x = x 3 + 3x when x = 4 SimplifyingAlgebraicExpressions 1. 5n 2 (n +1) 3n 3 2n 2. 2[(3n +1) 2 n] SolvingEquations 1. 5(x 2) = 4(2x + 7) + x x = x 1 6

8 x = 1 5x 1 5 ( ) x = x x + 2 4x = 3(2x + 1) 2 2x (2x + 3) = 2(4 3x) 4x WordProblemPractice 1.) Findfourconsecutiveevenintegersthattotal92. 2.) Findthreeconsecutiveintegerssuchthatifthesumofthefirsttwoisdecreasedbythethird, theresultwillbe68.

9 3.) Findthreeconsecutiveevenintegerssuchthattwicethesmallestplusthreetimesthelargest willequalthemiddleintegerincreasedby82. 4.) Mrs.Bunkerpaidher7.15grocerybillwithaten\dollarbillandaskedforherchangeindimes andquarters.ifshereceived21coinsinchange,howmanyquartersdidshereceive? 5.) 65studentsandteachersfromPenncrestHighSchoolaregoingtoaplay.Ticketscosting4for teachersand3.60forstudentswerepurchasedatatotalpriceof244.howmany4tickets werebought? 6.) Astampcollectorhasagroupoftencent,fifteencentandtwentycentstampsthattotal4.75in value.ifhehastwiceasmanytwenty\centstampsastencentstampsandthreefewerfifteen centstampsthan10centstamps,howmanytwentycentstampsdoeshehave?

10 1.2 and 1.3 Homework Evaluatethefollowingexpressions. 1.) (3) 4 2.) ( 2) 4 3.) )( 2) 4 5.) (5 2) )((3 1) 2 + ( 3)) 5 7.) 1 2 ( 2) 2 + (4 5) 4 8.) x 2 4xy when x = 2 and y = 3 9.) 6 x 2 + x when x = 2 Simplifythefollowingexpressions. 10.) 5(n 2 + n) 3(n 2 2n) 11.) 8(y x) 2(x y) Solvethefollowingequations. 12.) 6(2x 1) + 3 = 6(2 x) 1 13.)5x+2=2(2x+1)+x

11 14.) 5(2x + 3) = 2(4 3x) 4x 15.) 1 2 x 5 3 = 1 2 x ) x 5 3 = 2 17.) x 7 10 = )Findthreeconsecutiveintegerssuchthatifthreetimesthesmalleris decreasedbythesumoftheothertwo,thedifferencewillbe )Nancyhasabagofcoinstotaling3.60invalue.Ifshehastwomorenickels thanquarters,andtwiceasmanyquartersasdimes,howmanyofeachcoin doesshehave?

12 1.4RewritingEquationsandFormulas Warmup: Solvetheequation 3 2 x = 7 2 x Example1:Solvefory:11x 9y = 4 Example2:Solvefory:6x y = 21 Example3:Solvefory. xy + 2x = 20

13 Solveeachformulafortheindicatedorunderlinedvariable. a.) P = 2l + 2w b.) A 2 = π r c.) 1 A = bh (solveforh) d.) E = mc (solveform) e.) F = C f.) S = C rc (solveforc) g.) F = Gm 1m 2 (form2) h.) I = E r 2 R + r (forr)

14 i.) A = 1 2 h b 1 + b 2 ( )forb2 j.) 1 R = 1 R R 2 (forr2) k.) S = 2WH + 2WL + 2LH (forh)

15 1.4Homework:RewritingEquationsandFormulas 1.) A=P+Prt(solvefort) 2.) PV=nRT(solveforR) 3.) P 1 V 1 T 1 = P 2 V 2 T 2 (Solvefor P 2 ) 4.) S = V 0 t 16t 2 (SolveforV 0 ) 5.) V = 1 3 πr2 h(solveforh)

16 6.) 1 f = 1 a + 1 b (Solveforb) 7.) P = R C n (SolveforR) 8.) S = 2πr 2 + 2πrH (SolveforH)

17 1.4HomeworkDay2

18 1.6SolvingLinearInequalities Graphthefollowinginequalities: \4<x 5 x And inequalities.thesearealsoknownasunions,denotedbythesymbol x \3andx 4 x<3andx 6 Or inequalities.thesearealsoknowasintersections,denotedbythesymbol x 4orx 0 x>10orx 6 SolveandGraph: 1.)\11y 9 13

19 2.) x x 3.) 12 < 3x 3 <15 4.) x or x

20 1.6Homework Matchtheinequalitywithitsgraph. 1.)x 4 2.)x<4 3.) 4<x 4 4.)x 4orx<\4 5.)\4 x 4 6.)x>4orx \4 Determinewhetherthegivennumberisasolutiontotheinequality. 7.) 1 x 2 4 Is9asolutiontothisinequality? 3 8.) 8 < x 11 < 6 Is5asolutiontothisinequality?

21 Solvetheinequality.Thengraphyoursolution. 9.) x 6 10.)5 5x>4(3 x) 11.) 5 n 6 0

22 12.) 8 < 2 3 x 4 < ) 3x + 2 < 10 or 2x 4 > 4 14.) 3n + 1 > 10 and 1 2 n 1 > 3 15.) 2(x + 3) < 14 or 5 x < 1

23 1.7AbsoluteValueEquationsandInequalities AbsoluteValueEquations GeneralForm: ax + b = c Thesolutionsetforthisequationcanbefoundbysolvingthesetwoequations: ax + b = c ax + b = c Example: 5x + 2 = 27 AbsoluteValueInequalities GeneralForm: ax + b > c or ax + b < c or ax + b c or ax + b c Whenyousolveanyinequality,rewritetheinequalityasanequalsign.Breaktheequation downintotwo cases,andsolveeachindividually.ploteachsolutiononanumberlineand pickatestpointtoplugintotheoriginalinequality.writethesolutionsetusingset notation. Examples: 3x + 4 5

24 4x PracticeProblems: 1.) 2 3 `2 1 = x 2.) < + x 3.) 3x +10 > 7 4.) x + 5 6

25 5.) 2x ) 4 2y < 9 7.) 3x 5 < 1 8.) 3x 5 > 1 9.) 2x ) x 3 > 0

26 1.7Homework Decidewhetherthegivennumberisasolutiontotheinequality. 8 2n = 2 ; n = 5 3x + 5 = 7 ; x = 4 Solvetheequation. 2 3 x + 2 = 10 Solvetheinequality. 7x + 5 < x 6

27 416 x x n x 2 > 6 Solveforx.Assumeaandbarepositive. x + a < b x + a a

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