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Lesson 2.1Skills PracticeNameDateThe Plane!Modeling Linear Situations2VocabularyDefine each term in your own words.1. first differencesFirst differences are the differences between successive data points.2. solutionThe solution of a linear equation is any value that makes an open sentence true.3. intersection pointThe intersection point is the point on the graph where one line crosses another.Problem SetIdentify the independent and dependent quantities in each problem situation. Then write a function torepresent the problem situation.1. Nathan is riding his scooter to school at a rate of 6 miles per hour.The distance Nathan travels depends on the time. Distance, D, is the dependent quantity andtime, t, is the independent quantity. 2012 Carnegie LearningD(t) 5 6t2. Sophia is walking to the mall at a rate of 3 miles per hour.The distance Sophia travels depends on the time. Distance, D, is the dependent quantity and time,t, is the independent quantity.D(t) 5 3t3. Mario is stuffing envelopes with invitations to the school’s Spring Carnival. He stuffs 5 envelopeseach minute.The total number of envelopes Mario stuffs depends on the time. The total number of envelopes,E, is the dependent quantity and time, t, is the independent quantity.E(t) 5 5tChapter 2 Skills Practice8069 Skills Ch02.indd 2812814/23/12 11:56 AM

Lesson 2.1Skills Practicepage 24. Shanise plays on the varsity soccer team. She averages 4 goals per game.The total number of goals Shanise scores depends on the number of games she plays. The totalnumber of goals scored, S, is the dependent quantity and the number of games played, g, is theindependent quantity.S(g) 5 4g25. The football booster club sells hot chocolate during the varsity football games. Each cup of hotchocolate costs 2.The amount of money the booster club earns depends on the number of cups sold. The amount ofmoney, M, is the dependent quantity and the number of cups sold, c, is the independent quantity.M(c) 5 2c6. The basketball booster club sells t-shirts at the varsity basketball games. Each t-shirt costs 12.The amount of money the booster club earns depends on the number of t-shirts sold.The amount of money, M, is the dependent quantity and the number of t-shirts sold, t, is theindependent quantity.M(t) 5 12tUse each scenario to complete the table of values and calculate the unit rate of change.7. Miguel is riding his bike to lacrosse practice at a rate of 7 miles per hour.Dependent 53.5171.510.5214Expression282Chapter 28069 Skills Ch02.indd 282(0.5, 3.5) and (1, 7)  7 2 3.5  5  3.5  1 2 0.5 0.55  7  1The unit rate of change is 7. 2012 Carnegie LearningIndependent QuantitySkills Practice4/23/12 11:56 AM

Lesson 2.1Skills Practicepage 3NameDate8. Jada is walking to school at a rate of 2 miles per hour.Independent QuantityDependent 0.50.51121.252.51.53Expression2(0.25, 0.5) and (0.5, 1)   1 2 0.5   5  0.5   0.5 2 0.25 0.255  2  1The unit rate of change is 2.9. Noah is stuffing envelopes with invitations to the school’s Harvest Festival. He stuffs 4 envelopeseach minute. 2012 Carnegie LearningQuantityUnitsExpressionIndependent QuantityDependent QuantityTimeNumber of , 20) and (10, 40)  40 2 20  5  20  510 2 545     1The unit rate of change is 4.Chapter 2 Skills Practice8069 Skills Ch02.indd 2832834/23/12 11:56 AM

Lesson 2.1Skills Practicepage 410. Terell plays on the varsity basketball team. He averages 12 points per game.Quantity2UnitsIndependent QuantityDependent QuantityNumber of games playedTotal number of ion(3, 36) and (5, 60) 5  24   60 2 365232125     1The unit rate of change is 12.11. The volleyball boosters sell bags of popcorn during the varsity matches to raise money for newuniforms. Each bag of popcorn costs 3.Dependent QuantityNumber of bags ofpopcorn soldAmount of money sion284Chapter 28069 Skills Ch02.indd 284(5, 15) and (10, 30)  30 2 15  5  15510 2 5 5  3  1The unit rate of change is 3. 2012 Carnegie LearningQuantityIndependent QuantitySkills Practice4/23/12 11:56 AM

Lesson 2.1Skills Practicepage 5NameDate12. The football boosters sell hooded sweatshirts to raise money for new equipment. Each sweatshirtcosts 18.QuantityIndependent QuantityDependent QuantityNumber of sweatshirtssoldAmount of money 0UnitsExpression2(5, 90) and (10, 180) 5  90   180 2 90510 2 5185     1The unit rate of change is 18.Identify the input value, the output value, and the rate of change for each function.13. Belinda is making greeting cards. She makes 4 cards per hour. The function C(t) 5 4t represents thetotal number of cards Belinda makes as a function of time.The input value is t. 2012 Carnegie LearningThe output value is 4t.The rate of change is 4.14. Owen is riding his bike to his friend’s house at a rate of 6 miles per hour. The function D(t) 5 6trepresents the distance Owen rides as a function of time.The input value is t.The output value is 6t.The rate of change is 6.Chapter 2 Skills Practice8069 Skills Ch02.indd 2852854/23/12 11:56 AM

Lesson 2.1Skills Practicepage 615. Rochelle is shopping for earrings. Each pair of earrings costs 15 dollars. The functionC(e) 5 15e represents the total cost of the earrings as a function of the number of pairsof earrings Rochelle buys.The input value is e.The output value is 15e.2The rate of change is 15.16. Lavon is driving to visit a college campus. He is traveling 65 miles per hour. The functionD(t) 5 65t represents the total distance he travels as a function of time.The input value is t.The output value is 65t.The rate of change is 65.17. Kiana is selling coupon books to raise money for her school. Each coupon book cost 35. Thefunction M(b) 5 35b represents the total amount of money raised as a function of the numberof coupon books sold.The input value is b.The output value is 35b.The rate of change is 35.The input value is m.The output value is 16m.The rate of change is 16.286Chapter 28069 Skills Ch02.indd 286 2012 Carnegie Learning18. Cisco mows lawns in his neighborhood to earn money. He earns 16 for each lawn. The functionA(m) 5 16m represents the total amount of money earned as a function of the number oflawns mowed.Skills Practice4/23/12 11:56 AM

Lesson 2.1Skills PracticeNamepage 7DateSolve each function for the given input value. The function A(t) 7t represents the total amount of moneyin dollars Carmen earns babysitting as a function of time in hours.219. A(3) 5A(3) 5 7(3)5 21Carmen earns 21 when she babysits for 3 hours.20. A(2) 5A(2) 5 7(2)5 14Carmen earns 14 when she babysits for 2 hours.21. A(5) 5A(5) 5 7(5)5 35Carmen earns 35 when she babysits for 5 hours.22. A(4.5) 5A(4.5) 5 7(4.5)5 31.5Carmen earns 31.50 when she babysits for 4.5 hours.23. A(3.5) 5 2012 Carnegie LearningA(3.5) 5 7(3.5)5 24.5Carmen earns 24.50 when she babysits for 3.5 hours.24. A(6) 5A(6) 5 7(6)5 42Carmen earns 42 when she babysits for 6 hours.Chapter 2 Skills Practice8069 Skills Ch02.indd 2872874/23/12 11:56 AM

Lesson 2.1Skills Practicepage 8Use the graph to determine the input value for each given output value. The function D(t) 5 40t representsthe total distance traveled in miles as a function of time in hours.y2D(t) 5 400360Distance (miles)320D(t) 5 320280240D(t) 5 240200160D(t) 5 160120D(t) 5 12080D(t) 5 804001234 5 6 7Time (hours)8925. D(t) 5 12026. D(t) 5 320t53t5827. D(t) 5 24028. D(t) 5 160tt 5 6 t 5 429. D(t) 5 8030. D(t) 5 400 2012 Carnegie Learningt 5 2 t 5 10288Chapter 28069 Skills Ch02.indd 288Skills Practice4/23/12 11:56 AM

Lesson 2.2Skills PracticeNameDateWhat Goes Up Must Come DownAnalyzing Linear Functions2Problem SetComplete the table to represent each problem situation.1. A hot air balloon cruising at 1000 feet begins to ascend. It ascends at a rate of 200 feet per minute.Quantity 2012 Carnegie LearningUnitsExpressionIndependent QuantityDependent 2600t200t 1 1000Chapter 2 Skills Practice8069 Skills Ch02.indd 2892894/23/12 11:56 AM

Lesson 2.2Skills Practicepage 22. A bathtub contains 10 gallons of water. The faucet is turned on and fills the tub at a rateof 5.25 gallons per minute.2Independent QuantityDependent .25746.75t5.25t 1 10QuantityUnitsExpressionIndependent QuantityDependent 1925t2550t 1 4125QuantityUnitsExpression290Chapter 28069 Skills Ch02.indd 290 2012 Carnegie Learning3. A helicopter flying at 4125 feet begins its descent. It descends at a rate of 550 feet per minute.Skills Practice4/23/12 11:56 AM

Lesson 2.2Skills Practicepage 3NameDate4. A fish tank filled with 12 gallons of water is drained. The water drains at a rateof 1.5 gallons per minute.QuantityUnitsExpressionIndependent QuantityDependent .5t21.5t 1 1225. A submarine is traveling at a depth of 2300 feet. It begins ascending at a rate of 28 feet per minute. 2012 Carnegie LearningQuantityUnitsExpressionIndependent QuantityDependent 76t28t 2 300Chapter 2 Skills Practice8069 Skills Ch02.indd 2912914/23/12 11:56 AM

Lesson 2.2Skills Practicepage 46. A free-diver is diving from the surface of the water at a rate of 15 feet per minute.2Independent QuantityDependent tQuantityUnitsExpressionIdentify the input value, the output value, the y-intercept, and the rate of change for each function.7. A hot air balloon at 130 feet begins to ascend. It ascends at a rate of 160.5 feet per minute.The function f(t) 5 160.5t 1 130 represents the height of the balloon as it ascends.The input value is t, time in minutes. The output value is f(t), height in feet.8. A backyard pool contains 500 gallons of water. It is filled with additional water at a rate of 6 gallonsper minute. The function f(t) 5 6t 1 500 represents the volume of water in the pool as it is filled.The input value is t, time in minutes. The output value is f(t), volume in gallons.The y-intercept is 500. The rate of change is 6.9. A submarine is diving from the surface of the water at a rate of 17 feet per minute. The functionf(t) 5 217t represents the depth of the submarine as it dives. 2012 Carnegie LearningThe y-intercept is 130. The rate of change is 160.5.The input value is t, time in minutes. The output value is f(t), depth in feet.The y-intercept is 0. The rate of change is 217.292Chapter 28069 Skills Ch02.indd 292Skills Practice4/23/12 11:56 AM

Lesson 2.2Skills Practicepage 5NameDate10. A helicopter flying at 3505 feet begins its descent. It descends at a rate of 470 feet per minute.The function f(t) 5 2470t 1 3505 represents the height of the helicopter as it descends.2The input value is t, time in minutes. The output value is f(t), height in feet.The y-intercept is 3505. The rate of change is 2470.11. A bathtub contains 5 gallons of water. The faucet is turned on and water is added to the tub at a rateof 4.25 gallons per minute. The function f(t) 5 4.25t 1 5 represents the volume of water in the bathtubas it is filled.The input value is t, time in minutes. The output value is f(t), volume in gallons.The y-intercept is 5. The rate of change is 4.25.12. A free-diver is diving from the surface of the water at a rate of 8 feet per minute. The functionf(t) 5 28t represents the depth of the diver.The input value is t, time in minutes. The output value is f(t), depth in feet.The y-intercept is 0. The rate of change is 28.Sketch the line for the dependent value to estimate each intersection point.13. f(x) 5 240x 1 1200 when f(x) 5 72014. f(x) 5 6x 1 15 when f(x) 5 75 2012 Carnegie swers will vary. Answers will vary.f(x) 5 720 at x 5 12 f(x) 5 75 at x 5 10Chapter 2 Skills Practice8069 Skills Ch02.indd 2932934/23/12 11:56 AM

Lesson 2.2Skills Practicepage 615. f(x) 5 22x 1 5 when f(x) 5 2716. f(x) 5 4x 2 7 when f(x) 5 8yy281661248240 228 26 24 22468x0 4216 212 28 2424–2–428–6212–8812 16x216Answers will vary. Answers will vary.f(x) 5 27 at x 5 6 f(x) 5 8 at x 417. f(x) 5 2200x 2400 when f(x) 45018. f(x) 5 12x 1 90 when f(x) 5 420y24004801800360120024060012002468 10 12 14 16 18x048 12 16 20 24 28 32 36Answers will vary. Answers will vary.f(x) 5 450 at x 10 f(x) 5 420 at x 28294Chapter 28069 Skills Ch02.indd 294x 2012 Carnegie LearningySkills Practice4/23/12 11:56 AM

Lesson 2.2Skills Practicepage 7NameDateSubstitute and solve for x to determine the exact value of each intersection point.19. f(x) 5 240x 1 1200 when f(x) 5 720220. f(x) 5 6x 1 15 when f(x) 5 75f(x) 5 240x 1 1200 f(x) 5 6x 1 15720 5 240x 1 1200   75 5 6x 1 152480 5 240x   60 5 6x12 5 x   10 5 x21. f(x) 5 22x 1 5 when f(x) 5 2722. f(x) 5 4x 2 7 when f(x) 5 8f(x) 5 22x 1 5      f(x) 5 4x 2 727 5 22x 1 5            8 5 4x 2 7212 5 22x          15 5 4x6 5 x 3.75 5 x23. f(x) 5 2200x 1 2400 when f(x) 5 45024. f(x) 5 12x 1 90 when f(x) 5 420f(x) 5 2200x 1 2400      f(x) 5 12x 1 90450 5 2200x 1 2400   420 5 12x 1 9021950 5 2200x   330 5 12x 2012 Carnegie Learning9.75 5 x 27.5 5 xChapter 2 Skills Practice8069 Skills Ch02.indd 2952954/23/12 11:56 AM

2012 Carnegie Learning2296Chapter 28069 Skills Ch02.indd 296Skills Practice4/23/12 11:56 AM

Lesson 2.3Skills PracticeNameDateScouting for Prizes!Modeling Linear Inequalities2VocabularyDefine the term in your own words.1. solve an inequalityTo solve an inequality means to determine the values of the variable that make the inequality true.Problem SetCarlos works at an electronics store selling computer equipment. He can earn a bonus if he sells 10,000 worth of computer equipment this month. So far this month, he has sold 4000 worth ofcomputer equipment. He hopes to sell additional laptop computers for 800 each to reach his goal.The function f(x) 5 800x 1 4000 represents Carlos’s total sales as a function of the number of laptopcomputers he sells.yTotal Sales (dollars) 2012 Carnegie 200001 2 3 4 5 6 7 8 9Number of Laptop Computers SoldxChapter 2 Skills Practice8069 Skills Ch02.indd 2972974/23/12 11:56 AM

Lesson 2.3Skills Practicepage 2Use the graph to write an equation or inequality to determine the number of laptop computersCarlos would need to sell to earn each amount.1. at least 10,0002. less than 7000Carlos would need to sell at least Carlos would need to sell fewer than8 laptop computers. 4 laptop computers.2x 8 x , 43. less than 60004. at least 9000Carlos would need to sell fewer than Carlos would need to sell at least3 laptop computers. 7 laptop computers.x , 3 x 75. more than 12,0006. exactly 8000Carlos would need to sell more than Carlos would need to sell exactly10 laptop computers. 5 laptop computers.x . 10 x 5 5Elena works at the ticket booth of a local playhouse. On the opening night of the play, tickets are 10 each. The playhouse has already sold 500 worth of tickets during a presale. The functionf(x) 5 10x 1 500 represents the total sales as a function of tickets sold on opening night.y16001400120010008006004002000298Chapter 28069 Skills Ch02.indd 29810 20 30 40 50 60 70 80 90Tickets Sold Opening Nightx 2012 Carnegie LearningTotal Sales (dollars)1800Skills Practice4/23/12 11:56 AM

Lesson 2.3Skills Practicepage 3NameDateUse the graph of the function to answer each question. Graph each solution on the number line.27. How many tickets must Elena sell in order to make at least 1000?Elena must sell at least 50 tickets.    x 0080901008. How many tickets must Elena sell in order to make less than 800?Elena must sell fewer than 30 tickets.    x , 300102030405060709. How many tickets must Elena sell in order to make at least 1200?Elena must sell at least 70 tickets.    x 7001020304050607010. How many tickets must Elena sell in order to make exactly 1400?Elena must sell exactly 90 tickets.    x 5 9001020304050607011. How many tickets must Elena sell in order to make less than 600? 2012 Carnegie LearningElena must sell fewer than 10 tickets.    x , 1001020304050607012. How many tickets must Elena sell in order to make exactly 900?Elena must sell exactly 40 tickets.    x 5 40010203040506070Chapter 2 Skills Practice8069 Skills Ch02.indd 2992994/23/12 11:56 AM

Lesson 2.3Skills Practicepage 4Leon plays on the varsity basketball team. So far this season he has scored a total of 52 points. He scoresan average of 13 points per game. The function f(x) 5 13x 1 52 represents the total number of pointsLeon will score this season. Write and solve an inequality to answer each question.13. How many more games must Leon play in order to score at least 117 points?2f(x) 5 13x 1 52117 # 13x 1 5265 # 13x5#xLeon must play in 5 or more games to score at least 117 points.14. How many more games must Leon play in order to score fewer than 182 points?f(x) 5 13x 1 52182 . 13x 1 52130 . 13x10 . xLeon must play in fewer than 10 games to score fewer than 182 points.15. How many more games must Leon play in order to score more than 143 points?f(x) 5 13x 1 52143 , 13x 1 5291 , 13x7,x 2012 Carnegie LearningLeon must play in more than 7 games to score more than 143 points.300Chapter 28069 Skills Ch02.indd 300Skills Practice4/23/12 11:56 AM

Lesson 2.3Skills Practicepage 5NameDate16. How many more games must Leon play in order to score at least 100 points?f(x) 5 13x 1 522100 # 13x 1 5248 # 13x3.69 # xLeon must play in 4 or more games to score at least 100 points.17. How many more games must Leon play in order to score fewer than 85 points?f(x) 5 13x 1 5285 . 13x 1 5233 . 13x2.54 . xLeon must play in 2 or fewer games to score fewer than 85 points.18. How many more games must Leon play in order to score more than 200 points?f(x) 5 13x 1 52200 , 13x 1 52148 , 13x11.38 , x 2012 Carnegie LearningLeon must play in 12 or more games to score more than 200 points.Chapter 2 Skills Practice8069 Skills Ch02.indd 3013014/23/12 11:56 AM

Lesson 2.3Skills Practicepage 6Draw an oval on the graph to represent the solution to each question. Write the correspondinginequality statement.19. A hot air balloon at 4000 feet begins its descent. It descends at a rate of 200 feet per minute.The function f(x) 5 2200x 1 4000 represents the height of the balloon as it descends. How manyminutes have passed if the balloon is below 3000 feet?2More than 5 minutes havepassed if the balloon isbelow 3000 feet.yHeight (feet)5000x.54000300020001000051015Time (minutes)x20. A bathtub filled with 55 gallons of water is drained. The water drains at a rate of 5 gallons per minute.The function f(x) 5 25x 1 55 represents the volume of water in the tub as it drains. How manyminutes have passed if the tub still has more than 20 gallons of water remaining in it?80Less than 7 minutes havepassed if the tub has morethan 20 gallons of waterremaining in it.70x,7y6050403020100302Chapter 28069 Skills Ch02.indd 30251015Time (minutes)x 2012 Carnegie LearningVolume (gallons)90Skills Practice4/23/12 11:56 AM

Lesson 2.3Skills Practicepage 7NameDate21. Lea is walking to school at a rate of 250 feet per minute. Her school is 5000 feet from her home.The function f(x) 5 250x represents the distance Lea walks. How many minutes have passed ifLea still has more than 2000 feet to walk?Less than 12 minutes havepassed if Lea still has morethan 2000 feet to walk.y4000Distance (feet)2x , 12300020001000051015Time (minutes)x22. Franco is riding his bike to school at a rate of 600 feet per minute. His school is 9000 feet from hishome. The function f(x) 5 600x represents the distance Franco rides. How many minutes havepassed if Franco has less than 3000 feet left to ride?More than 10 minutes havepassed if Franco has lessthan 3000 feet to ride.yDistance (feet) 2012 Carnegie Learning8000x . 10600040002000051015Time (minutes)xChapter 2 Skills Practice8069 Skills Ch02.indd 3033034/23/12 11:56 AM

Lesson 2.3Skills Practicepage 823. A submarine is diving from the surface of the water at a rate of 20 feet per minute. The functionf(x) 5 220x represents the depth of the submarine as it dives. How many minutes have passed ifthe submarine is at least 160 feet below the surface?2002At least 8 minutes havepassed if the submarine isat least 160 feet below thesurface.yx 810210x220024. A scuba diver is diving from the surface of the water at a rate of 14 feet per minute. The functionf(x) 5 214x represents the depth of the diver as he dives. How many minutes have passed if the diveris less than 42 feet below the surface?60Less than 3 minutes havepassed if the diver is lessthan 42 feet below thesurface.yx,3260304Chapter 28069 Skills Ch02.indd 304 2012 Carnegie Learningx10210Skills Practice4/23/12 11:56 AM

Lesson 2.4Skills PracticeNameDateWe’re Shipping Out!Solving and Graphing Compound Inequalities2VocabularyMatch each definition to its corresponding term.1. compound inequalityb.2. solution of a compound inequalityc.3. conjunctiona.4. disjunctiond.a. a solution of a compound inequality in the forma , x , b, where a and b are any real numbersb. an inequality that is formed by the union, “or,” orthe intersection, “and,” of two simple inequalitiesc. the part or parts of the solutions that satisfyboth of the inequalitiesd. a solution of a compound inequality in theform x , a or x . b, where a and b are anyreal numbersProblem SetWrite each compound inequality in compact form.1. All numbers less than or equal to 22 and greater than 2422 x 242. All numbers less than 55 and greater than 45 2012 Carnegie Learning55 x 453. All numbers greater than or equal to 0 and less than or equal to 60 x 64. All numbers greater than 10 and less than 100010 x 10005. All numbers less than or equal to 87 and greater than or equal to 8387 x 836. All numbers greater than 21 and less than or equal to 3921 x 39Chapter 2 Skills Practice8069 Skills Ch02.indd 3053054/23/12 11:56 AM

Lesson 2.4Skills Practicepage 2Write an inequality for each graph.7.0210 29 28 27 26 25 24 23 22 211234567810 11928 x 1128.012345678910112 x 69.13579111315171921232527293133357 x 2510.21001021001021001025 x 911.214 x 512.22 x 18Graph each inequality.303540455055606570758085909510014. 25 , x , 521521025051015 2012 Carnegie Learning13. 45 x 7515. 213 x 5210306Chapter 28069 Skills Ch02.indd 306010Skills Practice4/23/12 11:56 AM

Lesson 2.4Skills Practicepage 3NameDate16. 26 x 19021021017. 235 x . 25 x 45250240Write a compound inequality for each situation.19. The flowers in the garden are 6 inches or taller or shorter than 3 inches.x 6 or x 320. People with a driver’s license are at least 16 years old and no older than 85 years old.16 x 8521. Kyle’s car gets more than 31 miles per gallon on the highway or 26 miles or less per gallon in the city.x 31 or x 2622. The number of houses that will be built in the new neighborhood must be at least 14 and no morethan 28. 2012 Carnegie Learning14 x 2823. At the High and Low Store, they sell high-end items that sell for over 1000 and low-end items thatsell for less than 10.x 1000 or x 1024. The heights of the twenty tallest buildings in New York City range from 229 meters to 381 meters.229 x 381Chapter 2 Skills Practice8069 Skills Ch02.indd 3073074/23/12 11:56 AM

Lesson 2.4Skills Practicepage 4Represent the solution to each part of the compound inequality on the number line. Then write the finalsolution that is represented by each graph.25. x 2 and x 7201234567891010112 x 726. x 10 or x 60123456789x 627. x 5 or x 30123456789102345678910232221012345x 5 or x 328. x 4 and x 30129. x 21 or x 02524x 21 or x 0308Chapter 28069 Skills Ch02.indd 308 2012 Carnegie LearningNo solutionSkills Practice4/23/12 11:56 AM

Lesson 2.4Skills Practicepage 5NameDate30. 8 x 2822100255108 x 2831. x 9 and x 20123456789102 x 932. x 211 or x 211220215210250All real numbersSolve each compound inequality. Then graph and describe the solution.33. 23 x 1 7 1723 x 1 7 17 2012 Carnegie Learning23 2 7 x 1 7 2 7 17 2 7210 x 10210010Solution: 210 x 10Chapter 2 Skills Practice8069 Skills Ch02.indd 3093094/23/12 11:56 AM

Lesson 2.4Skills Practicepage 634. 4 2x 1 2 124 2x 1 2 124 2 2 2x 1 2 2 2 12 2 22 2x 10  2   2x   10  22221 x 50123456Solution: 1 x 535. x 1 5 14 or 3x 9x 1 5 14 or   3x 9x 1 5 2 5 14 2 5          3x   9  33x 9            x 3012345678910Solution: x 9 or x 336. 25x 1 1 16 or x 2 6 2825x 1 1 16 or            x 2 6 2825x 1 1 2 1 16 2 1         x 2 6 1 6 28 1 625x 15               x 22x 23025Solution: x 22310Chapter 28069 Skills Ch02.indd 3105 2012 Carnegie Learning  25x    15   2525Skills Practice4/23/12 11:56 AM

Lesson 2.4Skills Practicepage 7NameDate37. 28  7   x 42828  7   x 4282( )  8   (28)  8     7   x  8   (42)77 8732 x 48304050Solution: 32 x 4838. 22x 1 5 9 or 2x 2 13 23122x 1 5 9 or      2x 2 13 23122x 1 5 2 5 9 2 5         2x 2 13 1 13 231 1 1322x 4              2x 218  218  22x    4                   2x222221x 2225021x 185101520 2012 Carnegie LearningSolution: All real numbersChapter 2 Skills Practice8069 Skills Ch02.indd 3113114/23/12 11:56 AM

2012 Carnegie Learning2312Chapter 28069 Skills Ch02.indd 312Skills Practice4/23/12 11:56 AM

Lesson 2.5Skills PracticeNameDatePlay Ball!Absolute Value Equations and Inequalities2VocabularyDefine each term in your own words.1. oppositesOpposites are two numbers that are equal distance, but are in different directions, from zeroon the number line.2. absolute valueThe absolute value of a number is its distance from zero on the number line.Give an example of each term.3. linear absolute value equationAnswers will vary. x 1 2 5 44. linear absolute value inequalityAnswers will vary. x 2 3 . 8 2012 Carnegie LearningMatch each equivalent compound inequality to its corresponding absolute value inequality.5. ax 1 b , ca.6. ax 1 b # cc.7. ax 1 b . ca. 2c , ax 1 b , cb. ax 1 b , 2c or ax 1 b . cc. 2c # ax 1 b # cb.8. ax 1 b cd. ax 1 b # 2c or ax 1 b cd.Problem SetEvaluate each absolute value.1. 3 5 3 14. 2       5  1  44 2. 23 5 33.  1    5  1  445. 3.7 5 3.76. 23.7 5 3.7Chapter 2 Skills Practice8069 Skills Ch02.indd 3133134/23/12 11:56 AM

Lesson 2.5Skills Practicepage 2Determine the number of solutions for each equation. Then calculate the solution.7. x 5 298. x 5 26There is only one solution. There are no solutions.x 5 2929. x 5 410. 2x 5 28There are two solutions. There are no solutions.x 5 4 or x 5 2411. x 5 012. 2x 5 15There is only one solution. There are two solutions.x 5 0 x 5 15 or x 5 215Solve each linear absolute value equation.13. x 1 9 5 2(x 1 9) 5 2      2(x 1 9) 5 2x 1 9 2 9 5 2 2 9          x 1 9 5 22x 5 27 x 1 9 2 9 5 22 2 9x 5 21114. x 1 4 5 10(x 1 4) 5 10      2(x 1 4) 5 10x 1 4 2 4 5 10 2 4           x 1 4 5 210x 5 6 x 1 4 2 4 5 210 2 4x 5 214(x 2 12) 5 5          2(x 2 12) 5 5x 2 12 1 12 5 5 1 12       x 2 12 5 25x 5 17 x 2 12 1 12 5 25 1 12x 5 716. 2x 2 6 5 18(2x 2 6) 5 18   2(2x 2 6) 5 18 2012 Carnegie Learning15. x 2 12 5 52x 2 6 1 6 5 18 1 6    2x 2 6 5 2182x 5 24 2x 2 6 1 6 5 218 1 6x 5 12        2x 5 212x 5 26314Chapter 28069 Skills Ch02.indd 314Skills Practice4/23/12 11:56 AM

Lesson 2.5Skills Practicepage 3NameDate17. 3x 1 1 5 29There are no solutions.218. 5x 1 1 5 14(5x 1 1) 5 14   2(5x 1 1) 5 145x 1 1 2 1 5 14 2 1    5x 1 1 5 2145x 5 13  5x 1 1 2 1 5 214 2 1x 5  13          5x 5 2155x 5 23Solve each linear absolute value equation.19. x 2 8 5 25 x 2 8 5 25 x 2 8 1 8 5 25 1 8 x 5 332(x) 5 33x 5 33     x 5 23320. x 1 3 2 7 5 40 x 1 3 2 7 5 40 x 1 3 2 7 1 7 5 40 1 7 x 1 3 5 47      2(x 1 3) 5 47 2012 Carnegie Learning(x 1 3) 5 47                 x 1 3 5 247x 1 3 2 3 5 47 2 3 x 1 3 2 3 5 247 2 3x 5 44 �              x 5 25021. 2 x 2 6 5 482 x 2 6 5 482 x 2 6 48 5     22 x 2 6 5 24   2(x 2 6) 5 24(x 2 6) 5 24        x 2 6 5 224x 2 6 1 6 5 24 1 6 x 2 6 1 6 5 224 1 6x 5 30             x 5 218Chapter 2 Skills Practice8069 Skills Ch02.indd 3153154/23/12 11:56 AM

Lesson 2.5Skills Practicepage 422. 3 x 1 8 5 363 x 1 8 5 363 x 1 8 36 5     33 x 1 8 5 122(x 1 8) 5 12     2(x 1 8) 5 12x 1 8 2 8 5 12 2 8      x 1 8 5 212x 5 4 x 1 8 2 8 5 212 2 8x 5 22023. 5 x 1 4 5 795 x 1 4 5 795 x 1 4 2 4 5 79 2 45 x 5 755 x     5  75  55 x 5 15 2(x) 5 15x 5 15            x 5 21524. 2 x 2 5 5 112 x 2 5 5 112 x 2 5 1 5 5 11 1 52 x 5 162 x     5  16  22 x 5 8 2(x) 5 8 2012 Carnegie Learningx 5 8            x 5 28Solve each linear absolute value inequality. Graph the solution on the number line.25. x 1 5 , 2(x 1 5) , 2      2(x 1 5) , 2x 1 5 2 5 , 2 2 5       x 1 5 . 22x , 23 x 1 5 2 5 . 22 2 5x . 27220316Chapter 28069 Skills Ch02.indd 3162152102505101520Skills Practice4/23/12 11:56 AM

Lesson 2.5Skills Practicepage 5NameDate26. x 2 3 # 6(x 2 3) # 6      2(x 2 3) # 62x 2 3 1 3 # 6 1 3       x 2 3 26x # 9 x 2 3 1 3 26 1 3x 2322021521025051015201520152027. 2 x 2 1 , 142 x 2 1 , 142 x 2 1 ,  14  22 x 2 1 , 7   2(x 2 1) , 7(x 2 1) , 7        x 2 1 . 27x 2 1 1 1 , 7 1 1 x 2 1 1 1 . 27 1 1x , 8        x . 2622021521025051028. 3 x 1 4 93 x 1 4 93 x 1 4  9  2012 Carnegie Learning33 x 1 4 3   2(x 1 4) 3(x 1

286 Chapter 2 Skills Practice 2 Lesson 2.1 Skills Practice page 6 15. Rochelle is shopping for earrings. Each pair of earrings costs 15 dollars. The function C(e) 5 15e represents the total cost of the earrings as a function of the number of pairs of earrings Rochelle buys. The input value

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