Practice 2-1 Evaluating and Writing Algebraic Expressions

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Name

Class

Date

Practice 2-1

Evaluating and Writing Algebraic Expressions

Evaluate each expression using the values m 5 7, r 5 8, and t 5 2.

1. 5m 2 6

2. 4m 1 t

3. r 4 t

4. m 3 t

5. 5t 1 2m

6. r 3 m

7. 3m 2 5t

8. (m 3 r) 4 t

9. mrt

10. Write an algebraic expression for the nth term of the table below.

A

0

1

2

3

4

5

n

B

3

5

7

9

11

13

?

Write a word phrase for each algebraic expression.

11. n 1 16

12. 3.2n

14. n 4 24

15.

45 n

13. 25.6 2 n

16. 15.4 2 n

Write an algebraic expression for each word phrase.

17. 12 more than m machines

18.six times the daily amount of fiber f in your diet

19. your aunt's age a minus 25

20.the total number of seashells s divided by 10

21. You and four friends plan a surprise party. Each of you contributes the same amount of money m for food.

a. Write an algebraic expression for the total amount of money contributed for food.

b. Evaluate your expression for m 5 $5.25.

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Practice

Course 2 Lesson 2-1

125

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Name

Class

Date

Practice 2-2

Simplify each expression.

1.

12 2

23m 1 4 2

3 4

m

4. 8 2 g 2 2 1 5g

7. 0.2(15 2 3t) 2 1.8

2. a 2 2 1 13 1 8a

5. 2.2k 1 5 1 7.9k 1 8

8. 7x 2 5(3x 1 12)

Simplifying Expressions

3. 10q 2 2q 1 3 2 9

6. 24r 2 2r 2 6 2 4

9.

1 3

(9z

2

27)

1

12

Factor each expression completely.

10. 42r 2 18

11. 100 2 50d

14. 60 2 24x

15. 9w 2 81

12. 24x 1 64

16. 132 1 77t

13. 29y 2 39

17. 16y 2 56

Use ., ,, or 5 to make each statement true. 18. 24 1 p 1 2 4p 1 2 ? 4 2 3p 19. 2m 1 2n 2 5 6 1 2(m 1 n) 2 11 20. 3x 1 4 2 4x 1 2 3(5 2 x) 1 2x 21. Find the perimeter of a rectangle with length 3c 2 5 and width 2c.

Simplify your answer.

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Practice

Course 2 Lesson 2-2

127

Name

Class

Practice 2-3

Solve each equation. Check your answer.

1. n 1 2 5 5

2. x 2 1 5 23

3. 7 5 a 1 2

5.

218

5

y 2

6.

y 16

5 3

7. 256 5 8r

Date

Solving One-Step Equations 4. p 1 2 5 26 8. 9w 5 263

Use a calculator, paper and pencil, or mental math. Solve each equation.

9. 23v 5 248

10.

13

5

x 4

11. 28 5 24a

12.

t 42

5

3

13. t 1 43 5 28

14. 219 5 r 1 6

15. 25 5 r 1 7

16. 13 5 24 1 c

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Write and solve an equation to represent each situation.

17. The odometer on your family car reads 20,186.7 after going 62.3 miles. How many miles were on the odometer before going 62.3 miles?

18. Michael bought a $25.00 gift for a friend. After he bought the gift, Michael had $176.89. Write and solve an equation to calculate how much money Michael had before he bought the gift.

19. This spring it rained a total of 11.5 inches. This was 3 inches less than last spring. Write and solve an equation to find the amount of rain last season.

20. One of the largest flowers, the Rafflesia, weighs about 15 lb. How many Rafflesia flowers can be placed in a container that can hold a maximum of 240 lb?

21. "Heavy water" is a name given to a compound used in some nuclear reactors. Heavy water costs about $1,500 per gallon. If a nuclear plant spent $10,500 on heavy water, how many gallons of heavy water were bought?

Practice

Course 2 Lesson 2-3

129

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Name

Class

Date

Practice 2-4

Exploring Two-Step Equations

Define a variable and write an algebraic expression for each phrase. 1. six times the price of gas minus 20 2. one-half the distance from Boston to New York minus 25 3. two fewer than five times the number of eggs needed in the recipe 4. 10 megabytes less than the number of megabytes in a computer, divided by 6

Solve each equation using number sense.

5. 10 1 5h 5 25

6. 8s 2 8 5 64

7. 3y 1 78 5 81

8. 2g 1 4 5 12

9. 5j 1 5 5 15

10. 3w 1 8 5 20

11.

h 2

1 1 5 4

12.

g g

1

12

5

16

13.

2

1

b 7

5

3

14. For a walk-a-thon a sponsor committed to give you a flat fee of $5 plus $2 for every mile you walk. Write an expression for the total amount you will collect from your sponsor at the end of the walk-a-thon. Then evaluate your expression for 20 miles walked.

? Pearson Education, Inc., publishing as Pearson Prentice Hall.

Practice

Course 2 Lesson 2-4

131

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Name

Class

Date

Practice 2-5

Solving Two-Step Equations

Solve each equation. Then check your answer.

1. 7m 1 8 5 71

y 2. 7 1 6 5 11

3. 12y 1 2 5 146

5. y 1 1 5 6 -12

9. b 2 8 5 26 -2

13.

f -9

1

4 5 2

6. 2a 2 1 5 19

10. 3d 1 14 5 11

14. 22y 1 16 5 10

7.

c 9

2

8

5

17

11.

z 17

2

1

5

8

15. 4w 2 26 5 82

4.

m 9

2

17

5

21

8. 24t 1 16 5 24

12.

e 5

2

14

5

21

16.

j 19

2

2

5

25

Solve each equation. 17. 3n 2 8 5 4 19. 2n 2 3 5 9

18.

n 5

2

4

5

11

20.

1

1

n 4

5

9

Match each sentence with a two-step equation. 21. Half of the height of a tree minus five equals fifteen.

22. Two less than three times the number of feet of fencing required equals twelve feet.

A. 3n 2 2 5 12

B. 3n 1 2 5 12

C.

n 2

2

5

5

15

D.

n 4

2

8

5

25

23. Eight less than the quotient of Dave's golf score and four equals negative five.

24. Three times Gail's age increased by two years equals twelve years.

? Pearson Education, Inc., publishing as Pearson Prentice Hall.

Practice

Course 2 Lesson 2-5

133

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