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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 685 · 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: 5n + 14 = 3n + 18. What is n?
  2. 2.Solve: 3t + 10 = t + 36. What is t?
  3. 3.Solve: n/5 + n/3 = 16. What is n?
  4. 4.Solve: p/5 + p/4 = 18. What is p?
  5. 5.The sum of two consecutive whole numbers is 61. What is the largest of them?
  6. 6.The length of a rectangle is 4 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  7. 7.Solve: 4(x − 2) = x + 10. What is x?
  8. 8.The length of a rectangle is 14 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  9. 9.Solve: 3(t − 1) = t + 3. What is t?
  10. 10.Solve: n/2 + n/5 = 56. What is n?
  11. 11.The sum of four consecutive whole numbers is 206. What is the smallest of them?
  12. 12.Solve: 6n + 1 = n + 16. What is n?
  13. 13.Solve: 4y + 4 = 3y + 10. What is y?
  14. 14.The sum of two consecutive whole numbers is 107. What is the largest of them?
  15. 15.Solve: 7y + 4 = 5y + 32. What is y?
  16. 16.A father is 30 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?
  17. 17.Solve: p/2 + p/3 = 15. What is p?
  18. 18.The length of a rectangle is 2 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  19. 19.Solve: 3(p − 1) = 2p + 6. What is p?
  20. 20.Solve: p/5 + p/4 = 54. What is p?
  21. 21.The length of a rectangle is 12 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  22. 22.Solve: 6(x − 4) = 2x + 24. What is x?
  23. 23.Solve: p/2 + p/4 = 3. What is p?
  24. 24.The sum of three consecutive whole numbers is 138. What is the smallest of them?
  25. 25.The sum of three consecutive whole numbers is 132. What is the largest of them?
  26. 26.Solve: m/6 + m/3 = 9. What is m?
  27. 27.A father is 36 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?
  28. 28.A father is 24 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?
  29. 29.The sum of three consecutive whole numbers is 21. What is the largest of them?
  30. 30.Solve: 3y + 1 = y + 17. What is y?
  31. 31.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?
  32. 32.A father is 15 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  33. 33.Solve: 4x + 4 = 2x + 26. What is x?
  34. 34.The sum of two consecutive whole numbers is 11. What is the largest of them?
  35. 35.The sum of three consecutive whole numbers is 54. What is the smallest of them?
  36. 36.Solve: 4m + 5 = 2m + 31. What is m?
  37. 37.Solve: 4(x − 4) = x + 17. What is x?
  38. 38.Solve: 4t + 6 = 2t + 12. What is t?
  39. 39.Solve: 3x + 7 = 2x + 20. What is x?
  40. 40.The length of a rectangle is 8 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?

Answer key

  1. 2
  2. 13
  3. 30
  4. 40
  5. 31
  6. 8
  7. 6
  8. 13
  9. 3
  10. 80
  11. 50
  12. 3
  13. 6
  14. 54
  15. 14
  16. 12
  17. 18
  18. 22
  19. 9
  20. 120
  21. 23
  22. 12
  23. 4
  24. 45
  25. 45
  26. 18
  27. 7
  28. 4
  29. 8
  30. 8
  31. 11
  32. 4
  33. 11
  34. 6
  35. 17
  36. 13
  37. 11
  38. 3
  39. 13
  40. 20

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