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SECONDARY MATH I // MODULE 4
SOLVING EQUATIONS AND INEQUALITIES - 4.6
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
4.6
READY
Topic:Solvingequationsandinequalitiesfromacontext.
Writethegivensituationasanequationorinequalityandthensolveit.1. Thelocalamusementparksellssummermembershipsfor$50each.Normaladmissiontothe
parkcosts$25;admissionformemberscosts$15.
a.IfDarrenwantstospendnomorethan$100ontripstotheamusementparkthissummer,
howmanyvisitscanhemakeifhebuysamembershipwithpartofthatmoney?
b.Howmanyvisitscanhemakeifhepaysnormaladmissioninstead?
c.Ifheincreaseshisbudgetto$160,howmanyvisitscanhemakeasamember?
d.Howmanycanhemakeasanon-memberwiththeincreasedbudgetof$160?
2. Jadejusttookamathtestwith20questions,eachquestionisworthanequalnumberofpoints.
Thetestisworth100pointstotal.
a.WriteanequationthatcanbeusedtocalculateJade’sscorebasedonthenumberof
questionsshegotrightonthetest.
b.Ifascoreof70pointsearnsagradeofC-,howmanyquestionswouldJadeneedtogetrighttogetatleastaC-onthetest?
c.Ifascoreof83pointsearnsagradeofB,howmanyquestionswouldJadeneedtogetrighttogetatleastaBonthetest?
d.SupposeJadegotascoreof60%andthenwasallowedtoretakethetest.Ontheretake,she
gotallthequestionsrightthatshegotrightthefirsttime,andalsogothalfthequestions
rightthatshegotwrongthefirsttime.WhatpercentofthequestionsdidJadegetright,in
total,ontheretake?
READY, SET, GO! Name PeriodDate
Homework help at www.rsgsupport.org 171
SECONDARY MATH I // MODULE 4
SOLVING EQUATIONS AND INEQUALITIES - 4.6
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
4.6
SET Topic:Solveandjustifyonevariableinequalities
Solveeachinequality,justifyingeachstepyouuse.
3.
−5! < 35 Justification
4.
! + 68 ≥ 75 Justification
5.
2! − 4 ≤ 10 Justification
6.
5 − 4! ≤ 17 Justification
7.!−3 > − 109
Justification
8.
2 ! − 3 ≤ 3! − 2 Justification
Homework help at www.rsgsupport.org 172
SECONDARY MATH I // MODULE 4
SOLVING EQUATIONS AND INEQUALITIES - 4.6
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
4.6
Solveeachinequalityandgraphthesolutiononthenumberline.9.x–8>-20
10.x+11>13
Solveeachmulti-stepinequality.11.4x+3<-1
12.4 − 6! ≤ 2(2! + 3)
13.5 4! + 3 ≥ 9 ! − 2 − ! 14.!! ! −
!! 4! − 1 ≥ ! + 2(! − 3)
Topic:Solveliteralequations
15. SolvethefollowingequationforC:! = !!! + 32
16. Given! = !!!!
!ℎ,rewritetheformulatoisolatethevariabler.
17. Theareaformulaofaregularpolygonis! = !!!".ThevariablearepresentstheapothemandP
representstheperimeterofthepolygon.Solvetheequationfortheapothem,a.
–10 –5 5 100
–10 –5 5 100
Homework help at www.rsgsupport.org 173
SECONDARY MATH I // MODULE 4
SOLVING EQUATIONS AND INEQUALITIES - 4.6
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
4.6
18. Theequation! = !" + !istheequationofaline.Isolatethevariableb.
19.Theequationforthecircumferencecofacirclewithradiusris! = 2!". Solvetheequationfortheradius,r.
20.TheequationfortheareaofacircleAbasedondiameterdis! = ! !!! .
Solvetheequationtoisolatethediameter,d.
GO
Topic:Solvesystemsofequationsbygraphing
Graphbothlinesonthesamecoordinategrid.Identifythepointofintersection.Thentestthexandyvaluesofthepointofintersectioninthetwoequations.
21.! = 2! + 5−! + ! = 1 22.
10 + ! = 3!2! + ! = 0 23.
! + ! = 9! − ! = −7
-10
-10
10
10
-10
-10
10
10
-10
-10
10
10
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