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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 571 · 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: 8t + 19 = 6t + 27. What is t?
  2. 2.Solve: 6(n − 4) = 3n + 15. What is n?
  3. 3.Solve: 5(x − 5) = 3x + 19. What is x?
  4. 4.Solve: n/5 + n/6 = 77. What is n?
  5. 5.The sum of two consecutive whole numbers is 51. What is the smallest of them?
  6. 6.The sum of four consecutive whole numbers is 110. What is the largest of them?
  7. 7.The length of a rectangle is 3 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  8. 8.The length of a rectangle is 3 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  9. 9.Solve: x/4 + x/5 = 36. What is x?
  10. 10.Solve: 4x + 9 = 3x + 23. What is x?
  11. 11.A father is 18 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?
  12. 12.Solve: 5(y − 5) = y + 31. What is y?
  13. 13.The sum of two consecutive whole numbers is 59. What is the smallest of them?
  14. 14.Solve: 3(m − 4) = 2m + 4. What is m?
  15. 15.The sum of four consecutive whole numbers is 74. What is the smallest of them?
  16. 16.A father is 26 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?
  17. 17.A father is 45 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  18. 18.The sum of four consecutive whole numbers is 222. What is the largest of them?
  19. 19.Solve: 7x + 12 = x + 30. What is x?
  20. 20.Solve: 8x + 4 = 4x + 48. What is x?
  21. 21.Solve: 5(n − 5) = 3n + 17. What is n?
  22. 22.Solve: 5(m − 5) = 2m + 17. What is m?
  23. 23.Solve: t/3 + t/2 = 30. What is t?
  24. 24.A father is 14 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?
  25. 25.The length of a rectangle is 6 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  26. 26.Solve: 6t + 4 = 3t + 13. What is t?
  27. 27.Solve: 3(y − 3) = 2y + 10. What is y?
  28. 28.A father is 24 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?
  29. 29.The length of a rectangle is 8 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  30. 30.Solve: 9m + 3 = 4m + 38. What is m?
  31. 31.Solve: 5(n − 3) = 4n + 10. What is n?
  32. 32.The length of a rectangle is 15 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  33. 33.Solve: 4n + 7 = 2n + 21. What is n?
  34. 34.Solve: n/3 + n/2 = 40. What is n?
  35. 35.Solve: 4n + 13 = 3n + 26. What is n?
  36. 36.The sum of two consecutive whole numbers is 121. What is the largest of them?
  37. 37.The length of a rectangle is 10 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  38. 38.Solve: x/4 + x/3 = 35. What is x?
  39. 39.Solve: 8n + 10 = 5n + 40. What is n?
  40. 40.The length of a rectangle is 10 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?

Answer key

  1. 4
  2. 13
  3. 22
  4. 210
  5. 25
  6. 29
  7. 11
  8. 21
  9. 80
  10. 14
  11. 5
  12. 14
  13. 29
  14. 16
  15. 17
  16. 8
  17. 11
  18. 57
  19. 3
  20. 11
  21. 21
  22. 14
  23. 36
  24. 5
  25. 8
  26. 3
  27. 19
  28. 9
  29. 21
  30. 7
  31. 25
  32. 18
  33. 7
  34. 48
  35. 13
  36. 61
  37. 9
  38. 60
  39. 10
  40. 14

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