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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 725 · 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 34 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?
  2. 2.Solve: t/3 + t/5 = 32. What is t?
  3. 3.Solve: p/6 + p/2 = 12. What is p?
  4. 4.The length of a rectangle is 4 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
  5. 5.The sum of four consecutive whole numbers is 86. What is the smallest of them?
  6. 6.The length of a rectangle is 7 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  7. 7.The sum of two consecutive whole numbers is 85. What is the smallest of them?
  8. 8.Solve: n/6 + n/3 = 3. What is n?
  9. 9.Solve: y/5 + y/3 = 32. What is y?
  10. 10.The length of a rectangle is 13 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  11. 11.The length of a rectangle is 15 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  12. 12.A father is 54 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?
  13. 13.Solve: 3(x − 4) = 2x + 9. What is x?
  14. 14.Solve: 3(y − 2) = y + 26. What is y?
  15. 15.Solve: p/4 + p/6 = 20. What is p?
  16. 16.The sum of two consecutive whole numbers is 19. What is the largest of them?
  17. 17.A father is 36 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?
  18. 18.A father is 36 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?
  19. 19.Solve: n/4 + n/2 = 21. What is n?
  20. 20.A father is 28 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?
  21. 21.The sum of two consecutive whole numbers is 97. What is the smallest of them?
  22. 22.Solve: 7y + 20 = 6y + 21. What is y?
  23. 23.Solve: y/2 + y/3 = 5. What is y?
  24. 24.The length of a rectangle is 1 cm more than its width. Its perimeter is 10 cm. What is its width (in cm)?
  25. 25.A father is 26 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  26. 26.Solve: 5m + 12 = 2m + 42. What is m?
  27. 27.Solve: p/2 + p/3 = 40. What is p?
  28. 28.Solve: 6(x − 2) = 2x + 44. What is x?
  29. 29.Solve: m/2 + m/3 = 35. What is m?
  30. 30.Solve: 4p + 9 = p + 21. What is p?
  31. 31.Solve: 3(x − 3) = 2x + 13. What is x?
  32. 32.The sum of two consecutive whole numbers is 47. What is the largest of them?
  33. 33.Solve: 5(t − 4) = 4t + 2. What is t?
  34. 34.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  35. 35.Solve: n/4 + n/3 = 7. What is n?
  36. 36.Solve: 5p + 19 = 3p + 29. What is p?
  37. 37.Solve: y/3 + y/4 = 49. What is y?
  38. 38.Solve: 4m + 11 = 3m + 19. What is m?
  39. 39.Solve: 4x + 15 = x + 48. What is x?
  40. 40.Solve: 3x + 17 = x + 23. What is x?

Answer key

  1. 10
  2. 60
  3. 18
  4. 3
  5. 20
  6. 12
  7. 42
  8. 6
  9. 60
  10. 7
  11. 10
  12. 12
  13. 21
  14. 16
  15. 48
  16. 10
  17. 9
  18. 10
  19. 28
  20. 10
  21. 48
  22. 1
  23. 6
  24. 2
  25. 10
  26. 10
  27. 48
  28. 14
  29. 42
  30. 4
  31. 22
  32. 24
  33. 22
  34. 6
  35. 12
  36. 5
  37. 84
  38. 8
  39. 11
  40. 3

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