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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 52 · 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: 4n + 6 = 3n + 7. What is n?
  2. 2.Solve: 6(x − 5) = 3x + 6. What is x?
  3. 3.The length of a rectangle is 14 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  4. 4.The sum of three consecutive whole numbers is 168. What is the smallest of them?
  5. 5.Solve: 3(m − 4) = 2m + 5. What is m?
  6. 6.Solve: 6(p − 4) = p + 11. What is p?
  7. 7.Solve: 4t + 14 = 3t + 28. What is t?
  8. 8.The length of a rectangle is 9 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  9. 9.A father is 17 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  10. 10.Solve: 3(n − 5) = 2n + 3. What is n?
  11. 11.The length of a rectangle is 4 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  12. 12.Solve: 3(x − 5) = x + 11. What is x?
  13. 13.Solve: 9x + 13 = 2x + 62. What is x?
  14. 14.Solve: 3(y − 5) = 2y + 9. What is y?
  15. 15.A father is 11 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  16. 16.Solve: 9p + 6 = p + 22. What is p?
  17. 17.Solve: x/3 + x/4 = 14. What is x?
  18. 18.Solve: 4(p − 1) = 2p + 14. What is p?
  19. 19.Solve: 3(x − 3) = 2x + 11. What is x?
  20. 20.A father is 10 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  21. 21.The length of a rectangle is 7 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  22. 22.The length of a rectangle is 15 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  23. 23.Solve: 5y + 3 = 2y + 15. What is y?
  24. 24.Solve: 6(t − 2) = t + 3. What is t?
  25. 25.Solve: m/2 + m/5 = 49. What is m?
  26. 26.Solve: t/3 + t/4 = 49. What is t?
  27. 27.A father is 32 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
  28. 28.Solve: 8n + 9 = 5n + 54. What is n?
  29. 29.A father is 4 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  30. 30.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?
  31. 31.The sum of three consecutive whole numbers is 21. What is the smallest of them?
  32. 32.A father is 30 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?
  33. 33.Solve: y/2 + y/5 = 14. What is y?
  34. 34.Solve: 4y + 9 = y + 24. What is y?
  35. 35.Solve: x/5 + x/6 = 33. What is x?
  36. 36.A father is 15 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  37. 37.A father is 30 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
  38. 38.Solve: 6(n − 5) = 5n + 2. What is n?
  39. 39.Solve: 7t + 13 = 2t + 18. What is t?
  40. 40.Solve: 8y + 2 = 2y + 38. What is y?

Answer key

  1. 1
  2. 12
  3. 18
  4. 55
  5. 17
  6. 7
  7. 14
  8. 3
  9. 10
  10. 18
  11. 19
  12. 13
  13. 7
  14. 24
  15. 3
  16. 2
  17. 24
  18. 9
  19. 20
  20. 4
  21. 11
  22. 7
  23. 4
  24. 3
  25. 70
  26. 84
  27. 8
  28. 15
  29. 2
  30. 3
  31. 6
  32. 9
  33. 20
  34. 5
  35. 90
  36. 12
  37. 10
  38. 32
  39. 1
  40. 6

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