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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 758 · 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 8 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  2. 2.Solve: y/4 + y/5 = 9. What is y?
  3. 3.Solve: 6x + 2 = 4x + 24. What is x?
  4. 4.Solve: n/4 + n/3 = 21. What is n?
  5. 5.Solve: t/4 + t/3 = 28. What is t?
  6. 6.Solve: m/4 + m/3 = 56. What is m?
  7. 7.Solve: y/6 + y/3 = 18. What is y?
  8. 8.Solve: 7x + 2 = 4x + 5. What is x?
  9. 9.The length of a rectangle is 11 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  10. 10.A father is 12 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
  11. 11.Solve: 4(n − 2) = 3n + 7. What is n?
  12. 12.Solve: m/2 + m/6 = 28. What is m?
  13. 13.Solve: x/3 + x/4 = 49. What is x?
  14. 14.Solve: 4m + 1 = 3m + 2. What is m?
  15. 15.The length of a rectangle is 12 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  16. 16.Solve: 7n + 10 = 6n + 23. What is n?
  17. 17.The sum of three consecutive whole numbers is 27. What is the smallest of them?
  18. 18.Solve: 5y + 5 = 3y + 29. What is y?
  19. 19.Solve: n/6 + n/3 = 24. What is n?
  20. 20.The sum of four consecutive whole numbers is 46. What is the largest of them?
  21. 21.Solve: 6x + 12 = 3x + 27. What is x?
  22. 22.Solve: x/6 + x/2 = 12. What is x?
  23. 23.Solve: 3(t − 4) = 2t + 3. What is t?
  24. 24.The sum of four consecutive whole numbers is 106. What is the smallest of them?
  25. 25.Solve: t/4 + t/2 = 18. What is t?
  26. 26.Solve: m/6 + m/2 = 24. What is m?
  27. 27.The sum of two consecutive whole numbers is 105. What is the largest of them?
  28. 28.A father is 15 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  29. 29.The length of a rectangle is 13 cm more than its width. Its perimeter is 146 cm. What is its width (in cm)?
  30. 30.Solve: y/5 + y/2 = 21. What is y?
  31. 31.Solve: p/6 + p/2 = 28. What is p?
  32. 32.Solve: 6(p − 3) = 4p + 10. What is p?
  33. 33.Solve: t/4 + t/5 = 54. What is t?
  34. 34.Solve: 3t + 13 = t + 17. What is t?
  35. 35.Solve: 7p + 5 = 5p + 19. What is p?
  36. 36.The sum of three consecutive whole numbers is 108. What is the largest of them?
  37. 37.A father is 10 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  38. 38.The sum of two consecutive whole numbers is 59. What is the smallest of them?
  39. 39.Solve: 5(n − 2) = 3n + 4. What is n?
  40. 40.The length of a rectangle is 3 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?

Answer key

  1. 7
  2. 20
  3. 11
  4. 36
  5. 48
  6. 96
  7. 36
  8. 1
  9. 26
  10. 2
  11. 15
  12. 42
  13. 84
  14. 1
  15. 21
  16. 13
  17. 8
  18. 12
  19. 48
  20. 13
  21. 5
  22. 18
  23. 15
  24. 25
  25. 24
  26. 36
  27. 53
  28. 9
  29. 30
  30. 30
  31. 42
  32. 14
  33. 120
  34. 2
  35. 7
  36. 37
  37. 2
  38. 29
  39. 7
  40. 8

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