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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 554 · 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 21 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?
  2. 2.The sum of three consecutive whole numbers is 24. What is the largest of them?
  3. 3.Solve: 6(x − 4) = x + 36. What is x?
  4. 4.A father is 16 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?
  5. 5.The length of a rectangle is 4 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  6. 6.The length of a rectangle is 15 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
  7. 7.The length of a rectangle is 9 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  8. 8.The sum of four consecutive whole numbers is 90. What is the largest of them?
  9. 9.Solve: 4n + 20 = 3n + 23. What is n?
  10. 10.The sum of four consecutive whole numbers is 238. What is the smallest of them?
  11. 11.The length of a rectangle is 10 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  12. 12.The sum of three consecutive whole numbers is 24. What is the smallest of them?
  13. 13.Solve: y/4 + y/2 = 6. What is y?
  14. 14.Solve: 9t + 4 = 2t + 67. What is t?
  15. 15.Solve: 9t + 3 = 3t + 9. What is t?
  16. 16.The length of a rectangle is 1 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  17. 17.Solve: 6(x − 5) = x + 30. What is x?
  18. 18.Solve: 3x + 3 = x + 11. What is x?
  19. 19.Solve: 6n + 14 = 2n + 54. What is n?
  20. 20.Solve: 4(y − 2) = 2y + 14. What is y?
  21. 21.Solve: 4x + 17 = x + 38. What is x?
  22. 22.The sum of three consecutive whole numbers is 150. What is the smallest of them?
  23. 23.Solve: n/6 + n/2 = 20. What is n?
  24. 24.Solve: x/4 + x/2 = 12. What is x?
  25. 25.Solve: 4(y − 3) = 3y + 1. What is y?
  26. 26.A father is 8 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?
  27. 27.Solve: p/5 + p/6 = 22. What is p?
  28. 28.A father is 48 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?
  29. 29.Solve: 8x + 3 = 7x + 8. What is x?
  30. 30.A father is 18 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?
  31. 31.The sum of four consecutive whole numbers is 154. What is the smallest of them?
  32. 32.Solve: t/4 + t/6 = 10. What is t?
  33. 33.The sum of two consecutive whole numbers is 59. What is the largest of them?
  34. 34.Solve: 6(n − 5) = 2n + 22. What is n?
  35. 35.Solve: 8y + 6 = 6y + 34. What is y?
  36. 36.Solve: 5x + 2 = 2x + 11. What is x?
  37. 37.The length of a rectangle is 5 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  38. 38.The sum of four consecutive whole numbers is 214. What is the largest of them?
  39. 39.Solve: x/3 + x/2 = 30. What is x?
  40. 40.A father is 26 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?

Answer key

  1. 2
  2. 9
  3. 12
  4. 2
  5. 12
  6. 13
  7. 6
  8. 24
  9. 3
  10. 58
  11. 2
  12. 7
  13. 8
  14. 9
  15. 1
  16. 9
  17. 12
  18. 4
  19. 10
  20. 11
  21. 7
  22. 49
  23. 30
  24. 16
  25. 13
  26. 3
  27. 60
  28. 12
  29. 5
  30. 3
  31. 37
  32. 24
  33. 30
  34. 13
  35. 14
  36. 3
  37. 11
  38. 55
  39. 36
  40. 10

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