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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 644 · 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.The sum of two consecutive whole numbers is 57. What is the largest of them?
  2. 2.A father is 34 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
  3. 3.Solve: 6(x − 1) = 5x + 4. What is x?
  4. 4.The sum of three consecutive whole numbers is 33. What is the smallest of them?
  5. 5.Solve: 6(n − 4) = 5n + 2. What is n?
  6. 6.Solve: y/3 + y/4 = 42. What is y?
  7. 7.Solve: 3p + 6 = p + 30. What is p?
  8. 8.Solve: 4y + 8 = 3y + 10. What is y?
  9. 9.Solve: x/2 + x/3 = 5. What is x?
  10. 10.The sum of four consecutive whole numbers is 86. What is the largest of them?
  11. 11.Solve: 5(x − 1) = 2x + 16. What is x?
  12. 12.Solve: 6m + 18 = 5m + 29. What is m?
  13. 13.Solve: n/5 + n/3 = 48. What is n?
  14. 14.Solve: 6(t − 2) = 2t + 8. What is t?
  15. 15.The sum of three consecutive whole numbers is 180. What is the smallest of them?
  16. 16.The sum of three consecutive whole numbers is 168. What is the smallest of them?
  17. 17.Solve: 7y + 14 = 3y + 74. What is y?
  18. 18.The length of a rectangle is 10 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  19. 19.The length of a rectangle is 6 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  20. 20.Solve: 6(y − 5) = 2y + 6. What is y?
  21. 21.The length of a rectangle is 11 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  22. 22.A father is 19 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  23. 23.Solve: t/3 + t/5 = 56. What is t?
  24. 24.A father is 13 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  25. 25.Solve: 3p + 15 = 2p + 20. What is p?
  26. 26.Solve: t/6 + t/4 = 10. What is t?
  27. 27.The sum of three consecutive whole numbers is 165. What is the smallest of them?
  28. 28.The sum of two consecutive whole numbers is 17. What is the smallest of them?
  29. 29.Solve: 4y + 6 = y + 18. What is y?
  30. 30.Solve: 8n + 10 = 3n + 70. What is n?
  31. 31.Solve: 6m + 1 = 4m + 15. What is m?
  32. 32.The length of a rectangle is 13 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  33. 33.Solve: 3(n − 1) = 2n + 8. What is n?
  34. 34.Solve: 8n + 7 = 4n + 39. What is n?
  35. 35.The sum of two consecutive whole numbers is 113. What is the smallest of them?
  36. 36.Solve: 4(y − 1) = 2y + 22. What is y?
  37. 37.A father is 12 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  38. 38.Solve: 8p + 9 = 2p + 63. What is p?
  39. 39.The length of a rectangle is 9 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  40. 40.Solve: 6p + 1 = p + 56. What is p?

Answer key

  1. 29
  2. 12
  3. 10
  4. 10
  5. 26
  6. 72
  7. 12
  8. 2
  9. 6
  10. 23
  11. 7
  12. 11
  13. 90
  14. 5
  15. 59
  16. 55
  17. 15
  18. 21
  19. 4
  20. 9
  21. 14
  22. 11
  23. 105
  24. 9
  25. 5
  26. 24
  27. 54
  28. 8
  29. 4
  30. 12
  31. 7
  32. 10
  33. 11
  34. 8
  35. 56
  36. 13
  37. 5
  38. 9
  39. 21
  40. 11

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