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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 873 · 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 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?
  2. 2.The sum of two consecutive whole numbers is 55. What is the smallest of them?
  3. 3.Solve: 3y + 1 = 2y + 16. What is y?
  4. 4.The sum of four consecutive whole numbers is 202. What is the largest of them?
  5. 5.Solve: 4y + 1 = 2y + 3. What is y?
  6. 6.Solve: t/4 + t/5 = 9. What is t?
  7. 7.Solve: 6(p − 2) = p + 58. What is p?
  8. 8.Solve: 7t + 13 = 2t + 73. What is t?
  9. 9.The sum of two consecutive whole numbers is 17. What is the smallest of them?
  10. 10.Solve: 9n + 14 = n + 46. What is n?
  11. 11.A father is 28 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  12. 12.Solve: p/2 + p/5 = 28. What is p?
  13. 13.The length of a rectangle is 11 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  14. 14.Solve: 3(n − 5) = 2n + 5. What is n?
  15. 15.Solve: 6(m − 3) = 3m + 3. What is m?
  16. 16.The sum of three consecutive whole numbers is 51. What is the smallest of them?
  17. 17.Solve: 6(n − 5) = 2n + 10. What is n?
  18. 18.A father is 48 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?
  19. 19.The sum of four consecutive whole numbers is 142. What is the largest of them?
  20. 20.Solve: 5y + 5 = 4y + 20. What is y?
  21. 21.The length of a rectangle is 8 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  22. 22.Solve: 8n + 20 = 5n + 29. What is n?
  23. 23.Solve: p/3 + p/2 = 30. What is p?
  24. 24.Solve: 8n + 1 = n + 15. What is n?
  25. 25.A father is 30 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
  26. 26.A father is 36 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  27. 27.Solve: y/5 + y/2 = 21. What is y?
  28. 28.The length of a rectangle is 6 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
  29. 29.Solve: 3(m − 1) = 2m + 3. What is m?
  30. 30.Solve: 6(n − 3) = 3n + 27. What is n?
  31. 31.The length of a rectangle is 4 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  32. 32.Solve: x/3 + x/2 = 30. What is x?
  33. 33.Solve: x/4 + x/3 = 14. What is x?
  34. 34.Solve: 3(m − 2) = m + 24. What is m?
  35. 35.The sum of four consecutive whole numbers is 246. What is the smallest of them?
  36. 36.Solve: 4(t − 3) = t + 9. What is t?
  37. 37.Solve: 4(y − 2) = y + 31. What is y?
  38. 38.Solve: x/2 + x/3 = 20. What is x?
  39. 39.Solve: 3x + 11 = x + 35. What is x?
  40. 40.Solve: 9y + 4 = 3y + 52. What is y?

Answer key

  1. 12
  2. 27
  3. 15
  4. 52
  5. 1
  6. 20
  7. 14
  8. 12
  9. 8
  10. 4
  11. 12
  12. 40
  13. 2
  14. 20
  15. 7
  16. 16
  17. 10
  18. 11
  19. 37
  20. 15
  21. 13
  22. 3
  23. 36
  24. 2
  25. 9
  26. 11
  27. 30
  28. 5
  29. 6
  30. 15
  31. 12
  32. 36
  33. 24
  34. 15
  35. 60
  36. 7
  37. 13
  38. 24
  39. 12
  40. 8

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