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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 812 · 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.The sum of two consecutive whole numbers is 13. What is the smallest of them?
  2. 2.A father is 12 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  3. 3.The sum of four consecutive whole numbers is 122. What is the largest of them?
  4. 4.Solve: n/4 + n/2 = 15. What is n?
  5. 5.Solve: 4n + 14 = 3n + 16. What is n?
  6. 6.A father is 15 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  7. 7.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  8. 8.Solve: 6(p − 5) = 5p + 10. What is p?
  9. 9.Solve: x/4 + x/2 = 18. What is x?
  10. 10.Solve: 6(t − 4) = 3t + 39. What is t?
  11. 11.Solve: 8n + 6 = 3n + 56. What is n?
  12. 12.Solve: 3(m − 3) = 2m + 6. What is m?
  13. 13.Solve: 5(x − 4) = 2x + 34. What is x?
  14. 14.Solve: 3t + 4 = t + 34. What is t?
  15. 15.Solve: 6(t − 4) = 5t + 12. What is t?
  16. 16.A father is 15 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  17. 17.Solve: 8y + 4 = 7y + 16. What is y?
  18. 18.Solve: 6(t − 2) = 5t + 7. What is t?
  19. 19.The length of a rectangle is 5 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  20. 20.The length of a rectangle is 8 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
  21. 21.The sum of four consecutive whole numbers is 58. What is the largest of them?
  22. 22.Solve: 4n + 20 = 2n + 30. What is n?
  23. 23.The sum of two consecutive whole numbers is 85. What is the largest of them?
  24. 24.Solve: x/6 + x/5 = 55. What is x?
  25. 25.Solve: 7x + 5 = 5x + 15. What is x?
  26. 26.Solve: p/2 + p/6 = 8. What is p?
  27. 27.A father is 20 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?
  28. 28.The sum of three consecutive whole numbers is 183. What is the smallest of them?
  29. 29.Solve: n/3 + n/5 = 48. What is n?
  30. 30.The length of a rectangle is 4 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  31. 31.Solve: x/3 + x/2 = 5. What is x?
  32. 32.Solve: p/3 + p/5 = 64. What is p?
  33. 33.Solve: 5(y − 4) = 4y + 3. What is y?
  34. 34.A father is 26 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?
  35. 35.Solve: 3(p − 4) = 2p + 4. What is p?
  36. 36.Solve: 3(t − 1) = 2t + 11. What is t?
  37. 37.Solve: 5(x − 3) = 4x + 10. What is x?
  38. 38.Solve: y/5 + y/3 = 64. What is y?
  39. 39.Solve: 3x + 3 = x + 27. What is x?
  40. 40.A father is 6 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?

Answer key

  1. 6
  2. 7
  3. 32
  4. 20
  5. 2
  6. 12
  7. 6
  8. 40
  9. 24
  10. 21
  11. 10
  12. 15
  13. 18
  14. 15
  15. 36
  16. 7
  17. 12
  18. 19
  19. 9
  20. 29
  21. 16
  22. 5
  23. 43
  24. 150
  25. 5
  26. 12
  27. 5
  28. 60
  29. 90
  30. 12
  31. 6
  32. 120
  33. 23
  34. 6
  35. 16
  36. 14
  37. 25
  38. 120
  39. 12
  40. 4

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