SECONDARY MATH I // MODULE 4 SOLVING EQUATIONS AND INEQUALITIES...
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SECONDARY MATH I // MODULE 4 SOLVING EQUATIONS AND INEQUALITIES – 4.4 Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org 4.4 READY Topic: Write an equation from a context. Interpret notation for inequalities. Write an equation that describes the story. Then answer the question asked by the story. 1. Virginia’s Painting Service charges $10 per job and $0.20 per square foot. If Virginia earned $50 for painting one job, how many square feet did she paint at the job? 2. Renting the ice-skating rink for a party costs $200 plus $4 per person. If the final charge for Dane’s birthday party was $324, how many people attended his birthday party? Indicate if the following statements are true or false. Explain your thinking. 3. The notation 12 < ! means the same thing as ! < 12. It works just like 12 = ! !"# ! = 12. 4. The inequality −2 ! + 10 ≥ 75 says the same thing as −2! − 20 ≥ 75. I can multiply by -2 on the left side without reversing the inequality symbol. 5. When solving the inequality 10! + 22 < 2, the second step should say 10! > −20 because I added -22 to both sides and I got a negative number on the right. 6. When solving the inequality −5! ≥ 45, the answer is ! ≤ −9 because I divided both sides of the inequality by a negative number. 7. The words that describe the inequality ! ≥ 100 are “x is greater than or equal to 100.” SET Topic: Solve inequalities. Verify that given numbers are elements of the solution set. Solve for x. (Show your work.) Indicate if the given value of x is an element of the solution set. 8. 2! − 9 < 3 Is this value part ! = 6; !"#? !"? of the solution set? 9. 4! + 25 > 13 Is this value part ! = −5; !"#? !"? of the solution set? READY, SET, GO! Name Period Date Homework help at www.rsgsupport.org 160
Transcript of SECONDARY MATH I // MODULE 4 SOLVING EQUATIONS AND INEQUALITIES...
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SECONDARY MATH I // MODULE 4
SOLVING EQUATIONS AND INEQUALITIES – 4.4
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
4.4
READY Topic:Writeanequationfromacontext.Interpretnotationforinequalities.Writeanequationthatdescribesthestory.Thenanswerthequestionaskedbythestory.
1.Virginia’sPaintingServicecharges$10perjoband$0.20persquarefoot.IfVirginiaearned$50forpaintingonejob,howmanysquarefeetdidshepaintatthejob?
2.Rentingtheice-skatingrinkforapartycosts$200plus$4perperson.IfthefinalchargeforDane’sbirthdaypartywas$324,howmanypeopleattendedhisbirthdayparty?
Indicateifthefollowingstatementsaretrueorfalse.Explainyourthinking.3.Thenotation12 < ! meansthesamethingas! < 12.Itworksjustlike12 = ! !"# ! = 12.4.Theinequality−2 ! + 10 ≥ 75saysthesamethingas−2! − 20 ≥ 75.Icanmultiplyby-2ontheleftsidewithoutreversingtheinequalitysymbol.
5.Whensolvingtheinequality10! + 22 < 2,thesecondstepshouldsay10! > −20becauseIadded-22tobothsidesandIgotanegativenumberontheright.
6.Whensolvingtheinequality−5! ≥ 45,theansweris! ≤ −9becauseIdividedbothsidesoftheinequalitybyanegativenumber.
7.Thewordsthatdescribetheinequality! ≥ 100are“xisgreaterthanorequalto100.”
SET Topic:Solveinequalities.Verifythatgivennumbersareelementsofthesolutionset.Solveforx.(Showyourwork.)Indicateifthegivenvalueofxisanelementofthesolutionset.
8.2! − 9 < 3
Isthisvaluepart! = 6; !"#? !"?ofthesolutionset?
9.4! + 25 > 13
Isthisvaluepart! = −5; !"#? !"?ofthesolutionset?
READY, SET, GO! Name PeriodDate
Homework help at www.rsgsupport.org 160
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SECONDARY MATH I // MODULE 4
SOLVING EQUATIONS AND INEQUALITIES – 4.4
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
4.4
10.6! − 4 ≤ −28Isthisvaluepart! = −10; !"#? !"?ofthesolutionset?
11.3! − 5 ≥ −5Isthisvaluepart! = 1; !"#? !"?ofthesolutionset?
Solveeachinequalityandgraphthesolutiononthenumberline.
12.! + 9 ≤ 7
13.−3! − 4 > 2
14.3! < −6
15.!! > −!!"
16.−10! > 150
17. ! !! ≥ −5
Solveeachmulti-stepinequality.
18.! − 5 > 2! + 3 19.!(!!!)!" ≤!!!
20.2 ! − 3 ≤ 3! − 2
–10 –5 5 100
–10 –5 5 100
–10 –5 5 100
–10 –5 5 100
–25 –20 –15 –10 –5 0
10 20 30 400
Homework help at www.rsgsupport.org 161
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SECONDARY MATH I // MODULE 4
SOLVING EQUATIONS AND INEQUALITIES – 4.4
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
4.4
GO
Topic:Usesubstitutiontosolvelinearsystems
Solveeachsystemofequationsbyusingsubstitution.
Example: ! = 122! − ! = 14
Thefirstequationstatesthat! = 12.Thatinformationcanbeusedinthesecondequationtofindthevalueofxbyreplacingywith12.Thesecondequationnowsays!" − !" = !".Solvethisnewequationbyadding12tobothsidesandthendividingby2.Theresultisx=13.
21. ! = 5−! + ! = 1 22.! = 8
5! + 2! = 0
23.2! = 10
4! − 2! = 50 24.3! = 124! − ! = 5
25. ! = 2! − 5! = ! + 8 26.3! = 9
5! + ! = −5
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