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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 6 · 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.Solve: n/6 + n/5 = 44. What is n?
  2. 2.The length of a rectangle is 8 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  3. 3.Solve: 5(n − 3) = 2n + 21. What is n?
  4. 4.Solve: 5n + 2 = n + 6. What is n?
  5. 5.The length of a rectangle is 12 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  6. 6.Solve: 4(x − 2) = 3x + 3. What is x?
  7. 7.Solve: x/6 + x/3 = 9. What is x?
  8. 8.The length of a rectangle is 12 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  9. 9.Solve: m/2 + m/5 = 7. What is m?
  10. 10.Solve: 4(x − 2) = x + 4. What is x?
  11. 11.Solve: 5y + 8 = 3y + 36. What is y?
  12. 12.Solve: 3p + 14 = p + 16. What is p?
  13. 13.Solve: 8y + 10 = y + 38. What is y?
  14. 14.The sum of two consecutive whole numbers is 53. What is the smallest of them?
  15. 15.Solve: n/5 + n/4 = 63. What is n?
  16. 16.Solve: 4(m − 5) = m + 10. What is m?
  17. 17.Solve: 9t + 1 = 4t + 66. What is t?
  18. 18.A father is 51 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  19. 19.Solve: 5(x − 1) = 3x + 5. What is x?
  20. 20.The length of a rectangle is 5 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  21. 21.Solve: 6(m − 5) = 5m + 6. What is m?
  22. 22.Solve: 3n + 16 = n + 42. What is n?
  23. 23.Solve: 4(t − 5) = t + 31. What is t?
  24. 24.Solve: 5x + 3 = 3x + 17. What is x?
  25. 25.The length of a rectangle is 13 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  26. 26.Solve: 8t + 16 = 3t + 41. What is t?
  27. 27.Solve: 8y + 7 = 7y + 10. What is y?
  28. 28.A father is 10 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 length of a rectangle is 12 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  30. 30.A father is 51 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  31. 31.The length of a rectangle is 1 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  32. 32.The length of a rectangle is 4 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  33. 33.Solve: 8y + 1 = 3y + 26. What is y?
  34. 34.The sum of two consecutive whole numbers is 25. What is the largest of them?
  35. 35.Solve: 6(y − 1) = y + 24. What is y?
  36. 36.Solve: x/6 + x/3 = 6. What is x?
  37. 37.Solve: y/4 + y/3 = 7. What is y?
  38. 38.Solve: 5(y − 4) = y + 20. What is y?
  39. 39.Solve: 5n + 2 = 4n + 5. What is n?
  40. 40.Solve: 6n + 10 = 5n + 20. What is n?

Answer key

  1. 120
  2. 7
  3. 12
  4. 1
  5. 9
  6. 11
  7. 18
  8. 6
  9. 10
  10. 4
  11. 14
  12. 1
  13. 4
  14. 26
  15. 140
  16. 10
  17. 13
  18. 9
  19. 5
  20. 7
  21. 36
  22. 13
  23. 17
  24. 7
  25. 25
  26. 5
  27. 3
  28. 4
  29. 10
  30. 10
  31. 30
  32. 5
  33. 5
  34. 13
  35. 6
  36. 12
  37. 12
  38. 10
  39. 3
  40. 10

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