SECONDARY MATH I // MODULE 4
SOLVING EQUATIONS AND INEQUALITIES – 4.4
Mathematics Vision Project
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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 < 𝑥 meansthesamethingas𝑥 < 12.Itworksjustlike12 = 𝑥 𝑎𝑛𝑑 𝑥 = 12.4.Theinequality−2 𝑥 + 10 ≥ 75saysthesamethingas−2𝑥 − 20 ≥ 75.Icanmultiplyby-2ontheleftsidewithoutreversingtheinequalitysymbol.
5.Whensolvingtheinequality10𝑥 + 22 < 2,thesecondstepshouldsay10𝑥 > −20becauseIadded-22tobothsidesandIgotanegativenumberontheright.
6.Whensolvingtheinequality−5𝑥 ≥ 45,theansweris𝑥 ≤ −9becauseIdividedbothsidesoftheinequalitybyanegativenumber.
7.Thewordsthatdescribetheinequality𝑥 ≥ 100are“xisgreaterthanorequalto100.”
SET Topic:Solveinequalities.Verifythatgivennumbersareelementsofthesolutionset.Solveforx.(Showyourwork.)Indicateifthegivenvalueofxisanelementofthesolutionset.
8.2𝑥 − 9 < 3
Isthisvaluepart𝑥 = 6; 𝑦𝑒𝑠? 𝑛𝑜?ofthesolutionset?
9.4𝑥 + 25 > 13
Isthisvaluepart𝑥 = −5; 𝑦𝑒𝑠? 𝑛𝑜?ofthesolutionset?
READY, SET, GO! Name PeriodDate
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
10.6𝑥 − 4 ≤ −28Isthisvaluepart𝑥 = −10; 𝑦𝑒𝑠? 𝑛𝑜?ofthesolutionset?
11.3𝑥 − 5 ≥ −5Isthisvaluepart𝑥 = 1; 𝑦𝑒𝑠? 𝑛𝑜?ofthesolutionset?
Solveeachinequalityandgraphthesolutiononthenumberline.
12.𝑥 + 9 ≤ 7
13.−3𝑥 − 4 > 2
14.3𝑥 < −6
15.!!> − !
!"
16.−10𝑥 > 150
17. ! !!
≥ −5
Solveeachmulti-stepinequality.
18.𝑥 − 5 > 2𝑥 + 3 19.!(!!!)!"
≤ !!! 20.2 𝑥 − 3 ≤ 3𝑥 − 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
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: 𝑦 = 122𝑥 − 𝑦 = 14
Thefirstequationstatesthat𝑦 = 12.Thatinformationcanbeusedinthesecondequationtofindthe
valueofxbyreplacingywith12.Thesecondequationnowsays𝟐𝒙 − 𝟏𝟐 = 𝟏𝟒.Solvethisnewequation
byadding12tobothsidesandthendividingby2.Theresultisx=13.
21. 𝑦 = 5−𝑥 + 𝑦 = 1 22. 𝑥 = 8
5𝑥 + 2𝑦 = 0
23.2𝑦 = 10
4𝑥 − 2𝑦 = 50 24. 3𝑥 = 124𝑥 − 𝑦 = 5
25. 𝑦 = 2𝑥 − 5𝑦 = 𝑥 + 8 26. 3𝑥 = 9
5𝑥 + 𝑦 = −5
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