3.1 – Algebraic Expressions

Parts of an algebraic expression are called terms. One way to simplify an expression is to combine like terms. What does it mean to combine like terms?

4x2 You can only combine like terms that have the same: __________________________________ and __________________________________

Circle the like terms for each line: 4x 9 2x2 7x 5x 10x 5x2 10x2 7y y 2y 18y 14m 3n2 2n2 3m2

When simplifying an expression:

1. Distribute 2. Combine like terms 3. Remember: Keep the sign with the number that comes after it.

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7U3L1

Algebraic Expressions

Name___________________________________ ID: 1

Date________________

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-1-

Simplify each expression.

1) - 8 p - p 2) 13k + 7 + 12 - 9k

3) 11 + 12 x + 1 - 10 x 4) 1 - 4 x + 1 + 2 x

5) - 12r - 3r 6) 2b - 13b

7) - 14 x - 11 x 8) - 9m - 5m

9) - 7b - 10b 10) 9 - 14 x - 4 x

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-2-

11) 9 (5 + 2v) - 3v 12) 2 (8 + 11r) + 2r

13) 4 - 14 (4 - 11a) 14) 3 (n + 7 ) - 2

15) - 14n + 8 (1 + 5n) 16) - 12 (14 + 11a) - 5a

17) - 8 (- 13m - 9 ) - 10m 18) 14 (n - 1 ) + 4

19) - 7 + 7 (1 + 9b) 20) 14 (1 + 5 x) + 3

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3.1 Practice For use after Lesson 3.1

Name _________________________________________________________ Date _________

Identify the terms and like terms in the expression.

1. 3 4 7 6x x 2. 29 2.5 0.7 1 6.4y y y

Simplify the expression.

3. 5 2 9a a 4. 1 5

46 6

m m

5. 2.3 7 8.1 3w w 6. 7 1 2d

7. 13 2 4g k g 8. 20 2 16 3p p

9. Write an expression in simplest form that represents

the cost for shampooing and cutting w women’s hair

and m men’s hair.

Women Men

Cut $15 $7

Shampoo $5 $2

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3.2 Practice For use after Lesson 3.2

Name _________________________________________________________ Date _________

Find the sum or difference.

1. 2 6x x 2. 2 4 4 3n n

3. 2 3 1 2 7y y 4. 1 3 4 2 2.5k k

5. 1

6 9 15 93

g g 6. 1 1

2 4 16 82 4

r r

7. You earn 4 12x points after completing x levels of a video game and

then lose 2 5x points. Write an expression that represents the total

number of points you have now.

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3.2 Practice A

Name_________________________________________________________ Date __________

Find the sum.

1. 3 7p p 2. 3 1 4n n

3. 3 8 5 1r r 4. 6 3 2 9x x

5. 3 2 4 1.3 5c c 6. 10 2.1 2 7.5 18q q

7. 6 2 5 3 2.5y y 8. 1 1

6 10 6 92 3

x x

9. After a week of rain, tadpoles appeared in your pond. After t minutes, you

have (7t + 5) tadpoles and your friend has (8t – 3) tadpoles.

a. Write an expression that represents the number of tadpoles you and your

friend caught together.

b. Who has more tadpoles after 9 minutes?

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Find the difference.

10. 3 3 5k k 11. 6 2 7 2d d

12. 10 7 9 2j j 13. 3 8 6 2.5 3x x

14. 7 3 5 1.6 5t t 15. 1 1

12 8 10 52 5

w w

16. The admission to a local fair is $10 for each adult and $6 for each child.

Each rides costs $1.50 for an adult and $1 for a child.

a. Write an expression that represents how much more an adult will spend

at the fair.

b. An adult and a child each go on 7 rides. How much more did the adult

spend?

17. Write an expression that represents

the perimeter of the triangle.

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3.2 Practice B

Name_________________________________________________________ Date __________

Find the sum.

1. 5 3 2t t 2. 7 9 4 3k k

3. 2 5 6 2 8y y 4. 4 2.5 4 3 1.2 2g g

5. 5 0.3 2 2 5 3.4s s 6. 1 1

6 3 7 143 7

p p

7. 1 1

15 20 3 45 2

w w 8. 1 1

16 24 2 108 5

k k

9. You are selling tickets to a play. You have sold 3 2t tickets for $5 each

and 2 5t tickets for $7 each.

a. Write an expression that represents the total number of tickets sold

so far.

b. Write an expression that represents the total amount of money received

for the tickets that have been sold.

c. When 3,t what is the total amount of money received?

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Find the difference.

10. 8 5 1u u 11. 2 7 6 5 8x x

12. 3 4 6 5 1.4h h 13. 12 7.2 3 0.9 4b b

14. 1 1

16 12 18 454 9

j j 15. 2 1

12 6 10 23 5

n n

16.You are collecting pairs of socks and toothbrushes for a local charity. After

d days, you have collected 4 5d pairs of socks and 3 7d toothbrushes.

a. Write an expression that represents the total number of items that have

been collected.

b. How many more pairs of socks than toothbrushes have been collected

on day 7?

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Practice For use after Extension 3.2

Extension

3.2

Name_________________________________________________________ Date __________

Factor the expression using the GCF.

1. 7 28 2. 25 50 3. 7 7b

4. 8 16a 5. 8 12x 6. 12 24y t

7. 10 50w z 8. 10 12v u 9. 9 15a b

Factor out the coefficient of the variable.

10. 1 1

2 2a 11.

1 3

4 4d 12.

5 2

6 3s

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Extension

3.2

Practice (continued)

Name _________________________________________________________ Date _________

Factor out the coefficient of the variable.

13. 3 2

10 5y 14. 1.1 9.9x 15. 3.4 10.2c

16. Factor 2 out of 6 10.x

17. Factor 1 1 3

out of .3 3 2

y

18. A square window has a perimeter of 8 12 feet.x Write an expression

that represents the side length of the window (in feet).

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Extension

3.2 Practice

Name _________________________________________________________ Date _________

Factor the expression using the GCF.

1. 8 22 2. 25 30 3. 6 3y

4. 2 10t 5. 16 8p 6. 21 15s

7. 32 24v w 8. 9 24b c 9. 12 42y z

Factor out the coefficient of the variable.

10. 1 1

2 2m 11.

2 2

3 9j 12. 1.2 2.4k

13.1.5 4.5a 14. 3 5f 15. 3 3

10 5x

16.Factor 1 1

out of 12.3 3

x

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17. Factor 1 1 5

out of .6 3 6

x y

18. The area of the rectangle is 18 12 square inches.x Write an expression

that represents the length of the rectangle (in inches).

19. A concession stand sells hamburgers. The revenue from the hamburgers is

30 45 dollars.x

a. The price of a hamburger is $5. Write an expression that represents the

number of hamburgers sold.

b. The revenue from drinks is 63 84 dollars.x The price of a drink is $3.

Write an expression that represents the number of drinks sold.

c. Write and simplify an expression that represents how many more drinks

were sold.

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Solving Equations Using Addition or Subtraction

Name___________________________________ ID: 1

Date________________

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-1-

Solve each equation.

1) v - 8 = - 15 2) - 19 + x = - 34

3) b - 19 = - 38 4) k - 8 = - 21

5) - 8 = n - 5 6) m - 7 = - 16

7) - 32 = p - 16 8) - 16 = x - 13

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-2-

9) 110

17 = x +

10

1710) n -

2

9 =

653

99

11) 31

9 = 2 + p 12) 1 + n = -

2

19

13) 12 .2 = r + 3 .9 14) n + 1 .5 = 11 .8

15) x + 12 .47 = 5 .67 16) 14 .3 + k = - 3 .5

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7U3L3

Solving Equations Using Addition or Subtraction B

Name___________________________________ ID: 1

Date________________

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-1-

Solve each equation.

1) k + 7 = 22 2) x - 15 = - 32

3) b + 20 = 6 4) n - 13 = - 29

5) k - 19 = - 36 6) x + 15 = 22

7) n - 17 = - 27 8) 14 = n - 5

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-2-

9) - 67

26 = k - 6

10

1310)

149

6 = 16 + x

11) 37

6 =

85

18 + x

12) 6 = a + 6

13) 22 .1 = b + 15 .8 14) - 17 .9 = b - 14 .3

15) - 5 .5 = a - 6 .4 16) 24 .03 = b + 6 .93

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3.3 Practice For use after Lesson 3.3

Name _________________________________________________________ Date _________

Solve the equation. Check your solution.

1. 12 26y 2. 15 12c

3. 16 21d 4. 12.8 0.3n

5. 1 2

1 48 5

g 6. 5.47 14.19k

Write the word sentence as an equation. Then solve.

7. 42 less than is 50.x 8. 32 is the sum of a number z and 9.

9. A clothing company makes a profit of $2.3 million. This is $4.1 million

more than last year. What was the profit last year?

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3.3 Practice A

Name_________________________________________________________ Date __________

Solve the equation. Check your solution.

1. 3 10x 2. 6 14b

3. 5 9n 4. 2.1 7.5y

5. 6.4 4.3x 6. 1 5

3 6k

7. 10.5 8.32p 8. 3 1

34 8

r

9. 1.06 5m 10. 7 5

112 6

d

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11. 2 1

7 2t 12. 10.2 8.14c

Write the word sentence as an equation. Then solve.

13. 5 more than a number y is 2.

14. The sum of 8 and a number h is 12.

15. 13 is 4 less than a number n.

In Exercises 16–20, write an equation. Then solve.

16. You earn $9 per hour babysitting. This is $2 more than what you earned per

hour last year. What did you earn per hour last year?

17. Your mother asked you to turn the oven down to 325°F. This is 75°F less

than it was. What was the original temperature?

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18. The difference between the heights of your chair and your desk is

110

4 inches. The height of your desk is

329

4 inches. What is the

height of your chair?

19. Your Two-Day-Pass to a theme park is $76.50. This is $31.41 less than

your uncle’s Two-Day-Pass. What is the price of your uncle’s pass?

20. The perimeter of a triangle is 25 feet.

What is the length of the unknown side?

21.Find the value of 3 2x when 7 5.x

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3.3 Practice B

Name _________________________________________________________ Date _________

Solve the equation. Check your solution.

1. 12 100x 2. 16 52g

3. 4.5 1.9m 4. 12.1 7.53j

5. 4.003 3.14y 6. 1 2

4 23 3

z

7. 90.8 18.24q 8. 2 1

10 123 6

r

9. 4.006 9b 10. 5 5

7 18 6

d

11. 2 3

615 5

f 12. 10.216 12.014c

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Write the word sentence as an equation. Then solve.

13. 27 is 12 more than a number x.

14. The difference of a number p and 9 is 12.

15. 35 less than a number m is 72.

In Exercises 16–18, write an equation. Then solve.

16. You swim the 50-meter freestyle in 28.12 seconds. This is 0.14 second

less than your previous fastest time. What was your previous fastest time?

17. The perimeter of a rectangular backyard is 1

322

meters. The two shorter

sides are each 3

78

meters long. What is the length of the two longer sides?

(Hint: The sum of the shorter side and the longer side is equal to half of

the perimeter.)

18. The temperature of dry ice is 109.3 F, which is 183.6°F less than the

outside temperature. What is the outside temperature?

19. Your cell phone bill in August was $61.43, which was $21.75 more than

your bill in July. Your cell phone bill in July was $13.62 less than your bill

in June. What was your cell phone bill in June?

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7U3L4

Solving Equations Using Mult or Division A

Name___________________________________ ID: 1

Date________________

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-1-

Solve each equation.

1) - 6k = 182)

n8

= 4

3) x5

= 124) - 13n = - 65

5) 17n = - 68 6) - 247 = - 13a

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-2-

7) - 2b = - 128) 9 =

x10

9) -61

2 = - 4n 10) -

7

5x = -

9

2

11) -5

7n =

15

1312) -

9

5x =

18

5

13) - 14 .1 = - 9 .4m 14) - 7 .6n = 57

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-3-

15) - 279 .46 = - 17 .8m 16) - 3 .4 x = 42 .228

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7U3L4

Solving Equations Using Mult or Division B

Name___________________________________ ID: 1

Date________________

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-1-

Solve each equation.

1) - 19r = 190 2) - 15 p = 150

3) x

15 =

19

15

4) 6b = 48

5) m5

= - 16) 3v = - 45

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-2-

7) 15 = n

18

8) - 20v = 380

9) 5

7x =

19

2810) 5

2

3 =

2

3n

11) -2

3x = 0 12)

3

5n = -

18

25

13) 2 .2m = - 39 .3814) 19 =

r0 .7

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-3-

15) 42 .34 = - 14 .6m16)

k16

= 0 .81875

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3.4 Practice For use after Lesson 3.4

Name _________________________________________________________ Date _________

Solve the equation. Check your solution.

1. 65

d 2. 8 6x

3. 152

z

4. 3.2 0.8n

5. 3

1510

h 6. 1.1 1.21k

Write the word sentence as an equation. Then solve.

7. A number divided by –8 is 7. 8. The product of –12 and a number is 60.

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3.4 Practice A

Name_________________________________________________________ Date __________

Solve the equation. Check your solution.

1. 4 24b 2. 7 35n

3. 333

y

4. 32

5

p

5. 3 4.2t 6. 1.5 8.4q

7. 1

35

d 8. 14 3y

9. 6.82.1

g 10.

32

5a

11. 1

9 3

k

12.

510

8j

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Write the word sentence as an equation. Then solve.

13. A number multiplied by 1

2 is

5.

12

14. The quotient of a number and 0.2 is 2.6.

In Exercises 15–19, write an equation. Then solve.

15. You earn $7.50 per hour at a fast food restaurant. You earned $123.75 last

week. How many hours did you work last week?

16. Your family took a road trip on Saturday. You were in the car for

4.5 hours and averaged 70 miles per hour. How many miles did

you travel?

17. The area of a rectangle is 1

2 square inch. The length of the rectangle is

3

8 inch. What is the width of the rectangle?

18. You are in a room with other students and are asked to get in groups

of 3. When finished, there are 21 groups of 3. How many students are

in the room?

19. The perimeter of a square is 26.46 inches. What is the side length of

the square?

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3.4 Practice B

Name_________________________________________________________ Date __________

Solve the equation. Check your solution.

1. 16 60t 2. 14 21p

3. 7.355

q 4. 3.3

1.2

d

5. 8

415

k 6. 7.24 17.014q

7. 1 3

8 5d 8. 1.5 3.3y

9. 2.80.003

g 10.

10 15

21 28c

11. 19

k

12.

618

11h

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In Exercises 13 and 14, write an equation. Then solve.

13. You order an entree for $12.00. You pay $0.78 in taxes. What is the

tax rate?

14. If a project is handed in late, you receive 8

9 of your earned points. You

received 72 points on your late project. How many points did you lose?

15. Write a multiplication equation that has a solution of 14.8.

16. Write a division equation that has a solution of 9

.14

17. There are 92 students in a room. They are separated into 18 groups. How

many students are in each group? How many students are not in a group?

18. A bus token costs $1.75.

a. You spend $15.75 on tokens. Write and solve an equation to find how

many tokens you purchase.

b. If you purchase 10 tokens, you get 2 free tokens. Write and solve an

equation to find the approximate reduced price of each token.

c. You also receive free tokens if you purchase 20 tokens. The reduced

price for each token is $1.40. Write and solve an equation to find how

many free tokens you receive.

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7U3L5

Solving Two-Step Equations A

Name___________________________________ ID: 1

Date________________

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-1-

Solve each equation.

1) - 6r + 11 = 137 2) - 14 x + 13 = 279

3) - 1 + k

13 = - 3 4)

n27

- 10 = - 9

5) - 155 = - 8 p - 116)

x5

+ 11 = 6

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-2-

7) - 5 + p2

= - 15 8) - 11 = - 12 + n

28

9) -413

24 = - 2 -

5

4p 10) -

27

2 =

2

3 - 2 x

11) 157

30 = -

15

4 +

21

10r 12) -

4

3x -

3

2 = -

13

3

13) x

13 .5 + 11 .4 = 10 .325 14) 5 .14 =

x5 .7

+ 10

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-3-

15) - 19 .085 = - 12 .2 + p2

16) 204 .16 = - 12 .3 + 13 .7m

17) 4 .258 = x + 10

8 .518) 3 .395 =

- 1 .4 + n4 .8

19) 1 .6 + r

8 .3 = - 1 .267 20)

a + 7 .8

4 .4 = - 1 .727

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7U3L5

Solving Two-Step Equations B

Name___________________________________ ID: 1

Date________________

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-1-

Solve each equation.

1) 6 + 7b = 20 2) - 14 + 12 x = - 2

3) v + 14

8 = 5 4)

a18

- 13 = - 12

5) 13 + m9

= 16 6) x2

+ 13 = 10

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Worksheet by Kuta Software LLC

-2-

7) - 5 + n

11 = - 3

8) - 40 = - 10 + 5 x

9) -104

55 =

6

5 + 2v 10) - 3

17

24 =

2

3 + 7

1

2x

11) 29

12 - k =

67

2412)

34

5x +

2

5 =

1366

15

13) - 59 .8 = 2 .2n + 1 .8 14) 208 .14 = 8 .2b - 2 .6

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Worksheet by Kuta Software LLC

-3-

15) - 2 .442 = - 0 .2 + a

10 .416) 13 .512 =

n8

+ 13 .3

17) 0 .5 - 5 .1b = 118 .31 18) - 2 .3 - 2 .4r = 34 .42

19) 4 .253 = p + 7 .8

7 .5

20) - 1 .3b - 6 .5 = 12 .22

Big Ideas Math Red Accelerated Copyright © Big Ideas Learning, LLC

Record and Practice Journal All rights reserved. 64

3.5 Practice For use after Lesson 3.5

Name _________________________________________________________ Date _________

Solve the equation. Check your solution.

1. 3 5 14a 2. 10 2 22c

3. 18 5 17b 4. 12 8 12z

5. 1.3 0.03 9n 6. 5 7 2

11 9 9h

7. The length of a rectangle is 3 meters less than twice its width.

a. Write an equation to find the length of the rectangle.

b. The length of the rectangle is 11 meters. What is the width of the

rectangle?

Copyright © Big Ideas Learning, LLC Big Ideas Math Red

All rights reserved. Resources by Chapter 93

3.5 Practice A

Name_________________________________________________________ Date __________

Solve the equation. Check your solution.

1. 3 2 10k 2. 5 2 10p

3. 4 3 11x 4. 12 2 3.2d

5. 1 5 14h 6. 1.25 7 2.5r

7. 4 3.6 7.8k 8. 6 2 3n

9. 4 16.3 53.1y 10. 1 9 7

2 4 4b

Big Ideas Math Red Copyright © Big Ideas Learning, LLC

Resources by Chapter All rights reserved. 94

11. 5 2

36 3

j 12. 9 3

310 5

p

In Exercises 13–15, write an equation. Then solve.

13. It costs $4 to enter the fair. Each ride costs $2.50. You have $21.50. How

many rides can you go on?

14. The cable company charges a monthly fee of $45. Each movie rental is

$1.99. You owe $68.88. How many movies did you rent?

15. The perimeter of the rectangle is 24 feet.

What is the width of the rectangle?

Solve the equation. Check your solution.

16. 7 2 45c c 17. 3 5 16k

18. 2( 1) 10m

Copyright © Big Ideas Learning, LLC Big Ideas Math Red

All rights reserved. Resources by Chapter 95

19. The senior class has 412 students. They are assigned to different

homerooms. There are 28 students in the smallest homeroom and the

remaining 12 homerooms have the same number of students. How many

students are in each of the remaining 12 homerooms?

20. You purchased paint for the rooms in your house. You have 1.5 cans of

paint left. You painted 4 rooms and each room required 2 cans of paint.

You spilled 1

2 of a can of paint. How many cans of paint did you purchase?

a. Solve the problem by working backwards.

b. Solve the equation 2

2.4

x How does the answer compare to

part (a)?

Big Ideas Math Red Copyright © Big Ideas Learning, LLC

Resources by Chapter All rights reserved. 96

3.5 Practice B

Name _________________________________________________________ Date _________

Solve the equation. Check your solution.

1. 5 8 7k 2. 6 9 15b

3. 3.2 2 4.5w 4. 13 2 27n

5. 25 4.5 12z 6. 5.25 2.01 8.94s

7. 84 51 14p 8. 81 7 81t

9. 16 2.4 22.5c 10. 1 3

43 4

h

Copyright © Big Ideas Learning, LLC Big Ideas Math Red

All rights reserved. Resources by Chapter 97

11.1 1 9

57 2 14

f 12. 1 3 1

2 5 6u

In Exercises 13 and 14, write an equation. Then solve.

13. You purchased $132.49 worth of wheels and bearings for your skateboards.

The shop charges $15 per board to install them. The total cost is $192.49.

How many skateboards will be repaired?

14. A music download service charges a flat fee each month and $0.99 per

download. The total cost for downloading 27 songs this month is $42.72.

How much is the flat fee?

Solve the equation. Check your solution.

15. 5 2 3 9x x x 16. 5 4 27m

17. 12( 2) 50a

18. The perimeter of a triangle is 60 feet. One leg is 12 feet long. Of the two

unknown sides, one of them is twice as long as the other. Find the lengths

of the two unknown sides.