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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 682 · 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: 5(y − 3) = y + 5. What is y?
  2. 2.A father is 7 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  3. 3.Solve: 7p + 1 = p + 31. What is p?
  4. 4.Solve: x/5 + x/3 = 56. What is x?
  5. 5.Solve: 6n + 13 = 2n + 69. What is n?
  6. 6.Solve: 4(x − 5) = 3x + 13. What is x?
  7. 7.Solve: 5(m − 1) = m + 51. What is m?
  8. 8.The length of a rectangle is 1 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
  9. 9.The length of a rectangle is 15 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
  10. 10.Solve: 3(m − 2) = m + 22. What is m?
  11. 11.Solve: 5(x − 4) = 4x + 12. What is x?
  12. 12.Solve: 4(y − 4) = y + 35. What is y?
  13. 13.The sum of four consecutive whole numbers is 34. What is the smallest of them?
  14. 14.The length of a rectangle is 6 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  15. 15.The sum of three consecutive whole numbers is 21. What is the largest of them?
  16. 16.Solve: n/2 + n/5 = 28. What is n?
  17. 17.Solve: 7n + 9 = n + 27. What is n?
  18. 18.The sum of two consecutive whole numbers is 13. What is the largest of them?
  19. 19.Solve: 5(y − 5) = y + 27. What is y?
  20. 20.The length of a rectangle is 8 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  21. 21.Solve: x/2 + x/3 = 5. What is x?
  22. 22.A father is 12 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  23. 23.Solve: 5n + 5 = 4n + 10. What is n?
  24. 24.A father is 40 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?
  25. 25.Solve: 8x + 8 = 2x + 74. What is x?
  26. 26.Solve: 9n + 8 = n + 16. What is n?
  27. 27.Solve: y/4 + y/3 = 49. What is y?
  28. 28.Solve: 6(n − 5) = n + 65. What is n?
  29. 29.Solve: 3(y − 3) = 2y + 3. What is y?
  30. 30.The sum of three consecutive whole numbers is 105. What is the largest of them?
  31. 31.A father is 9 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  32. 32.The sum of two consecutive whole numbers is 55. What is the largest of them?
  33. 33.Solve: 4(t − 5) = 3t + 2. What is t?
  34. 34.Solve: 3(m − 1) = 2m + 2. What is m?
  35. 35.Solve: p/5 + p/3 = 48. What is p?
  36. 36.The length of a rectangle is 6 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  37. 37.A father is 13 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  38. 38.Solve: m/4 + m/5 = 54. What is m?
  39. 39.Solve: 4y + 4 = y + 31. What is y?
  40. 40.Solve: 6(x − 4) = 3x + 6. What is x?

Answer key

  1. 5
  2. 6
  3. 5
  4. 105
  5. 14
  6. 33
  7. 14
  8. 4
  9. 26
  10. 14
  11. 32
  12. 17
  13. 7
  14. 13
  15. 8
  16. 40
  17. 3
  18. 7
  19. 13
  20. 26
  21. 6
  22. 5
  23. 5
  24. 12
  25. 11
  26. 1
  27. 84
  28. 19
  29. 12
  30. 36
  31. 4
  32. 28
  33. 22
  34. 5
  35. 90
  36. 26
  37. 12
  38. 120
  39. 9
  40. 10

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