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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 723 · 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 30 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?
  2. 2.Solve: 6(m − 1) = 2m + 18. What is m?
  3. 3.Solve: 8p + 18 = 7p + 19. What is p?
  4. 4.A father is 33 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?
  5. 5.Solve: 3(p − 3) = 2p + 5. What is p?
  6. 6.Solve: 4(x − 4) = x + 23. What is x?
  7. 7.Solve: 6(t − 4) = 4t + 6. What is t?
  8. 8.Solve: 6x + 16 = 5x + 29. What is x?
  9. 9.Solve: 3(n − 3) = n + 3. What is n?
  10. 10.Solve: 3(p − 1) = 2p + 3. What is p?
  11. 11.Solve: t/4 + t/3 = 7. What is t?
  12. 12.A father is 42 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  13. 13.A father is 15 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  14. 14.Solve: 9m + 16 = 3m + 28. What is m?
  15. 15.The sum of two consecutive whole numbers is 57. What is the smallest of them?
  16. 16.Solve: 6p + 5 = 3p + 14. What is p?
  17. 17.Solve: x/4 + x/2 = 3. What is x?
  18. 18.The length of a rectangle is 14 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  19. 19.Solve: y/6 + y/5 = 88. What is y?
  20. 20.Solve: 9m + 19 = 5m + 55. What is m?
  21. 21.A father is 21 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?
  22. 22.A father is 36 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
  23. 23.The sum of three consecutive whole numbers is 78. What is the smallest of them?
  24. 24.The sum of three consecutive whole numbers is 177. What is the largest of them?
  25. 25.Solve: p/2 + p/4 = 6. What is p?
  26. 26.Solve: y/5 + y/3 = 24. What is y?
  27. 27.Solve: p/2 + p/6 = 32. What is p?
  28. 28.The length of a rectangle is 2 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  29. 29.Solve: 6m + 13 = 2m + 25. What is m?
  30. 30.The sum of three consecutive whole numbers is 162. What is the largest of them?
  31. 31.The length of a rectangle is 15 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  32. 32.Solve: 4(n − 4) = n + 29. What is n?
  33. 33.Solve: 7y + 8 = 3y + 28. What is y?
  34. 34.A father is 7 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  35. 35.Solve: 3y + 1 = y + 3. What is y?
  36. 36.A father is 20 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?
  37. 37.Solve: 4m + 6 = 3m + 17. What is m?
  38. 38.The length of a rectangle is 4 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  39. 39.Solve: 5n + 3 = 4n + 10. What is n?
  40. 40.Solve: 4(y − 4) = 3y + 5. What is y?

Answer key

  1. 10
  2. 6
  3. 1
  4. 6
  5. 14
  6. 13
  7. 15
  8. 13
  9. 6
  10. 6
  11. 12
  12. 7
  13. 4
  14. 2
  15. 28
  16. 3
  17. 4
  18. 14
  19. 240
  20. 9
  21. 3
  22. 12
  23. 25
  24. 60
  25. 8
  26. 45
  27. 48
  28. 15
  29. 3
  30. 55
  31. 5
  32. 15
  33. 5
  34. 3
  35. 1
  36. 2
  37. 11
  38. 21
  39. 7
  40. 21

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