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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 426 · 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.A father is 8 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  2. 2.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?
  3. 3.The sum of four consecutive whole numbers is 190. What is the largest of them?
  4. 4.The sum of three consecutive whole numbers is 75. What is the smallest of them?
  5. 5.Solve: 4(p − 5) = 2p + 16. What is p?
  6. 6.Solve: 8x + 13 = 4x + 33. What is x?
  7. 7.Solve: 5x + 14 = 3x + 42. What is x?
  8. 8.Solve: 4(t − 2) = 2t + 4. What is t?
  9. 9.Solve: p/3 + p/2 = 35. What is p?
  10. 10.Solve: x/2 + x/3 = 15. What is x?
  11. 11.The length of a rectangle is 5 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  12. 12.Solve: 5x + 12 = 2x + 48. What is x?
  13. 13.Solve: p/5 + p/4 = 27. What is p?
  14. 14.Solve: 3(m − 4) = 2m + 5. What is m?
  15. 15.A father is 24 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?
  16. 16.Solve: 3m + 13 = m + 33. What is m?
  17. 17.The sum of two consecutive whole numbers is 45. What is the largest of them?
  18. 18.A father is 11 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  19. 19.Solve: 8n + 20 = 7n + 31. What is n?
  20. 20.Solve: 9n + 3 = 2n + 31. What is n?
  21. 21.The length of a rectangle is 13 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  22. 22.The sum of two consecutive whole numbers is 77. What is the smallest of them?
  23. 23.Solve: 3p + 8 = p + 28. What is p?
  24. 24.Solve: 5(m − 3) = 3m + 15. What is m?
  25. 25.Solve: 7x + 11 = 5x + 19. What is x?
  26. 26.The sum of two consecutive whole numbers is 27. What is the largest of them?
  27. 27.The sum of three consecutive whole numbers is 144. What is the largest of them?
  28. 28.Solve: x/6 + x/2 = 24. What is x?
  29. 29.Solve: 4(x − 1) = 3x + 11. What is x?
  30. 30.Solve: 3p + 9 = p + 35. What is p?
  31. 31.Solve: 4m + 5 = m + 23. What is m?
  32. 32.Solve: p/3 + p/5 = 24. What is p?
  33. 33.The length of a rectangle is 4 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  34. 34.The length of a rectangle is 4 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  35. 35.The sum of two consecutive whole numbers is 65. What is the largest of them?
  36. 36.Solve: 5m + 6 = m + 58. What is m?
  37. 37.The sum of four consecutive whole numbers is 234. What is the smallest of them?
  38. 38.Solve: 7m + 8 = 5m + 18. What is m?
  39. 39.Solve: 4t + 11 = t + 35. What is t?
  40. 40.The sum of three consecutive whole numbers is 87. What is the smallest of them?

Answer key

  1. 5
  2. 4
  3. 49
  4. 24
  5. 18
  6. 5
  7. 14
  8. 6
  9. 42
  10. 18
  11. 17
  12. 12
  13. 60
  14. 17
  15. 4
  16. 10
  17. 23
  18. 7
  19. 11
  20. 4
  21. 9
  22. 38
  23. 10
  24. 15
  25. 4
  26. 14
  27. 49
  28. 36
  29. 15
  30. 13
  31. 6
  32. 45
  33. 19
  34. 12
  35. 33
  36. 13
  37. 57
  38. 5
  39. 8
  40. 28

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