SECONDARY MATH I // MODULE 4

SOLVING EQUATIONS AND INEQUALITIES – 4.5

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

4.5

READY Topic:Interpretphrasesthatimplyaninequality.Rewritethegiven“wordsentence”asa“mathsentence.”Eachmathsentencewilluseoneofthefollowingsymbols:>, <, ≤, ≥.Use“x”inplaceofthenumber. WordSentence MathSentenceExample: Iamthinkingofanumberthatisgreaterthan13. 𝑥 > 131. Iamthinkingofanumberthatisatleast13. 2. Iamthinkingofanumberthatisnofewerthan13. 3. Iamthinkingofanumberthatdoesnotexceed13. 4. Iamthinkingofanumberthatisatmost13. 5. Iamthinkingofanumberthatisnomorethan13. 6. Iamthinkingofanumberthatisfewerthan13. 7. Iamthinkingofanumberthatisnotabove13. 8. Iamthinkingofanumberthatislessthan13. 9. Iamthinkingofanumberthatisnotunder13. 10. Iamthinkingofanumberthatisnotgreaterthan13. SET Topic:Writeandsolveinequalitiesfromacontext.11.TotakesweepstakesforthelargestpumpkincropattheRiversideCountyFair,theaverageweight

ofEthan’stwopumpkinsmustbegreaterthan875lbs.Oneofhispumpkinsweighs903lbs.WhatistheleastamountofpoundsthesecondpumpkincouldweighinorderforEthantowintheprize?

a) Writeaninequalitythatmodelsthissituation.Besuretodefineyourvariables.

b) Describeinwordsthequantitiesthatwouldworkinthissituation.

c) Writeyouranswerinbothintervalandsetnotation.

12.TheaverageofAaron’sthreetestscoresmustbeatleast93toearnanAintheclass.Aaronscored89onthefirsttestand94onthesecondtest.WhatscorescanAarongetonhisthirdtesttoguaranteeanAintheclass?(Thehighestpossiblescoreis100.)

a) Writeandsolveaninequalitythatmodelsthissituation.Besuretodefineyourvariables.

b) Describeinwordsthequantitiesthatwouldworkinthissituation.

c) Writeyouranswerinbothintervalandsetnotation.

READY, SET, GO! Name PeriodDate

SECONDARY MATH I // MODULE 4

SOLVING EQUATIONS AND INEQUALITIES – 4.5

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

4.5

13.Acellphonecompanyoffersaplanthatcosts$35.99andincludesunlimitedtexting.Anothercompanyoffersaplanthatcosts$19.99andcharges$0.25pertext.Forwhatnumberoftextsdoesthesecondcompany’splancostmorethanthefirstcompany’splan?

a) Writeandsolveaninequalitythatmodelsthissituation.Besuretodefineyourvariables.

b) Describeinwordsthequantitiesthatwouldworkinthissituation.

c) Writeyouranswerinbothintervalandsetnotation.

GO

Topic:UsesubstitutiontosolvelinearsystemsSolveeachsystemofequationsbyusingsubstitution.

Example: 𝑦 = 𝑥 + 32𝑥 − 𝑦 = 14

Thefirstequationstatesthat𝑦 = 𝑥 + 3.Thatinformationcanbeusedinthesecondequationtofindthevalueofxbyreplacing𝑦with𝑥 + 3.Thesecondequationnowsays𝟐𝒙 − 𝒙 + 𝟑 = 𝟏𝟒.Solvethisnewequationbyfirstdistributingthenegativeover 𝑥 + 3 .Thenewequationwillbe𝟐𝒙 − 𝒙 − 𝟑 = 𝟏𝟒.Combineliketerms.Youwillgettheequivalentequation𝒙 − 𝟑 = 𝟏𝟒.Add3tobothsides.Youshouldget𝒙 = 𝟏𝟕.Butyoustilldon’tknowthevalueofy.Nowthatyouknowthevalueofx,youcanuseeitherequationtofigureoutthevalueof𝑦.Sincethefirstequationissimpler,youmaywanttosubstitutetheknownvalueofx(recallthat𝑥 = 17)intoit.Itshouldbeeasytoseewhatyequals.𝒚 = 𝟏𝟕 + 𝟑 = 𝟐𝟎.

21. 𝑦 = 𝑥 + 52𝑥 + 𝑦 = −1 22.

𝑥 = 𝑦 − 15𝑥 + 2𝑦 = 9

23. 𝑦 = 10 − 𝑥4𝑥 − 2𝑦 = 40 24. 𝑥 = 1 + 𝑦

4𝑥 − 𝑦 = 7