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SECONDARY MATH I // MODULE 4
EQUATIONS AND INEQUALITIES – 4.3
4. 3 Solving Equations Literally
A Practice Understanding Task
Solveeachofthefollowingequationsforx:
1.
3x + 2
=7
5
2.
3x + 2y
=7
5
3.
4x
− 5 = 11
3
4.
4x
− 5y = 11
3
5.
2
(x + 3) = 6
5
6.
2
(x + y) = 6
5
7.
2(3x + 4) = 4 x + 12
8.
2(3x + 4 y) = 4 x + 12y
Writeaverbaldescriptionforeachstepoftheequationsolvingprocessusedtosolvethefollowing
equationsforx.Yourdescriptionshouldincludestatementsabouthowyouknowwhattodonext.
Forexample,youmightwrite,“FirstI__________________,because_______________________...”
9.
ax + b
−d=e
c
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10.
r⋅
mx
+s=t
n
SECONDARY MATH I // MODULE 4
EQUATIONS AND INEQUALITIES – 4.3
4. 3 Solving Equations Literally – Teacher Notes
A Practice Understanding Task
Purpose:Thistaskprovidespracticeforsolvinglinearequationsinonevariable,solvinglinear
equationsintwovariablesforoneofitsvariables,andsolvingliteralequations.Theprocessfor
solvingmultivariableequationsforoneofitsvariablesbecomesmoreapparentwhenjuxtaposed
withsimilarly-formattedequationsinonevariable.Theonlydifferenceinthesolutionprocessis
theabilitytocarryoutnumericalcomputationstosimplifytheexpressionsintheone-variable
equations.
CoreStandardsFocus:
A.REI.1Explaineachstepinsolvingasimpleequationasfollowingfromtheequalityofnumbers
assertedatthepreviousstep,startingfromtheassumptionthattheoriginalequationhasasolution.
Constructaviableargumenttojustifyasolutionmethod.
A.REI.3Solvelinearequationsandinequalitiesinonevariable,includingequationswith
coefficientsrepresentedbyletters.
RelatedStandards:
StandardsforMathematicalPracticeofFocusintheTask:
SMP7–Lookandmakeuseofstructure
SMP8-Lookforandexpressregularityinrepeatedreasoning
AdditionalResourcesforTeachers:
Ananswerkeyforthequestionsinthetaskcanbefoundasaseparatepageattheendofthese
teachernotes.Itisrecommendedthatyouworkthroughthetaskyourselfbeforeconsultingthe
answerkeytodevelopabettersenseofhowyourstudentsmightengageinthetask.
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SECONDARY MATH I // MODULE 4
EQUATIONS AND INEQUALITIES – 4.3
TheTeachingCycle:
Launch(WholeClass):
Encouragestudentstonotethesimilaritiesintheirworkonthepairsofproblemsinquestions1-8.
Alsopointoutthattheyaretowritedetailedexplanationsoftheirsolutionstrategyonproblems9
and10.Onewaytofacilitatethiswouldbetohavestudentsfoldapieceofpaperinhalflengthwise.
Ontheleftsideofthepapertheywriteouttheiralgebrasteps,andontherightsidetheywriteout
theirjustifications.
Explore(SmallGroup):
Monitorstudentswhileworkingontheseproblemsandofferappropriatefeedback,asnecessary.
Someoftheproblemshavealternativestrategies,suchas#5whereyoucandistributethe2/5first,
ormultiplybothsidesoftheequationsby5/2first.
Helpstudentsrecognizethedifferencebetweenchangingtheformofanexpressionononesideof
anequation,vs.writinganequivalentequationbyapplyingthesameoperationtobothsides.
Ifstudentsarehavingdifficultieswith#9or#10,havethemwritearelatedequationinwhichthey
replaceallletterswithnumbersexceptforthex.Seeiftheycansolvetherelatedequationforxand
ifthatworkcanhelpthemsolvetheoriginalliteralequation.Problem10involvesasquarerootin
ordertoemphasizethatoneofthekeyissuesinsolvinganequationisto“un-do”anoperationby
applyingtheinverseoperationtobothsides.Helpstudentsthinkabouthowthatwouldplayoutin
problem10.Thatis,howmightthey“un-do”asquareroot?
Discuss(WholeClass):
Havestudentspresenttheirsolutionprocessforanyproblemsthatmayhavebeendifficultfora
numberofstudents.Youmightalsowanttohavestudentscritiqueeachother’sexplanationson
problems9and10byhavingstudentsexchangepapers.Theyshouldfoldtheirpartner’spaperin
half,sothatonlytherightsidewiththewrittenexplanationisshowing.Onaseparatesheetof
papertheyshouldwrite-outthealgebrastepstheywouldtaketosolveeachproblem,basedonlyon
thewordingoftheirpartners’explanation.Theyshoulddiscussanyexplanationsthatareunclear
withtheirpartner.
AlignedReady,Set,Go:EquationsandInequalities4.3
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SECONDARY MATH I // MODULE 4
4.3
SOLVING EQUATIONS AND INEQUALITIES – 4.3
READY, SET, GO!
Name
PeriodDate
READY
Topic:SolvingInequalities.
Usetheinequality−9 < 2tocompleteeachrowinthetable.
Applyeachoperationtotheoriginal
Result
Istheresulting
inequality−9 < 2
inequalitytrueorfalse?
Example:Add3tobothsides
-9+3<2+3→-6<5
True
1.Subtract7frombothsides.
2.Add15tobothsides.
3.Add-10tobothsides.
4.Multiplybothsidesby10.
5.Dividebothsidesby5.
6.Multiplybothsidesby-6.
7.Dividebothsidesby-3.
8.Whatoperationswhenperformedonaninequality,reversetheinequality?
(Beveryspecific!)
SET
Topic:Solveliteralequationsthatrequiremorethanonestep.
Solvefortheindicatedvariable.Showyourwork!!!
9.Solveforh.
! = 25!ℎ
10.Solveforh.
! = !! ! ℎ
11.Solveform.! = 7! + 6
12.Solveform.! = !" + !
13.Solveforz. ! = ! + 7 3
14.Solveforz. ! = ! + 7 !
15.Solveforx.
!!!
!
!!!!
= 4
16.Solveforx.
− 9 = 6
18.Solveforx.
!!
20.Solveforx.
!
!
= 4
!!
17.Solveforx.
!
!
− 9! = 6
19.Solveforx.
!
!
! − 2 = 12
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!
! − 2! = 12
12
SECONDARY MATH I // MODULE 4
4.3
SOLVING EQUATIONS AND INEQUALITIES – 4.3
GO
Topic:Identifyingx-interceptsandy-intercepts
Locatethex-interceptandy-interceptinthetable.Writeeachasanorderedpair.
21.
22.
23.
!
!
!
!
!
!
-4
12
0
-6
-3
10
-3
10
3
-5
-2
8
-2
8
6
-4
-1
6
-1
6
9
-3
0
4
0
4
12
-2
1
2
1
2
15
-1
2
0
2
0
18
0
3
-2
x–intercept:
x–intercept:
x–intercept:
y–intercept:
y–intercept:
y–intercept:
Locatethex-interceptandthey-interceptinthegraph.Writeeachasanorderedpair.
24.
25.
x–intercept:
x–intercept:
y–intercept:
y–intercept:
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SECONDARY MATH I // MODULE 4
4.3
SOLVING EQUATIONS AND INEQUALITIES – 4.3
Solveeachequationforx.Providethejustificationsforeachstep.Seethefirstexampleasa
reminderforthetypesofjustificationsthatmightbeused.
Example:
26.
4x–10=2
Justification
3x–6=15
Justification
+6+6
AdditionProperty
ofequality
3x=21
DivisionProperty
33
ofequality
x=7
27.
28.
–16=3x+11
Justification
6–2x=10
Justification
29.
6x+3=x+18
30.
Justification
3x–10=2x+12
Justification
31.
32.
X(B+7)=9
Justification
12x+3y=15
Justification
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