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Practice A For use with pages 132–140

State the inverse operation. 2. Subtract 218.

1. Add 23.

3. Add 250.

Check whether the given number is a solution of the equation. 4. x 2 8 5 11; 19

5. x 1 4 5 7; 11

6. x 2 5 5 13; 18

8. n 1 3 5 8

9. 15 5 w 1 4

Solve the equation. 7. x 1 6 5 14 10. y 2 7 5 12

11. a 2 2 5 10

12. 22 5 8 1 m

LESSON 3.1

Complete the sentence. 1 13. To isolate the variable in } x, multiply by 5

? or divide by ? .

14. To isolate the variable in 4x, multiply by

? or divide by ? .

2 15. To isolate the variable in 2} x, multiply by 3

? or divide by ? .

Tell whether the equations are equivalent. 17. 29x 5 18 and x 5 2

Solve the equation. 18. 8x 5 40

19. 23b 5 21

20. 12 5 2m

21. 234 5 2y

1 22. } n 5 13 2

1 23. 2} a 5 5 7

24. Altitude An airplane was at a cruising altitude, then descended 2000 feet. If the

airplane is at 18,000 feet now, what was the cruising altitude? Cruising altitude 2000 ft

25. Banner You are working on a banner for Friday’s pep rally..

The length of the banner is 3 times the width. The length is 15 feet. What is the width?

GO WILDCATS! 15 ft

26. Exercising Every week, you run for cardiovascular fitness and lift weights for 1 strength training. You spend about }3 of your weekly exercising time lifting weights.

You exercise 12 hours a week. How much time do you spend lifting weights?

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Algebra 1 Chapter 3 Resource Book

w

Copyright © by McDougal Littell, a division of Houghton Mifflin Company.

16. 6x 5 30 and x 5 5

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Practice B For use with pages 132–140

Solve the equation. 1. x 1 16 5 25

2. n 2 9 5 17

3. 230 5 w 1 8

4. y 1 5 5 213

5. a 2 17 5 210

6. 41 5 52 1 m

7. c 2 2.4 5 1.8

8. z 1 4.1 5 9.6

9. 23.2 5 4.5 1 p

10. 9x 5 54

11. 25b 5 55

12. 242 5 3m

13. 252 5 24y

1 14. } n 5 36 3

3 15. 2} a 5 12 4

16. 0.5y 5 17

17. 21.4a 5 2.8

18. 26.5 5 21.3m

19. A 5 70 in.2

20. A 5 30 in.2

x

LESSON 3.1

The rectangle or triangle has area A. Write and solve an equation to find the value of x.

x 12 in.

Copyright © by McDougal Littell, a division of Houghton Mifflin Company.

10 in.

21. Caves Cumberland Caverns in Tennessee is 44.4 kilometers long. This cave is

10.9 kilometers longer than Carlsbad Caverns in New Mexico. How long is Carlsbad Caverns? 22. Bocce Bocce is a lawn bowling game that originated in Italy. The bocce court below

has an area of 1032 square feet. The width of the court is 12 feet. What is the length of the court? 12 ft

23. Speedskating In the 2002 Winter Olympics, Cartriona LeMay Doan won the

500-meter race. Her winning time was 74.75 seconds. Find her average speed to the nearest tenth of a meter per second. 24. Part-Time Job You work at a grocery store part-time. You estimate that you 3 spend }5 of your time stocking shelves. You work 20 hours each week. How many

hours of your work week do you spend stocking shelves?

Algebra 1 Chapter 3 Resource Book

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Practice C For use with pages 132–140

LESSON 3.1

Solve the equation. 1. 21 5 x 2 15

2. n 2 13 5 8

3. 244 5 w 1 32

4. y 1 10.5 5 29.4

5. a 2 4.8 5 23.6

6. m 1 6.25 5 3.5

3 1 7. c 2 } 5 } 2 2

5 2 8. x 1 } 5 } 3 6

3 2 9. 2} 5 } 1 p 5 8

10. 14x 5 42

11. 21.5b 5 7.5

12. 29.6 5 2.4m

y 13. 2} 5 223 4

8 2 14. } n 5 2} 3 3

4 12 15. 2}a 5 } 5 17

a 16. } 5 21.5 6.4

4 8 17. 2} p 5 } 9 21

28 14 18. 2} z 5 2} 3 33

Find the value of b using the given information. 19. 3a 5 9 and b 5 a 2 2

20. a 2 5.4 5 8.3 and b 5 4a

21. Tallest Mountains Mount Kilimanjaro, the tallest mountain in Africa, is 1088 meters

taller than Mont Blanc, the tallest mountain in Europe. Mount McKinley is the highest point in North America at 6194 meters. Mount McKinley is 1387 meters taller than Mont Blanc. How tall are Mount Kilimanjaro and Mont Blanc? Explain how you got your answers. the day, you raised $342. You charged $6 for each car wash. a. How many cars were washed during the day? b. If you had instead charged $6.50 for each wash, how much more money would you have

made? Explain how you got your answer. 23. Swimming In the 2004 Summer Olympics, Pieter Van den Hoogenband won the 100-meter freestyle in 40.3 seconds. He also won the 200-meter freestyle in 105.35 seconds. a. Find his average speed in each competition. Round your answers to the nearest

tenth of a meter per second. b. In which competition was he faster? By how much? 2 24. Camping You are saving money for a tent that costs $265. You have } of the money 5

from gifts at your recent birthday party. You will save the rest of the money from your part-time job. a. How much money will you need to save? Explain how you got your answer. b. If you make $8 an hour, how many hours will you have to work to earn enough

money to buy the tent?

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Algebra 1 Chapter 3 Resource Book

Copyright © by McDougal Littell, a division of Houghton Mifflin Company.

22. Car Wash You are working at a car wash to raise money for a charity. By the end of

Name ——————————————————————— LESSON

3.1

Date ————————————

Challenge Practice For use with pages 132–140

In Exercises 1– 5, find the value of b. 1. 2a 1 3 5 5 and 3b 1 1 5 2a 2. a 2 4 5 24 and 2b 5 a 3. 6 2 3a 5 2 2 2a and 2b 1 a 5 0 4. 3a 1 2 5 11 and 2b 1 1 5 2a 5. 2a 2 5 5 7 and b 5 12 2 a

In Exercises 6 –12, use the fact that there are 180 pennies in a pound of pennies, 90 nickels in a pound of nickels, 200 dimes in a pound of dimes, and 80 quarters in a pound of quarters.

half full, weighs 2 pounds. When empty the bucket weighed 0.2 pound. When the bucket is full, how much money in dimes will John have? 7. Angela has a bucket that is two-thirds full of quarters and weighs 1.75 pounds.

When empty the bucket weighed 0.25 pound. When the bucket is full, how much money in quarters will Angela have?

LESSON 3.1

6. John is saving money by placing all of his spare dimes in a bucket. The bucket, when

8. Carrie has a bucket of nickels that is one-fourth full and weighs 2.8 pounds. When

Copyright © by McDougal Littell, a division of Houghton Mifflin Company.

empty the bucket weighed 0.3 pound. When the bucket is full, how much money in nickels will Carrie have? 9. James has a jar weighing 12 pounds that is three-fourths full of pennies. The empty

jar weighed 3.75 pounds. When the jar is full, how much money in pennies will James have? 10. Emma has one pound of quarters and one pound of dimes. How much money does

Emma have in quarters and dimes combined? 11. Josie has 25 pounds of quarters and dimes mixed together. How much money does

Josie have in quarters and dimes combined? 12. Luis has 12 pounds of pennies and nickels mixed together. He knows he has twice

as many pennies as he does nickels. How much money in pennies and nickels combined does Luis have?

Algebra 1 Chapter 3 Resource Book

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Interdisciplinary Application For use with pages 134–140

Pony Express

LESSON 3.1

History In the 1850s, the only way the merchants and bankers on the West Coast could receive information from the East Coast was by ship or by stagecoach, which often took months. To meet the need for transcontinental communication, William Russell, William Waddell, and Alexander Majors founded the Pony Express. On April 3, 1860, the Pony Express completed the 1966-mile journey from St. Joseph, Missouri to Sacramento, California in just 10 days, which became the standard delivery time. Eighty riders were hired at a wage of $100 per month (4 weeks) to race between 190 stations along the trail that goes through the present day states of Kansas, Nebraska, Colorado, Wyoming, Utah, Nevada, and California. Riders switched horses approximately every 10 miles and averaged 75 miles per run. The riders continued day and night no matter the weather, establishing the first high-speed link between the two coasts. Financially, the Pony Express was far from a success. Although the delivery charge was around $5 per ounce, it did not come close to covering the actual expenses. In 1861, on the brink of the Civil War, President Lincoln’s Inaugural Address was telegraphed from Washington to St. Joseph and then delivered to Sacramento by the Pony Express. This was the fastest trip ever made by the Pony Express, for the riders covered about 255 miles per day.

In Exercises 1–4, use the information above to write and solve an equation to answer the question. 1. How many miles per day did the riders usually travel on the journey from St. Joseph

to Sacramento? 2. How long did it take the riders to make the delivery of Lincoln’s Inaugural Address? 3. How much did it cost to send a 9-ounce package with the Pony Express? 4. How much would a rider earn delivering for the Pony Express for 30 weeks?

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Algebra 1 Chapter 3 Resource Book

Copyright © by McDougal Littell, a division of Houghton Mifflin Company.

On October 24, 1861, the transcontinental telegraph was finally completed and the Pony Express became obsolete overnight. Even though it existed for only 18 short months, the Pony Express will always be a legend of the American West.

Name ——————————————————————— LESSON

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Study Guide For use with pages 132–140 GOAL

Solve one-step equations using algebra.

Vocabulary Inverse operations are two operations that undo each other, such as addition and subtraction. Equivalent equations are equations that have the same solution(s). Properties of Equality

Addition Property of Equality Adding the same number to each side of an equation produces an equivalent equation. Subtraction Property of Equality Subtracting the same number from each side of an equation produces an equivalent equation.

Division Property of Equality Dividing each side of an equation by the same nonzero number produces an equivalent equation.

EXAMPLE 1

LESSON 3.1

Multiplication Property of Equality Multiplying each side of an equation by the same nonzero number produces an equivalent equation.

Solve an equation using subtraction

Copyright © by McDougal Littell, a division of Houghton Mifflin Company.

Solve x 1 11 5 15. Solution

x 1 11 5 15

Write original equation.

x 1 11 2 11 5 15 2 11

Use subtraction property of equality: Subtract 11 from each side.

x54

Simplify.

The solution is 4. Check by substituting 4 for x in the original equation. x 1 11 5 15 4 1 11 5 15 15 5 15 ✓

CHECK

EXAMPLE 2

Write original equation. Substitute 4 for x. Solution checks.

Solve an equation using addition Solve x 2 8 5 17. Solution

Horizontal format x 2 8 5 17 x 2 8 1 8 5 17 1 8 x 5 25

Vertical format Write original equation.

x 2 8 5 17 18

Add 8 to each side. Simplify.

x

18 5 25

The solution is 25. Algebra 1 Chapter 3 Resource Book

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Name ——————————————————————— LESSON

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Study Guide

Date ————————————

continued

For use with pages 132–140

Exercises for Examples 1 and 2 Solve the equation. Check your solution.

EXAMPLE 3

1. x 1 9 5 5

2.

y 1 2 5 25

3. 19 5 w 1 13

4. 8 5 z 2 11

5.

m2357

6. n 2 4 5 212

Solve an equation using division Solve 7x 5 263.

LESSON 3.1

7x 5 263 7x 7

Write original equation.

263 7

}5}

Divide each side by 7.

x 5 29 EXAMPLE 4

Simplify.

Solve an equation using multiplication x Solve } 5 4. 12

x 5 48 EXAMPLE 5

Write original equation. Multiply each side by 12. Simplify.

Solve an equation by multiplying by a reciprocal 3 Solve } x 5 6. 5

3

3

5

The coefficient of x is }5 . The reciprocal of }5 is }3. 3 5

}x 5 6

1 2

5 3 3 5

5 3

} }x 5 } (6)

x 5 10

Write original equation. 5

Multiply each side by the reciprocal, }3. Simplify.

Exercises for Examples 3, 4, and 5 Solve the equation. Check your solution. 7. 29x 5 236

y 10. 18 5 } 22

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Algebra 1 Chapter 3 Resource Book

8. 11.

7y 5 21 2

2}5 z 5 8

x 9. } 5 224 3 4 12. 16 5 } m 7

Copyright © by McDougal Littell, a division of Houghton Mifflin Company.

x }54 12 x 12 p } 5 12 p 4 12