More-Equations-West-Pender-Middle-School更多的方程課件

MoreEquations-WestPenderMiddleSchool更多的方程-西德中學MoreEquations-WestPenderMiddleSchool更多的方程-西德中學MoreEquations-WestPenderMiddleSchool更多的方程-西德中學MoreEquationsSolvingMultistepEquationsSomeequationsmayhavemorethantwostepstocomplete.Youmayhavetosimplifytheequationfirstbycombiningliketermsorevenremovefractionstomakesolvingeasier.SamanthaandRebeccawanttorentsportsequipmentatthecitypark.Samanthawantstorentinlineskates,andRebeccawantstorentamotorscooter.Howwouldyouwriteanequationandsolvetheproblemtofindthetotalcostforaspecifiednumberofhours.Let’stakealookathowyouwouldsolvethisproblem.MoreEquationsSolvingMultistepEquationsSomeequationsmayhavemorethantwostepstocomplete.Youmayhavetosimplifytheequationfirstbycombiningliketermsorevenremovefractionstomakesolvingeasier.SamanthaandRebeccawanttorentsportsequipmentatthecitypark.Samanthawantstorentinlineskates,andRebeccawantstorentamotorscooter.Howwouldyouwriteanequationandsolvetheproblemtofindthetotalcostforaspecifiednumberofhours.Let’stakealookathowyouwouldsolvethisproblem.Hereisthecostforeachoftheactivitiesthegirlswouldliketorent.Let’slookateachindividuallyandthentogether.InlineSkates$3.00plus$1.50/hourc=3+1.50xc=individualcostx=numberofhoursrentalMotorscooter$10.00plus$2.75/hourc=10+2.75xc=individualcostx=numberofhoursrentalIndependentvariableDependentvariableconstantIndependentvariableDependentvariableconstantCombinedcost(C)

UsetheequationC=3+1.50x+10+2.75xtoanswereachofthefollowingquestions.

C=4.25x+13HowmuchwouldSamanthaandRebeccapayfor2hours’rental?HowmuchwouldSamanthaandRebeccapayfor3hours’rental?Iftheirtotalrentalcostis$38.50,forhowmanyhoursdidtheyusetheequipment?MultistepEquationsEquationswithLikeTermsEquationsthatcontainFractionsEquationswithvariablesonbothsidesImportant!

Tosolvemultistepequations,firstclearfractionsandcombineliketerms.Thenaddorsubtractvariablestobothsidessothatthevariableisononesideonly.MultistepequationsSTEP1:ClearfractionsSTEP2:removeparenthesisSTEP3:moveallvariablestoonesideoftheequation.Solvingequationscontainingliketerms8x+6+3x–2=3711x+4=37 Combineliketerms11x+4–4=37–4 SubtractionPropertyofEquality

11x=33

DivisionPropertyofEquality1111x=3Remembertokeepyourequalsignslineduptopreventyoufrommakingamistake.Onthenextslidewewillcheckouranswerbysubstitutingforx.Checkyouranswerbysubstitutingforx8x+6+3x–2=378(3)+6+3(3)–2=37 Substitute3forx24+6+9–2=37 Combineliketerms37=37?TrueSolve:

1)8d–11+3d+2=13

2)8x–3x+2=-33

3)2y+5y+4=25

4)4x+8+7x-2x=89

5)30=7y–35+6y

Solvingequationsthatcontainfractions

5n+7=-3

Multiplybothsideby4toclearfractions4444·5n+7=-3·4

Multiplybothsidesby4,

MultiplicationPropertyofEquality444 5n+7=-3 Subtract7frombothsides,SubtractionPropertyofEquality5n+7–7=-3–7

5n=-10

Dividebothsidesby5,DivisionPropertyofEquality

5

5

n=-2RemembertogobackansubstitutefornSolve:

1)4–2p=6

555

2)9z+1=2

444

3)x+2=5

236

Solvingequationswithvariablesonbothsidesissimilartosolvinganequationwithavariableononlyoneside.Youcanaddorsubtractatermcontainingavariableonbothsidesofanequation.2a+3=3a2a–2a+3=3a–2a

Subtract2afrombothsides.3=aRemembertokeepequal(=)signslineduptopreventerrors.Alwaysgobackandcheckeachequationbysubstitutingthesolutionintotheoriginalequation.Movingtermsisjustlikemovingasinglenumber,youusethePropertiesofEquality.Solvingequationswithvariablesonbothsides.4x–7=5+7x4x–4x-7=5+7x-4xSubtract4xfrombothsides.-7=5+3x-7-5=5–5+3xSubtract5frombothsides.-12=3x

-12=3x

Dividebothsidesby3.

3

3-4=xRemembergobackandsubstituteforx.Remember,youcanmoveawholeterm.Solve:

1)5x+2=x+6

2)4y–2=6y+6

3)4(x-5)+2=x+3

4)4x–5+2x=13+9x–21

5)8x–3=15+5x

Bothfigureshavethesameperimeter.Whatistheperimeter.Rememberhowtofindtheperimeterofapolygon?Well,thesetwoperimetersarethesame.Writeanequationandsolvethefollowingproblem.SamandTedhavethesamenumberofbaseballtradingcardsintheircollection.Samhas6completesetsplus2individualcards,andTedhas3completesetsplus20individualcards.Howmanycardsareinacompleteset?Findthreeconsecutivewholenumberssuchthatthesumofthefirsttwonumbersequalsthethirdnumber.Hint:Letnrepresentthefirstnumber.)Solveandcheck.6x+3x–x+9=33-9=5x+21+3x4–2p=6555y–3y+1=1