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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 307 · 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: 3(x − 4) = 2x + 9. What is x?
  2. 2.A father is 33 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?
  3. 3.Solve: 3(m − 1) = 2m + 5. What is m?
  4. 4.The length of a rectangle is 11 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  5. 5.Solve: x/5 + x/2 = 49. What is x?
  6. 6.A father is 27 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?
  7. 7.The length of a rectangle is 4 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  8. 8.Solve: 4t + 13 = 2t + 23. What is t?
  9. 9.Solve: 4y + 5 = y + 20. What is y?
  10. 10.Solve: 5(t − 3) = t + 21. What is t?
  11. 11.Solve: 3(p − 1) = 2p + 2. What is p?
  12. 12.Solve: n/3 + n/4 = 49. What is n?
  13. 13.A father is 12 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?
  14. 14.The length of a rectangle is 7 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  15. 15.Solve: 5(m − 5) = m + 15. What is m?
  16. 16.The sum of two consecutive whole numbers is 63. What is the smallest of them?
  17. 17.Solve: 3(y − 1) = 2y + 2. What is y?
  18. 18.Solve: 4(y − 1) = 2y + 8. What is y?
  19. 19.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  20. 20.Solve: 3t + 19 = t + 29. What is t?
  21. 21.Solve: 9y + 8 = 3y + 26. What is y?
  22. 22.Solve: 7n + 8 = 6n + 22. What is n?
  23. 23.Solve: 4x + 1 = 3x + 14. What is x?
  24. 24.Solve: y/6 + y/4 = 5. What is y?
  25. 25.The length of a rectangle is 14 cm more than its width. Its perimeter is 136 cm. What is its width (in cm)?
  26. 26.Solve: 8n + 2 = 7n + 17. What is n?
  27. 27.The sum of two consecutive whole numbers is 41. What is the smallest of them?
  28. 28.The length of a rectangle is 4 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  29. 29.Solve: 5(t − 3) = 3t + 1. What is t?
  30. 30.A father is 21 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  31. 31.Solve: y/5 + y/3 = 56. What is y?
  32. 32.A father is 20 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  33. 33.Solve: 7m + 6 = 4m + 33. What is m?
  34. 34.Solve: n/6 + n/5 = 88. What is n?
  35. 35.The sum of four consecutive whole numbers is 174. What is the largest of them?
  36. 36.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?
  37. 37.A father is 11 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  38. 38.Solve: 6(m − 3) = 2m + 10. What is m?
  39. 39.A father is 27 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  40. 40.Solve: y/4 + y/5 = 54. What is y?

Answer key

  1. 21
  2. 5
  3. 8
  4. 21
  5. 70
  6. 8
  7. 19
  8. 5
  9. 5
  10. 9
  11. 5
  12. 84
  13. 5
  14. 25
  15. 10
  16. 31
  17. 5
  18. 6
  19. 6
  20. 5
  21. 3
  22. 14
  23. 13
  24. 12
  25. 27
  26. 15
  27. 20
  28. 18
  29. 8
  30. 4
  31. 105
  32. 12
  33. 9
  34. 240
  35. 45
  36. 7
  37. 10
  38. 7
  39. 4
  40. 120

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