solving equations and inequalities – 4 · pdf file12/4/2016 · secondary math...

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: Interpret phrases that imply an inequality. Rewrite the given “word sentence” as a “math sentence.” Each math sentence will use one of the following symbols: >, <, ≤, ≥. Use “x” in place of the number. Word Sentence Math Sentence Example: I am thinking of a number that is greater than 13. ! > 13 1. I am thinking of a number that is at least 13. 2. I am thinking of a number that is no fewer than 13. 3. I am thinking of a number that does not exceed 13. 4. I am thinking of a number that is at most 13. 5. I am thinking of a number that is no more than 13. 6. I am thinking of a number that is fewer than 13. 7. I am thinking of a number that is not above 13. 8. I am thinking of a number that is less than 13. 9. I am thinking of a number that is not under 13. 10. I am thinking of a number that is not greater than 13. SET Topic: Write and solve inequalities from a context. 11. To take sweepstakes for the largest pumpkin crop at the Riverside County Fair, the average weight of Ethan’s two pumpkins must be greater than 875 lbs. One of his pumpkins weighs 903 lbs. What is the least amount of pounds the second pumpkin could weigh in order for Ethan to win the prize? a) Write an inequality that models this situation. Be sure to define your variables. b) Describe in words the quantities that would work in this situation. c) Write your answer in both interval and set notation. 12. The average of Aaron’s three test scores must be at least 93 to earn an A in the class. Aaron scored 89 on the first test and 94 on the second test. What scores can Aaron get on his third test to guarantee an A in the class? (The highest possible score is 100.) a) Write and solve an inequality that models this situation. Be sure to define your variables. b) Describe in words the quantities that would work in this situation. c) Write your answer in both interval and set notation. READY, SET, GO! Name Period Date 22

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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

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

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.

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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