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. ! > 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
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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: ! = ! + 32! − ! = 14
Thefirstequationstatesthat! = ! + 3.Thatinformationcanbeusedinthesecondequationtofindthevalueofxbyreplacing!with! + 3.Thesecondequationnowsays!" − ! + ! = !".Solvethisnewequationbyfirstdistributingthenegativeover ! + 3 .Thenewequationwillbe!" − ! − ! = !".Combineliketerms.Youwillgettheequivalentequation! − ! = !".Add3tobothsides.Youshouldget! = !".Butyoustilldon’tknowthevalueofy.Nowthatyouknowthevalueofx,youcanuseeitherequationtofigureoutthevalueof!.Sincethefirstequationissimpler,youmaywanttosubstitutetheknownvalueofx(recallthat! = 17)intoit.Itshouldbeeasytoseewhatyequals.! = !" + ! = !!.
21. ! = ! + 52! + ! = −1 22.
! = ! − 15! + 2! = 9
23. ! = 10 − !4! − 2! = 40 24. ! = 1 + !
4! − ! = 7
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