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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 721 · 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 9 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?
  2. 2.The length of a rectangle is 6 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  3. 3.Solve: 6(t − 2) = t + 48. What is t?
  4. 4.The sum of three consecutive whole numbers is 60. What is the largest of them?
  5. 5.Solve: 4y + 11 = 3y + 26. What is y?
  6. 6.Solve: 6y + 10 = 3y + 49. What is y?
  7. 7.A father is 8 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  8. 8.Solve: x/2 + x/6 = 4. What is x?
  9. 9.Solve: 7x + 19 = 2x + 39. What is x?
  10. 10.Solve: 5m + 6 = m + 22. What is m?
  11. 11.A father is 30 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?
  12. 12.Solve: 6(t − 5) = 3t + 33. What is t?
  13. 13.A father is 10 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  14. 14.Solve: t/5 + t/6 = 22. What is t?
  15. 15.The length of a rectangle is 7 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
  16. 16.A father is 39 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  17. 17.The sum of two consecutive whole numbers is 67. What is the largest of them?
  18. 18.The length of a rectangle is 14 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  19. 19.The sum of two consecutive whole numbers is 77. What is the largest of them?
  20. 20.Solve: y/3 + y/6 = 21. What is y?
  21. 21.Solve: x/6 + x/5 = 66. What is x?
  22. 22.The length of a rectangle is 2 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  23. 23.Solve: 6(x − 3) = 4x + 16. What is x?
  24. 24.The length of a rectangle is 5 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  25. 25.Solve: 6(t − 4) = t + 61. What is t?
  26. 26.Solve: 4n + 3 = 2n + 23. What is n?
  27. 27.The sum of two consecutive whole numbers is 115. What is the smallest of them?
  28. 28.Solve: 9t + 5 = 4t + 75. What is t?
  29. 29.Solve: 3m + 19 = m + 41. What is m?
  30. 30.The sum of three consecutive whole numbers is 162. What is the smallest of them?
  31. 31.Solve: x/5 + x/4 = 27. What is x?
  32. 32.The sum of four consecutive whole numbers is 206. What is the smallest of them?
  33. 33.Solve: n/6 + n/4 = 35. What is n?
  34. 34.The sum of four consecutive whole numbers is 74. What is the smallest of them?
  35. 35.The sum of three consecutive whole numbers is 120. What is the smallest of them?
  36. 36.Solve: 6(p − 3) = 5p + 2. What is p?
  37. 37.Solve: n/6 + n/4 = 30. What is n?
  38. 38.Solve: x/5 + x/3 = 8. What is x?
  39. 39.Solve: 5(n − 5) = 3n + 15. What is n?
  40. 40.A father is 6 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?

Answer key

  1. 2
  2. 27
  3. 12
  4. 21
  5. 15
  6. 13
  7. 6
  8. 6
  9. 4
  10. 4
  11. 11
  12. 21
  13. 8
  14. 60
  15. 29
  16. 6
  17. 34
  18. 9
  19. 39
  20. 42
  21. 180
  22. 30
  23. 17
  24. 16
  25. 17
  26. 10
  27. 57
  28. 14
  29. 11
  30. 53
  31. 60
  32. 50
  33. 84
  34. 17
  35. 39
  36. 20
  37. 72
  38. 15
  39. 20
  40. 2

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