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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 324 · 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: m/4 + m/3 = 42. What is m?
  2. 2.Solve: 4y + 18 = 3y + 23. What is y?
  3. 3.Solve: 9y + 10 = 2y + 38. What is y?
  4. 4.The sum of three consecutive whole numbers is 72. What is the smallest of them?
  5. 5.A father is 48 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
  6. 6.The sum of two consecutive whole numbers is 53. What is the largest of them?
  7. 7.A father is 42 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?
  8. 8.Solve: 6n + 19 = 4n + 31. What is n?
  9. 9.A father is 34 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?
  10. 10.A father is 27 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?
  11. 11.Solve: 4n + 19 = 2n + 23. What is n?
  12. 12.Solve: 5(y − 5) = 4y + 6. What is y?
  13. 13.The length of a rectangle is 4 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  14. 14.The length of a rectangle is 2 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  15. 15.A father is 26 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?
  16. 16.Solve: 4(m − 2) = 3m + 12. What is m?
  17. 17.Solve: 5x + 3 = 3x + 33. What is x?
  18. 18.Solve: 3(t − 2) = 2t + 8. What is t?
  19. 19.Solve: 6m + 20 = m + 85. What is m?
  20. 20.The sum of two consecutive whole numbers is 93. What is the smallest of them?
  21. 21.The sum of two consecutive whole numbers is 59. What is the smallest of them?
  22. 22.Solve: 8x + 15 = 7x + 20. What is x?
  23. 23.Solve: 6(m − 3) = 2m + 6. What is m?
  24. 24.A father is 33 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?
  25. 25.Solve: 4p + 12 = p + 21. What is p?
  26. 26.Solve: 3(y − 3) = 2y + 3. What is y?
  27. 27.Solve: 4(y − 5) = 2y + 4. What is y?
  28. 28.The length of a rectangle is 15 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  29. 29.Solve: y/2 + y/3 = 40. What is y?
  30. 30.Solve: 4(p − 3) = 2p + 6. What is p?
  31. 31.Solve: 7m + 16 = 2m + 56. What is m?
  32. 32.Solve: 3n + 6 = 2n + 11. What is n?
  33. 33.Solve: 5p + 3 = 4p + 12. What is p?
  34. 34.Solve: 8x + 15 = 7x + 25. What is x?
  35. 35.The sum of two consecutive whole numbers is 23. What is the largest of them?
  36. 36.Solve: 6(x − 1) = x + 39. What is x?
  37. 37.The sum of two consecutive whole numbers is 19. What is the smallest of them?
  38. 38.Solve: p/2 + p/5 = 7. What is p?
  39. 39.The length of a rectangle is 3 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  40. 40.The sum of four consecutive whole numbers is 66. What is the smallest of them?

Answer key

  1. 72
  2. 5
  3. 4
  4. 23
  5. 10
  6. 27
  7. 9
  8. 6
  9. 12
  10. 5
  11. 2
  12. 31
  13. 25
  14. 15
  15. 9
  16. 20
  17. 15
  18. 14
  19. 13
  20. 46
  21. 29
  22. 5
  23. 6
  24. 3
  25. 3
  26. 12
  27. 12
  28. 14
  29. 48
  30. 9
  31. 8
  32. 5
  33. 9
  34. 10
  35. 12
  36. 9
  37. 9
  38. 10
  39. 16
  40. 15

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