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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 28 · 40 sums
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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.The sum of four consecutive whole numbers is 230. What is the smallest of them?
  2. 2.The length of a rectangle is 10 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  3. 3.The length of a rectangle is 14 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  4. 4.The length of a rectangle is 3 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  5. 5.Solve: 3m + 9 = m + 23. What is m?
  6. 6.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?
  7. 7.Solve: 7t + 3 = 6t + 5. What is t?
  8. 8.The sum of two consecutive whole numbers is 77. What is the smallest of them?
  9. 9.Solve: 4(y − 3) = 3y + 1. What is y?
  10. 10.The sum of three consecutive whole numbers is 27. What is the smallest of them?
  11. 11.Solve: 8y + 11 = y + 60. What is y?
  12. 12.A father is 5 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  13. 13.Solve: 5(y − 5) = y + 35. What is y?
  14. 14.Solve: 8x + 2 = 6x + 26. What is x?
  15. 15.Solve: 5(n − 2) = n + 38. What is n?
  16. 16.The sum of three consecutive whole numbers is 54. What is the largest of them?
  17. 17.The length of a rectangle is 4 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
  18. 18.The length of a rectangle is 13 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  19. 19.Solve: x/3 + x/4 = 56. What is x?
  20. 20.Solve: p/6 + p/2 = 20. What is p?
  21. 21.A father is 51 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?
  22. 22.The length of a rectangle is 4 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
  23. 23.Solve: 3t + 11 = 2t + 19. What is t?
  24. 24.Solve: y/2 + y/6 = 32. What is y?
  25. 25.Solve: 3(t − 4) = t + 26. What is t?
  26. 26.Solve: 6(x − 1) = 3x + 27. What is x?
  27. 27.Solve: 3(p − 5) = p + 1. What is p?
  28. 28.A father is 26 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?
  29. 29.The sum of two consecutive whole numbers is 37. What is the smallest of them?
  30. 30.Solve: 8n + 1 = 4n + 29. What is n?
  31. 31.Solve: 6t + 1 = 5t + 10. What is t?
  32. 32.Solve: 9p + 11 = 7p + 39. What is p?
  33. 33.Solve: 5(m − 1) = 2m + 4. What is m?
  34. 34.Solve: 5(n − 2) = 3n + 12. What is n?
  35. 35.Solve: 5(n − 4) = 2n + 7. What is n?
  36. 36.Solve: 3(t − 3) = t + 3. What is t?
  37. 37.Solve: y/2 + y/6 = 12. What is y?
  38. 38.Solve: 7x + 10 = 2x + 85. What is x?
  39. 39.Solve: 8y + 17 = 3y + 47. What is y?
  40. 40.The sum of two consecutive whole numbers is 55. What is the smallest of them?

Answer key

  1. 56
  2. 14
  3. 7
  4. 16
  5. 7
  6. 10
  7. 2
  8. 38
  9. 13
  10. 8
  11. 7
  12. 4
  13. 15
  14. 12
  15. 12
  16. 19
  17. 30
  18. 6
  19. 96
  20. 30
  21. 12
  22. 3
  23. 8
  24. 48
  25. 19
  26. 11
  27. 8
  28. 12
  29. 18
  30. 7
  31. 9
  32. 14
  33. 3
  34. 11
  35. 9
  36. 6
  37. 18
  38. 15
  39. 6
  40. 27

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