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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 786 · 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: n/4 + n/3 = 42. What is n?
  2. 2.Solve: 3t + 17 = t + 27. What is t?
  3. 3.The sum of three consecutive whole numbers is 69. What is the smallest of them?
  4. 4.Solve: y/6 + y/3 = 21. What is y?
  5. 5.The sum of two consecutive whole numbers is 41. What is the smallest of them?
  6. 6.Solve: 4(m − 2) = 2m + 4. What is m?
  7. 7.Solve: 6y + 20 = 5y + 29. What is y?
  8. 8.The sum of two consecutive whole numbers is 59. What is the largest of them?
  9. 9.A father is 7 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  10. 10.Solve: 3(y − 1) = 2y + 12. What is y?
  11. 11.The length of a rectangle is 6 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  12. 12.The sum of three consecutive whole numbers is 69. What is the largest of them?
  13. 13.Solve: 5(y − 4) = 3y + 10. What is y?
  14. 14.Solve: 5p + 7 = 2p + 31. What is p?
  15. 15.Solve: 6(x − 2) = 5x + 12. What is x?
  16. 16.Solve: 4(x − 1) = x + 14. What is x?
  17. 17.Solve: y/5 + y/6 = 55. What is y?
  18. 18.A father is 36 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
  19. 19.Solve: 5(y − 5) = 3y + 21. What is y?
  20. 20.The sum of three consecutive whole numbers is 81. What is the smallest of them?
  21. 21.Solve: 3(y − 1) = 2y + 2. What is y?
  22. 22.The sum of three consecutive whole numbers is 33. What is the largest of them?
  23. 23.Solve: 7m + 11 = 6m + 14. What is m?
  24. 24.Solve: 5(m − 1) = 2m + 10. What is m?
  25. 25.Solve: 3(p − 1) = p + 23. What is p?
  26. 26.The sum of three consecutive whole numbers is 174. What is the smallest of them?
  27. 27.A father is 48 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 4 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  29. 29.Solve: x/3 + x/4 = 56. What is x?
  30. 30.The length of a rectangle is 2 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  31. 31.The length of a rectangle is 7 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  32. 32.Solve: 3p + 2 = p + 24. What is p?
  33. 33.Solve: 7y + 6 = 5y + 32. What is y?
  34. 34.The sum of two consecutive whole numbers is 117. What is the largest of them?
  35. 35.The sum of two consecutive whole numbers is 95. What is the largest of them?
  36. 36.Solve: n/6 + n/4 = 15. What is n?
  37. 37.The sum of four consecutive whole numbers is 138. What is the largest of them?
  38. 38.A father is 13 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  39. 39.A father is 12 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  40. 40.The length of a rectangle is 11 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?

Answer key

  1. 72
  2. 5
  3. 22
  4. 42
  5. 20
  6. 6
  7. 9
  8. 30
  9. 3
  10. 15
  11. 27
  12. 24
  13. 15
  14. 8
  15. 24
  16. 6
  17. 150
  18. 6
  19. 23
  20. 26
  21. 5
  22. 12
  23. 3
  24. 5
  25. 13
  26. 57
  27. 8
  28. 22
  29. 96
  30. 9
  31. 23
  32. 11
  33. 13
  34. 59
  35. 48
  36. 36
  37. 36
  38. 6
  39. 2
  40. 20

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