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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 764 · 40 sums
TalentJR

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: 9m + 12 = 4m + 47. What is m?
  2. 2.Solve: 7n + 13 = 5n + 29. What is n?
  3. 3.Solve: x/5 + x/2 = 7. What is x?
  4. 4.Solve: n/5 + n/2 = 28. What is n?
  5. 5.Solve: 6(t − 4) = 5t + 4. What is t?
  6. 6.A father is 15 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  7. 7.Solve: 6(y − 1) = 4y + 10. What is y?
  8. 8.Solve: y/4 + y/2 = 21. What is y?
  9. 9.Solve: 8n + 17 = 7n + 22. What is n?
  10. 10.Solve: y/2 + y/6 = 20. What is y?
  11. 11.Solve: 6(x − 4) = 2x + 44. What is x?
  12. 12.The sum of two consecutive whole numbers is 41. What is the largest of them?
  13. 13.The length of a rectangle is 1 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  14. 14.The sum of four consecutive whole numbers is 242. What is the smallest of them?
  15. 15.Solve: 5(x − 2) = x + 14. What is x?
  16. 16.The length of a rectangle is 5 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  17. 17.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?
  18. 18.Solve: 3(m − 5) = m + 15. What is m?
  19. 19.The sum of three consecutive whole numbers is 135. What is the largest of them?
  20. 20.Solve: y/2 + y/5 = 42. What is y?
  21. 21.Solve: n/4 + n/3 = 14. What is n?
  22. 22.The length of a rectangle is 15 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  23. 23.The sum of three consecutive whole numbers is 60. What is the smallest of them?
  24. 24.The sum of two consecutive whole numbers is 37. What is the largest of them?
  25. 25.Solve: n/2 + n/6 = 12. What is n?
  26. 26.Solve: 3(y − 3) = y + 17. What is y?
  27. 27.A father is 18 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?
  28. 28.The sum of two consecutive whole numbers is 33. What is the smallest of them?
  29. 29.The sum of three consecutive whole numbers is 48. What is the smallest of them?
  30. 30.Solve: 8p + 1 = 3p + 6. What is p?
  31. 31.The sum of three consecutive whole numbers is 78. What is the largest of them?
  32. 32.A father is 34 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  33. 33.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  34. 34.Solve: 7y + 7 = y + 85. What is y?
  35. 35.Solve: m/6 + m/4 = 5. What is m?
  36. 36.Solve: 4(t − 2) = 3t + 8. What is t?
  37. 37.Solve: 5(t − 5) = 2t + 26. What is t?
  38. 38.Solve: 6(y − 1) = y + 64. What is y?
  39. 39.Solve: 4(p − 1) = 2p + 22. What is p?
  40. 40.The sum of two consecutive whole numbers is 79. What is the smallest of them?

Answer key

  1. 7
  2. 8
  3. 10
  4. 40
  5. 28
  6. 9
  7. 8
  8. 28
  9. 5
  10. 30
  11. 17
  12. 21
  13. 21
  14. 59
  15. 6
  16. 17
  17. 7
  18. 15
  19. 46
  20. 60
  21. 24
  22. 16
  23. 19
  24. 19
  25. 18
  26. 13
  27. 2
  28. 16
  29. 15
  30. 1
  31. 27
  32. 10
  33. 2
  34. 13
  35. 12
  36. 16
  37. 17
  38. 14
  39. 13
  40. 39

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