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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 249 · 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.A father is 17 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  2. 2.A father is 15 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  3. 3.Solve: 3(n − 1) = 2n + 7. What is n?
  4. 4.Solve: y/3 + y/5 = 64. What is y?
  5. 5.The length of a rectangle is 4 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  6. 6.Solve: 8n + 20 = 4n + 36. What is n?
  7. 7.Solve: t/2 + t/3 = 30. What is t?
  8. 8.Solve: 5(p − 5) = 2p + 14. What is p?
  9. 9.Solve: y/4 + y/5 = 9. What is y?
  10. 10.Solve: p/6 + p/3 = 15. What is p?
  11. 11.Solve: 8x + 8 = 2x + 44. What is x?
  12. 12.Solve: 8p + 18 = 7p + 23. What is p?
  13. 13.Solve: 9x + 7 = 6x + 46. What is x?
  14. 14.A father is 12 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  15. 15.Solve: p/6 + p/5 = 22. What is p?
  16. 16.Solve: n/2 + n/6 = 32. What is n?
  17. 17.Solve: x/4 + x/5 = 54. What is x?
  18. 18.The length of a rectangle is 3 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
  19. 19.Solve: 3n + 14 = 2n + 16. What is n?
  20. 20.A father is 30 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
  21. 21.Solve: 8t + 13 = 6t + 17. What is t?
  22. 22.Solve: 5(x − 3) = 4x + 4. What is x?
  23. 23.A father is 15 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?
  24. 24.A father is 51 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  25. 25.Solve: x/2 + x/3 = 20. What is x?
  26. 26.The length of a rectangle is 11 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  27. 27.A father is 42 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  28. 28.The length of a rectangle is 3 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  29. 29.Solve: t/4 + t/2 = 6. What is t?
  30. 30.Solve: 8m + 17 = 2m + 47. What is m?
  31. 31.Solve: y/6 + y/5 = 33. What is y?
  32. 32.Solve: 4(y − 4) = 3y + 1. What is y?
  33. 33.The sum of two consecutive whole numbers is 51. What is the smallest of them?
  34. 34.Solve: 5(t − 2) = 3t + 14. What is t?
  35. 35.Solve: 5(x − 1) = 2x + 25. What is x?
  36. 36.The sum of two consecutive whole numbers is 57. What is the largest of them?
  37. 37.A father is 9 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  38. 38.Solve: t/6 + t/2 = 24. What is t?
  39. 39.Solve: 3(x − 3) = 2x + 3. What is x?
  40. 40.A father is 4 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?

Answer key

  1. 10
  2. 7
  3. 10
  4. 120
  5. 26
  6. 4
  7. 36
  8. 13
  9. 20
  10. 30
  11. 6
  12. 5
  13. 13
  14. 4
  15. 60
  16. 48
  17. 120
  18. 3
  19. 2
  20. 9
  21. 2
  22. 19
  23. 4
  24. 9
  25. 24
  26. 14
  27. 6
  28. 30
  29. 8
  30. 5
  31. 90
  32. 17
  33. 25
  34. 12
  35. 10
  36. 29
  37. 6
  38. 36
  39. 12
  40. 2

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