Study Guide: Solving Linear Equations - Mr. Rogove's Site...
Transcript of Study Guide: Solving Linear Equations - Mr. Rogove's Site...
NAME:___________________________ Math7.2,Period____________
Mr.Rogove Date:__________
SolvingLinearEquationsStudyGuide1
Study Guide: Solving Linear Equations
Writing Equations
Whenreadingwordproblemsandtryingtocreateanequationusingsymbols,itisextremelyimportanttobeginbydefiningyourvariable.Example:YourfamilyistakingaroadtriptoChicago.Theydrive450milesonthefirstday,!
!oftheentiredistanceonthesecondday,!
!onthethirdday,andfinally
drivethefinal325milesonthefourthday.Letdbethedistanceoftheentiretripinmiles.Trytobreakmorecomplicatedwordsentencesdownintomoremanageablepieces.Example:Whenanumberistakenawayfrom57,whatremainsisfourmorethan5timesthenumber.Letxbethenumber.“Whenanumberistakenawayfrom57”à57− 𝑥“Whatremainsis”à=“Fourmorethan5timesthenumberà5𝑥 + 4
Solving Linear Equations LinearExpressionscontainconstants,variablesraisedtothefirstpower,orvariables(raisedtothefirstpower)multipliedbycoefficients.
Examples:12
−3𝑥
14 𝑥 − 2
32+ 21𝑥
Non-Examples:3𝑥!
14𝑥! + 19
𝑥! − 1
(𝑥 + 3)(𝑥 − 2)
WHENSOLVINGLINEAREQUATIONS,YOURULTIMATEGOALISTOISOLATETHEVARIABLE,
ALSOCALLEDSOLVINGFORX.
CHECKINGYOURSOLUTIONISAPARTOFSOLVINGTHELINEAREQUATION!!
NAME:___________________________ Math7.2,Period____________
Mr.Rogove Date:__________
SolvingLinearEquationsStudyGuide2
Inordertokeepyourequationinbalance,usethefollowingpropertiesofequality
Addition Property of Equality If 𝐴 = 𝐵, then 𝐴 + 𝐶 = 𝐵 + 𝐶
Subtraction Property of Equality If 𝐴 = 𝐵, then 𝐴 − 𝐶 = 𝐵 − 𝐶
Multiplication Property of Equality If 𝐴 = 𝐵, then 𝐴 × 𝐶 = 𝐵 × 𝐶
Division Property of Equality If 𝐴 = 𝐵 𝑎𝑛𝑑 𝐶 ≠ 0 , then
𝐴𝐶 =
𝐵𝐶
Different Moves to Make When Solving Equations
Whensolvingequationsyoumighthavetodooneormoreofthefollowingmoves:CombineLikeTermsbeforeyourusepropertiesofequality.Example:3𝑥 + 4− 5𝑥 + 13 = 26à−2𝑥 + 17 = 26Gatherallvariabletermsononesideoftheequationbeforeusingpropertiesofequalitytoisolateyourvariable.Example:3𝑥 − 23+ 4𝑥 = 24+ !
!𝑥 − 21à7𝑥 − !
!𝑥 − 23 = 24− 21
Usethedistributivepropertytoclearparenthesespriortousingpropertiesofequality.Example:43𝑥 − 3 21+ 12𝑥 = 3− 4𝑥 − 5 à43𝑥 − 63− 36𝑥 = 3− 4𝑥 + 5UseRulesofProportionstocreatelinearequationswhenyourequationscontainapairoffractions.Example: !!!!
!"!!!!= !
!à7 3𝑥 − 4 = 5 13𝑥 + !
!
Classifying Solutions to Linear Equations
OneSolution NoSolution InfinitelyMany
SolutionsExample:
7𝑥 − 3 = 5𝑥 + 5
Example:7𝑥 − 3 = 7𝑥 + 5
Example:7𝑥 − 3 = −3+ 7𝑥
-Differentcoefficients-Sameordifferentconstantterms(Ifthesameconstantterm,then𝑥 = 0)
-Samecoefficients-Differentconstantterms
-Samecoefficients-Sameconstantterms
NAME:___________________________ Math7.2,Period____________
Mr.Rogove Date:__________
SolvingLinearEquationsStudyGuide3
The Problem Set
Completethisproblemsetbeforeyoutakethetest!Ifyouarestuckorhavespecificquestionsaboutanyoftheseproblems,comefindmebeforethetestsowecanaddressyourconcerns.Writeanequationforeachwordproblemandanswerthequestion.Shannon’sgoalistorun40mileseachweek.Thisweek,shehasalreadyrundistancesof5.3miles,6.5miles,and6.2miles.Ifshewantstospreadouttheremainingmilesevenlyoverthenextfourdays,howmanymilesperdaydoessheneedtoruneachday?Writeanequationandsolve.
TheYchargesa$44signupfeeand$30/monthforanindividualgymmembership.CitySportsFitnesschargesa$99signupfeeandcharges$25/monthformembership.Writeanequationthatwillhelpyoudeterminehowmanymonthsitwilltakeforthetotalcostofmembershiptobethesame?Howmanymonthswillittake?
Twoverticalanglesaredescribedasfollows:oneoftheanglesisfourtimesthequantityofanumberaddedtothree,andtheotherangleis6lessthanthirteentimesthatsamenumber.Whatarethemeasuresofbothangles?
Oneacuteangleofarighttriangleisninelessthantwotimesthemeasureoftheotheracuteangle.Thethirdangleistherightangle.Drawthetriangleandfindtheanglemeasures.
NAME:___________________________ Math7.2,Period____________
Mr.Rogove Date:__________
SolvingLinearEquationsStudyGuide4
Solveeachequationandcheckyourwork.
−3 4𝑥 − 8 − 1 = 𝑥 + 3 𝑥 + 9
6 𝑥 − 11 − 3 11− 𝑥 = 11 𝑥 + 7
223 𝑥 + 2− 𝑥 = 9 𝑥 + 1 +
53 𝑥
2𝑥 − 3− 9𝑥 = 14+ 𝑥 − 1
NAME:___________________________ Math7.2,Period____________
Mr.Rogove Date:__________
SolvingLinearEquationsStudyGuide5
Solveeachequation.Noneedtocheckyourwork.
− −3+ 13𝑥 − 5𝑥 = 623 𝑥 −
25
165𝑥 − 12 +
233 − 5𝑥 = −4 − (𝑥 + 12)
−5 − 4 − 3𝑥 + 7𝑥 =58
16𝑥 − 20 + 4𝑥
23 12−
92 𝑥 =
3492−
32 𝑥
NAME:___________________________ Math7.2,Period____________
Mr.Rogove Date:__________
SolvingLinearEquationsStudyGuide6
Solveeachequation.Noneedtocheckyourwork.
2𝑥 − 346 =
3− 2𝑥10
5𝑥 − 33− 2𝑥 =
611
Pleaseclassifyeachsolutionashavingoneuniquesolution,nosolution,orinfinitelymanysolutions.Youshouldsimplifytheexpressions,butthereisnoneedtosolvetheequations.
9𝑥 + 12− 3𝑥 ÷ 3 = 2(2+ 𝑥)
3 4𝑥 − 1 − 13𝑥 = −(𝑥 + 3)
4 2𝑥 − 3 = 3 3𝑥 − 3 − 3
14 3+ 72𝑥 = 6 3𝑥 +
14