Distributive Property Equations Worksheet

Name: ___________________________
Date: ___________________________
Class: ___________________________

Quick Review

The distributive property means multiplying a number by every term inside the parentheses.$$a(b+c)=ab+ac$$

Example:$$3(x+4)=3x+12$$

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A. Use the Distributive Property

Expand each expression.

1. $2(x+5)=$ __________________
2. $3(x+4)=$ __________________
3. $4(x+6)=$ __________________
4. $5(x+2)=$ __________________
5. $6(x+3)=$ __________________
6. $7(x+8)=$ __________________
7. $8(x+5)=$ __________________
8. $9(x+2)=$ __________________
9. $3(2x+5)=$ __________________
10. $4(3x+2)=$ __________________
11. $5(2x+7)=$ __________________
12. $6(4x+3)=$ __________________
13. $2(5x+9)=$ __________________
14. $7(2x+4)=$ __________________
15. $8(3x+6)=$ __________________

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B. Solve Using the Distributive Property

Solve for $x$.

16. $2(x+3)=14$
17. $3(x+2)=18$
18. $4(x+5)=28$
19. $5(x+1)=30$
20. $6(x+2)=42$
21. $2(x+7)=24$
22. $3(x+5)=27$
23. $4(x+3)=36$
24. $5(x+4)=45$
25. $7(x+2)=63$
26. $2(3x+4)=20$
27. $3(2x+1)=21$
28. $4(2x+3)=44$
29. $5(2x+2)=50$
30. $2(4x+5)=34$

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C. Solve the Equations

31. $3(x+4)+2=20$
32. $4(x+2)-3=25$
33. $5(x+1)+5=35$
34. $2(x+6)-4=18$
35. $6(x+2)+4=40$
36. $3(2x+5)=33$
37. $4(2x+1)-4=28$
38. $5(x+3)+10=40$
39. $2(3x+4)+4=30$
40. $3(2x+2)-6=24$

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D. Multiple Choice

41. Which is the correct expansion of $3(x+5)$?

a) $3x+5$
b) $3x+15$
c) $x+15$
d) $8x$

42. Which is the correct expansion of $4(2x+3)$?

a) $8x+12$
b) $6x+7$
c) $8x+3$
d) $4x+6$

43. What is the first step in solving $2(x+4)=16$?

a) Divide by 4
b) Distribute 2
c) Add 4
d) Subtract 2

44. What is $5(2x+3)$?

a) $10x+8$
b) $7x+15$
c) $10x+15$
d) $5x+6$

45. Solve: $3(x+2)=21$.

a) $x=5$
b) $x=6$
c) $x=7$
d) $x=8$

46. Solve: $4(x+3)=32$.

a) $x=4$
b) $x=5$
c) $x=6$
d) $x=8$

47. Which equation demonstrates the distributive property?

a) $a+b=b+a$
b) $a(b+c)=ab+ac$
c) $a+a=2a$
d) $a-b=b-a$

48. What is $6(3x+2)$?

a) $18x+12$
b) $18x+2$
c) $9x+8$
d) $6x+12$

49. Solve: $2(x+5)=30$.

a) $x=10$
b) $x=15$
c) $x=20$
d) $x=25$

50. Solve: $5(x+2)=40$.

a) $x=5$
b) $x=6$
c) $x=7$
d) $x=8$

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E. Find the Missing Number

51. $3(x+4)=3x+\boxed{?}$
52. $5(x+6)=5x+\boxed{?}$
53. $7(2x+3)=14x+\boxed{?}$
54. $4(3x+5)=\boxed{?}x+20$
55. $6(2x+7)=12x+\boxed{?}$
56. $8(x+9)=8x+\boxed{?}$
57. $9(2x+4)=18x+\boxed{?}$
58. $5(3x+2)=\boxed{?}x+10$
59. $7(x+8)=7x+\boxed{?}$
60. $10(2x+5)=20x+\boxed{?}$

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Answer Key

A. Use the Distributive Property

1. $2x+10$
2. $3x+12$
3. $4x+24$
4. $5x+10$
5. $6x+18$
6. $7x+56$
7. $8x+40$
8. $9x+18$
9. $6x+15$
10. $12x+8$
11. $10x+35$
12. $24x+18$
13. $10x+18$
14. $14x+28$
15. $24x+48$

B. Solve Using the Distributive Property

16. x=4x=4
17. x=4x=4
18. x=2x=2
19. x=5x=5
20. x=5x=5
21. x=5x=5
22. x=4x=4
23. x=6x=6
24. x=5x=5
25. x=7x=7
26. x=2x=2
27. x=3x=3
28. x=4x=4
29. x=3x=3
30. x=3x=3

C. Solve the Equations

31. x=2x=2
32. x=5x=5
33. x=5x=5
34. x=5x=5
35. x=4x=4
36. x=3x=3
37. x=3x=3
38. x=3x=3
39. x=3x=3
40. x=4x=4

D. Multiple Choice

41. b) 3x+153x+15
42. a) 8x+128x+12
43. b) Distribute 2
44. c) 10x+1510x+15
45. a) x=5x=5
46. c) x=5x=5
47. b) a(b+c)=ab+aca(b+c)=ab+ac
48. a) 18x+1218x+12
49. a) x=10x=10
50. c) x=6x=6

E. Missing Numbers

51. 12
52. 30
53. 21
54. 12
55. 42
56. 72
57. 36
58. 15
59. 56
60. 50