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s to Equations and InequalitiesStudy GuideSOLUTIONS TO nWords:theequation𝑥 ! 16 hassolutionsof4 and 4.Or,𝑥 ! 16isatruestatementwhen𝑥 4 or 𝑥 4.GraphicallyonaNumberline:- ‐5- ‐4- ‐3- ‐2- hataretobeincludedintheset.UsingSetnotation:4, 4isthesetcontaining4 and iable symbol number type descriptionExample:𝑥 𝑟𝑒𝑎𝑙 𝑥 erticalbarmeans“suchthat ”Thenulloremptysetisdenotedbyanyofthefollowing: or(For more information on this, especially set notation, please refer to Lesson 85or pages s.54-s.69 from the Algebra 1 Module 1 workbook you yGuide
Name:ANSWERKEYMath7.2,PeriodMr.RogoveDate:STEPS USED IN SOLVING able.***You are trying to find out the values for the variable that make theequation nordertomaintainequality.Examples: Theequation𝑥 1 𝑥 6 3𝑥 34willhavethesamesolutionsetastheequation𝑥 1 𝑥 6 12 3𝑥 22becauseofthesubtractionpropertyofequality. Theequation3𝑥 4 𝑥 19 4𝑥 23willhavethesamesolutionsetastheequation2 3𝑥 4 𝑥 19 8𝑥 ple:Non- ‐example:3 𝑥 13 3𝑥 39𝟒 𝟑𝒙𝒚 𝟏𝟐 𝟒𝒙 er.Example:(addition)Example:(multiplication)3𝑥 4𝑦 𝑥 3𝑥 𝑥 4𝑦4𝑐 3𝑑 4 3 𝑐 g.Example:(addition)Example:(multiplication)3𝑥 5 12 3𝑥 (5 12)𝑎 𝑏 𝑐 (𝑎 𝑏) 𝑐(For more information on this, please refer to Lesson 86or pages s.70-s.82 from the Algebra 1 Module 1 workbook you yGuide
Name:ANSWERKEYMath7.2,PeriodMr.RogoveDate:SOLVING uality.***When finding solutions for inequalities, if you multiply or divide by anegative number, you reverse the inequality sign.Example: 3𝑥 15𝑥 dgraphicallyonanumberline.Example:𝑥 2- ‐5- ‐4- ‐3- ‐2- eplane.Example:𝑦 𝑥 ncommon.𝑦 𝑥 2Example:2𝑥 𝑦 4(For more information on this, please refer to Lessons 87 - 91 or pages s.83-104and s.137-s.150 from the Algebra 1 Module 1 workbook you yGuide
Name:ANSWERKEYMath7.2,PeriodMr.RogoveDate:SOLVING MORE COMPLICATED EQUATIONSTheZeroProductProperty:If𝑎𝑏 0,theneither𝑎 0 or 𝑏 0 or 𝑎 𝑏 0.Examples:𝑥 3 2𝑥 8 0Either𝑥 3 0 𝑜𝑟 2𝑥 8 � 12 4𝑥 3Thesolutionsetforthisequationwouldbe𝑥 𝑟𝑒𝑎𝑙 𝑥 3}(For more information on this, please refer to Lessons 92 and 93 or pages s.105s.115 from the Algebra 1 Module 1 workbook you yGuide
Name:ANSWERKEYMath7.2,PeriodMr.RogoveDate:PROBLEM Hstepandprovideananswerinsetnotation. 9 3𝑥 2 15 32𝑎 6𝑥 9𝑥 5𝑏 27𝑥 18 15 3DistributiveProperty2𝑎 6𝑥 2𝑎 9𝑥 SubtractionPropertyCollectliketerms5𝑏 2𝑎ofequality 27𝑥 33 3 27𝑥 33 33 3 33 27𝑥 361 27𝑥271 (36)274𝑥 36𝑥 9𝑥 5𝑏 ectliketerms6𝑥 9𝑥 9𝑥 5𝑏 SubtractionProperty2𝑎 9𝑥ofequalityPropofequalityformultiplication 3𝑥 5𝑏 2𝑎Collectliketerms 3𝑥 5𝑏 2𝑎 3 3DivisionPropertyof𝑥 Simplify5𝑏 2𝑎3equalitySimplify5 2𝑥 4 11 4 3𝑥2 7 4𝑥 1810𝑥 20 11 4DistributiveProperty14 8𝑥 18 3𝑥10𝑥 31 4 3𝑥CollectliketermsDistributiveProperty14 8𝑥 14 Subtractionpropof 18 14inequality10𝑥 31 3𝑥Propertyofequality 8𝑥 32Collectliketerms 4 3𝑥 3𝑥forsubtraction 8𝑥 32 8 8Divisionpropertyof7𝑥 31 47𝑥 31 31 4CollectliketermsPropertyofequality 31foradditioninequality(switchinequalitysigns)𝑥 4Simplify7𝑥 35Collectliketerms7𝑥 35 77Propertyofequality𝑥 lities:StudyGuide
nthesensibilitiesofperformingtheparticularmove :𝑥 122𝑥 3 𝑥 5 7 2𝑥 3 12 .𝑥 ! 1442𝑥 3 7𝑥 35 12 981Equalityisnotmaintained lutionsetbecame2𝑥 3 𝑥 5 7 12{4, thelinearoriginalequation.term𝑥 5,weaddit.Equation:Equation:32𝑥 4 3𝑥 2𝑥 2 3𝑥 143Move:Add𝑥 2tobothsides.Move:Multiplybothsidesby12.2𝑥 6 5𝑥 49 𝑥 2 8(3𝑥 ctionis2𝑥 6 4𝑥 anhavemaintainedequality thiswasequationlikethis.obviouslyatypo ionsandInequalities:StudyGuide
aph,andanswerthequestionsbelow.𝐿𝑒𝑡 𝑥 𝑒𝑙𝑙𝑖𝑝𝑡𝑖𝑐𝑎𝑙 𝑎𝑛𝑑𝐿𝑒𝑡 𝑦 𝑏𝑖𝑘𝑒 𝑚𝑎𝑐ℎ𝑖𝑛𝑒500𝑥 400𝑦 2000𝑦 esheshouldgettocoverherfloor.𝐿𝑒𝑡 𝑥 𝑝𝑢𝑟𝑝𝑙𝑒 𝑡𝑖𝑙𝑒𝑠 𝑎𝑛𝑑𝐿𝑒𝑡 𝑦 𝑏𝑙𝑢𝑒 𝑡𝑖𝑙𝑒𝑠𝑥 𝑦 10020𝑥 30𝑦 dyGuide
hequationbelowforxandanswerthequestions.𝑥 3 2𝑥 5 𝑥 3 (𝑥 7)𝑥 ! 36 7(𝑥 6)𝑥 3 2𝑥 5 𝑥 3 𝑥 7 0𝑥 32𝑥 5 𝑥 7 0𝑥 3 𝑥 12 0𝑥 3 0 𝑜𝑟 (𝑥 12) 0𝑥 3 𝑜𝑟 𝑥 12{3, nby𝑥 hat 3couldbeananswer.Createyourownequationthathas 2 and 5asitsonlysolutions.Answerswillvary butIsuspectmanywillsaythefollowing:𝑥 2 𝑥 5 0(𝑥 6)(𝑥 6) 7(𝑥 6)𝑥 6 𝑥 6 7 𝑥 6 0𝑥 6𝑥 6 7 0𝑥 6 𝑥 13 0𝑥 6 0 𝑜𝑟 𝑥 13 0𝑥 6 𝑜𝑟 𝑥 13{ 6, equation?Iwouldnotdivideby(𝑥 ficallythat nches.Writethewidthoftherectangleas15 𝑥inches.Whatistheexpressionforthelength?15 𝑥Whatistheexpressionforitsarea?(15 𝑥)(15 lue?when 𝑥 toEquationsandInequalities:StudyGuide
or pages s.70-s.82 from the Algebra 1 Module 1 workbook you received) & Name: . 5 2 ! 411 3 & & 10! 20 11 4 3!& Distributive&Property& 10! 31 4 3!& Collect&like&terms& 10! 31 3!& . Study Guide
