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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 403 · 40 sums
TalentJR

The method (Letters one side, numbers the other): Open brackets: a(x − b) = ax − ab. Fractions: multiply both sides by the LCM of the denominators — x/3 + x/4 = 14 → 4x + 3x = 168. Move letter terms to one side and numbers to the other (change the sign when a term crosses =), then divide. Word problems: consecutive numbers are n, n + 1, n + 2 …; ages in y years are age + y.

NameDateTime takenScore ___ / 40
  1. 1.Solve: 6(x − 2) = 5x + 12. What is x?
  2. 2.Solve: m/3 + m/6 = 15. What is m?
  3. 3.Solve: 6t + 19 = 4t + 45. What is t?
  4. 4.The length of a rectangle is 8 cm more than its width. Its perimeter is 72 cm. What is its width (in cm)?
  5. 5.Solve: 4(t − 3) = t + 21. What is t?
  6. 6.A father is 21 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  7. 7.Solve: 9n + 1 = 4n + 51. What is n?
  8. 8.Solve: m/6 + m/4 = 40. What is m?
  9. 9.Solve: p/4 + p/5 = 72. What is p?
  10. 10.Solve: 8m + 20 = 5m + 38. What is m?
  11. 11.Solve: 4(x − 2) = 3x + 7. What is x?
  12. 12.A father is 8 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  13. 13.Solve: 7t + 9 = t + 87. What is t?
  14. 14.Solve: 5x + 9 = x + 21. What is x?
  15. 15.A father is 20 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  16. 16.Solve: 3(n − 2) = 2n + 5. What is n?
  17. 17.Solve: n/5 + n/3 = 56. What is n?
  18. 18.The sum of four consecutive whole numbers is 74. What is the smallest of them?
  19. 19.Solve: p/5 + p/2 = 28. What is p?
  20. 20.The sum of four consecutive whole numbers is 58. What is the largest of them?
  21. 21.Solve: t/3 + t/6 = 3. What is t?
  22. 22.The length of a rectangle is 11 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  23. 23.Solve: 3(t − 1) = t + 1. What is t?
  24. 24.Solve: 5t + 1 = 2t + 19. What is t?
  25. 25.Solve: 6(y − 4) = 2y + 36. What is y?
  26. 26.The sum of four consecutive whole numbers is 94. What is the largest of them?
  27. 27.The length of a rectangle is 9 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  28. 28.Solve: 3x + 10 = x + 36. What is x?
  29. 29.A father is 9 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  30. 30.Solve: p/2 + p/5 = 49. What is p?
  31. 31.The length of a rectangle is 5 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  32. 32.Solve: 5(n − 1) = 4n + 8. What is n?
  33. 33.Solve: 3(m − 3) = 2m + 1. What is m?
  34. 34.The length of a rectangle is 4 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  35. 35.The length of a rectangle is 13 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  36. 36.The length of a rectangle is 7 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  37. 37.The sum of three consecutive whole numbers is 33. What is the smallest of them?
  38. 38.Solve: 5(y − 1) = 3y + 23. What is y?
  39. 39.Solve: 5(m − 4) = 3m + 10. What is m?
  40. 40.Solve: n/6 + n/2 = 8. What is n?

Answer key

  1. 24
  2. 30
  3. 13
  4. 14
  5. 11
  6. 6
  7. 10
  8. 96
  9. 160
  10. 6
  11. 15
  12. 3
  13. 13
  14. 3
  15. 9
  16. 11
  17. 105
  18. 17
  19. 40
  20. 16
  21. 6
  22. 11
  23. 2
  24. 6
  25. 15
  26. 25
  27. 6
  28. 13
  29. 8
  30. 70
  31. 5
  32. 13
  33. 10
  34. 15
  35. 4
  36. 20
  37. 10
  38. 14
  39. 15
  40. 12

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