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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 828 · 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 three consecutive whole numbers is 180. What is the largest of them?
  2. 2.A father is 30 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?
  3. 3.Solve: 3n + 1 = 2n + 14. What is n?
  4. 4.Solve: n/2 + n/6 = 24. What is n?
  5. 5.The length of a rectangle is 1 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  6. 6.Solve: 4(y − 2) = 3y + 13. What is y?
  7. 7.Solve: 5(m − 2) = m + 22. What is m?
  8. 8.Solve: 3y + 5 = y + 9. What is y?
  9. 9.The sum of four consecutive whole numbers is 58. What is the largest of them?
  10. 10.Solve: x/6 + x/2 = 4. What is x?
  11. 11.The length of a rectangle is 5 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  12. 12.The sum of three consecutive whole numbers is 123. What is the smallest of them?
  13. 13.A father is 13 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  14. 14.A father is 14 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?
  15. 15.Solve: t/2 + t/5 = 21. What is t?
  16. 16.The length of a rectangle is 8 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  17. 17.Solve: 7m + 7 = m + 13. What is m?
  18. 18.Solve: 3p + 3 = 2p + 17. What is p?
  19. 19.Solve: 7n + 7 = 6n + 11. What is n?
  20. 20.Solve: 5(t − 5) = 4t + 11. What is t?
  21. 21.Solve: n/4 + n/3 = 42. What is n?
  22. 22.The length of a rectangle is 5 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  23. 23.Solve: 5y + 1 = 3y + 5. What is y?
  24. 24.The length of a rectangle is 12 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  25. 25.The length of a rectangle is 15 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
  26. 26.Solve: y/6 + y/4 = 10. What is y?
  27. 27.Solve: 8x + 18 = 6x + 20. What is x?
  28. 28.Solve: 3(m − 5) = m + 1. What is m?
  29. 29.Solve: 6(y − 2) = y + 53. What is y?
  30. 30.Solve: 7y + 12 = 2y + 82. What is y?
  31. 31.Solve: x/4 + x/5 = 54. What is x?
  32. 32.Solve: 8p + 9 = p + 93. What is p?
  33. 33.Solve: 4t + 11 = 2t + 33. What is t?
  34. 34.A father is 4 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  35. 35.Solve: 3(t − 2) = t + 6. What is t?
  36. 36.Solve: 3y + 4 = 2y + 17. What is y?
  37. 37.Solve: 3x + 8 = 2x + 12. What is x?
  38. 38.The length of a rectangle is 11 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
  39. 39.The length of a rectangle is 9 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  40. 40.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?

Answer key

  1. 61
  2. 3
  3. 13
  4. 36
  5. 19
  6. 21
  7. 8
  8. 2
  9. 16
  10. 6
  11. 12
  12. 40
  13. 8
  14. 3
  15. 30
  16. 21
  17. 1
  18. 14
  19. 4
  20. 36
  21. 72
  22. 21
  23. 2
  24. 18
  25. 13
  26. 24
  27. 1
  28. 8
  29. 13
  30. 14
  31. 120
  32. 12
  33. 11
  34. 3
  35. 6
  36. 13
  37. 4
  38. 28
  39. 9
  40. 7

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