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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 386 · 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.A father is 24 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?
  2. 2.The length of a rectangle is 8 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  3. 3.Solve: 4x + 18 = 2x + 38. What is x?
  4. 4.Solve: 5(t − 5) = t + 19. What is t?
  5. 5.Solve: 9y + 6 = 2y + 55. What is y?
  6. 6.Solve: 4(n − 4) = n + 17. What is n?
  7. 7.Solve: y/5 + y/4 = 9. What is y?
  8. 8.A father is 18 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  9. 9.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?
  10. 10.A father is 45 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?
  11. 11.Solve: 3p + 15 = 2p + 27. What is p?
  12. 12.Solve: 3(y − 3) = y + 3. What is y?
  13. 13.Solve: 5t + 14 = 2t + 20. What is t?
  14. 14.The sum of four consecutive whole numbers is 122. What is the largest of them?
  15. 15.The length of a rectangle is 11 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  16. 16.Solve: 3(p − 2) = p + 2. What is p?
  17. 17.Solve: 4(y − 5) = 2y + 24. What is y?
  18. 18.Solve: 6(m − 2) = 3m + 15. What is m?
  19. 19.A father is 10 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  20. 20.Solve: y/5 + y/2 = 42. What is y?
  21. 21.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?
  22. 22.The sum of two consecutive whole numbers is 63. What is the largest of them?
  23. 23.The sum of three consecutive whole numbers is 39. What is the smallest of them?
  24. 24.Solve: 7y + 20 = 6y + 21. What is y?
  25. 25.Solve: 9t + 5 = 7t + 17. What is t?
  26. 26.Solve: 6(n − 5) = 2n + 22. What is n?
  27. 27.Solve: 6n + 20 = n + 25. What is n?
  28. 28.The sum of two consecutive whole numbers is 51. What is the smallest of them?
  29. 29.Solve: 9m + 15 = 6m + 45. What is m?
  30. 30.Solve: 5x + 7 = 3x + 11. What is x?
  31. 31.The length of a rectangle is 8 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  32. 32.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?
  33. 33.Solve: 4(p − 5) = 3p + 4. What is p?
  34. 34.A father is 24 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  35. 35.The sum of two consecutive whole numbers is 67. What is the smallest of them?
  36. 36.Solve: 4(y − 5) = y + 28. What is y?
  37. 37.The sum of three consecutive whole numbers is 21. What is the smallest of them?
  38. 38.Solve: 7t + 20 = 2t + 40. What is t?
  39. 39.The sum of two consecutive whole numbers is 31. What is the smallest of them?
  40. 40.Solve: 3n + 8 = n + 26. What is n?

Answer key

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

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