SECONDARY MATH I // MODULE 4

SOLVING EQUATIONS AND INEQUALITIES – 4.4

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4.4

READY Topic:Writeanequationfromacontext.Interpretnotationforinequalities.Writeanequationthatdescribesthestory.Thenanswerthequestionaskedbythestory.

1.Virginia’sPaintingServicecharges$10perjoband$0.20persquarefoot.IfVirginiaearned$50forpaintingonejob,howmanysquarefeetdidshepaintatthejob?

2.Rentingtheice-skatingrinkforapartycosts$200plus$4perperson.IfthefinalchargeforDane’sbirthdaypartywas$324,howmanypeopleattendedhisbirthdayparty?

Indicateifthefollowingstatementsaretrueorfalse.Explainyourthinking.3.Thenotation12 < ! meansthesamethingas! < 12.Itworksjustlike12 = ! !"# ! = 12.4.Theinequality−2 ! + 10 ≥ 75saysthesamethingas−2! − 20 ≥ 75.Icanmultiplyby-2ontheleftsidewithoutreversingtheinequalitysymbol.

5.Whensolvingtheinequality10! + 22 < 2,thesecondstepshouldsay10! > −20becauseIadded-22tobothsidesandIgotanegativenumberontheright.

6.Whensolvingtheinequality−5! ≥ 45,theansweris! ≤ −9becauseIdividedbothsidesoftheinequalitybyanegativenumber.

7.Thewordsthatdescribetheinequality! ≥ 100are“xisgreaterthanorequalto100.”

SET Topic:Solveinequalities.Verifythatgivennumbersareelementsofthesolutionset.Solveforx.(Showyourwork.)Indicateifthegivenvalueofxisanelementofthesolutionset.

8.2! − 9 < 3

Isthisvaluepart! = 6; !"#? !"?ofthesolutionset?

9.4! + 25 > 13

Isthisvaluepart! = −5; !"#? !"?ofthesolutionset?

READY, SET, GO! Name PeriodDate

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SECONDARY MATH I // MODULE 4

SOLVING EQUATIONS AND INEQUALITIES – 4.4

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

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4.4

10.6! − 4 ≤ −28Isthisvaluepart! = −10; !"#? !"?ofthesolutionset?

11.3! − 5 ≥ −5Isthisvaluepart! = 1; !"#? !"?ofthesolutionset?

Solveeachinequalityandgraphthesolutiononthenumberline.

12.! + 9 ≤ 7

13.−3! − 4 > 2

14.3! < −6

15.!! > −!!"

16.−10! > 150

17. ! !! ≥ −5

Solveeachmulti-stepinequality.

18.! − 5 > 2! + 3 19.!(!!!)!" ≤!!!

20.2 ! − 3 ≤ 3! − 2

–10 –5 5 100

–10 –5 5 100

–10 –5 5 100

–10 –5 5 100

–25 –20 –15 –10 –5 0

10 20 30 400

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SECONDARY MATH I // MODULE 4

SOLVING EQUATIONS AND INEQUALITIES – 4.4

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

4.4

GO

Topic:Usesubstitutiontosolvelinearsystems

Solveeachsystemofequationsbyusingsubstitution.

Example: ! = 122! − ! = 14

Thefirstequationstatesthat! = 12.Thatinformationcanbeusedinthesecondequationtofindthevalueofxbyreplacingywith12.Thesecondequationnowsays!" − !" = !".Solvethisnewequationbyadding12tobothsidesandthendividingby2.Theresultisx=13.

21. ! = 5−! + ! = 1 22.! = 8

5! + 2! = 0

23.2! = 10

4! − 2! = 50 24.3! = 124! − ! = 5

25. ! = 2! − 5! = ! + 8 26.3! = 9

5! + ! = −5

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