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Grade 6–8Common Core (CCSS) · Math: algebra

Math · Grade 6

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Equations · Grade 6

Name: ____________________

Worked example

  1. The goal: get x alone on one side. Do the same thing on both sides of the equals sign.
  2. Example: x + 5 = 12. Subtract 5 from both sides: x = 12 − 5.
  3. Answer: x = 7. Check: 7 + 5 = 12. ✓
Example: how to solve it
1.

Solve: 4x + 3 = 23

2.

Noa thinks of a number, multiplies it by 7 and adds 27. The result is 90. What is the number?

3.

Solve: 7x + 2 = 16

4.

6 equally priced tickets and a 13 kr programme cost 55 kr in total. What does one ticket cost? Answer with the correct unit.

5.

Solve: 6x + 12 = 48

6.

Sara thinks of a number, multiplies it by 4 and adds 10. The result is 22. What is the number?

7.

Solve: 3x + 21 = 39

8.

A gym charges 24 kr per month plus 2 kr per visit. Amira paid 38 kr. How many visits was that? Answer with the correct unit.

9.

Solve: 4x + 5 = 13

10.

Nour thinks of a number, multiplies it by 6 and adds 20. The result is 62. What is the number?

11.

Solve: 7x + 25 = 67

12.

A rectangle is 10 cm longer than it is wide. Its perimeter is 84 cm. How wide is it? Answer with the correct unit.

13.

Solve: 5x + 17 = 42

14.

9 equally priced tickets and a 28 kr programme cost 154 kr in total. What does one ticket cost? Answer with the correct unit.

15.

Solve: 8x + 25 = 49

16.

A taxi costs 2 kr to start plus 2 kr per km. A trip costs 14 kr. How many km was the trip? Answer with the correct unit.

17.

Solve: 8x + 6 = 38

18.

Vera thinks of a number, multiplies it by 4 and adds 28. The result is 56. What is the number?

19.

Solve: 3x + 6 = 39

20.

2 equally priced tickets and a 23 kr programme cost 41 kr in total. What does one ticket cost? Answer with the correct unit.

21.

Solve: 8x + 29 = 93

22.

A gym charges 28 kr per month plus 4 kr per visit. Ella paid 40 kr. How many visits was that? Answer with the correct unit.

23.

Solve: 5x + 15 = 75

24.

A taxi costs 21 kr to start plus 3 kr per km. A trip costs 45 kr. How many km was the trip? Answer with the correct unit.

25.

Solve: 7x + 10 = 66

26.

Ari thinks of a number, multiplies it by 3 and adds 16. The result is 31. What is the number?

27.

Solve: 7x + 30 = 86

28.

A plumber charges 14 kr for the visit plus 5 kr per hour. The bill is 34 kr. How many hours did the job take? Answer with the correct unit.

29.

Solve: 8x + 17 = 25

30.

6 equally priced tickets and a 10 kr programme cost 40 kr in total. What does one ticket cost? Answer with the correct unit.

Answer key

  1. 1. x = 5
  2. 2. 9
  3. 3. x = 2
  4. 4. 7 kr
  5. 5. x = 6
  6. 6. 3
  7. 7. x = 6
  8. 8. 7 visits
  9. 9. x = 2
  10. 10. 7
  11. 11. x = 6
  12. 12. 16 cm
  13. 13. x = 5
  14. 14. 14 kr
  15. 15. x = 3
  16. 16. 6 km
  17. 17. x = 4
  18. 18. 7
  19. 19. x = 11
  20. 20. 9 kr
  21. 21. x = 8
  22. 22. 3 visits
  23. 23. x = 12
  24. 24. 8 km
  25. 25. x = 8
  26. 26. 5
  27. 27. x = 8
  28. 28. 4 h
  29. 29. x = 1
  30. 30. 5 kr

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  • Algebra · 30

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Area
Algebra
Exercise type
Equations
Grade
6 (ages 11–12)
Difficulty
Easy
Number of tasks
30
Task format
Mixed
Paper size
US Letter
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Solve simple equations for x, a key step from arithmetic into pre-algebra.

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How do you solve 3x + 2 = 20?
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