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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 72 · 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: 6t + 9 = t + 69. What is t?
  2. 2.Solve: 4p + 3 = p + 27. What is p?
  3. 3.Solve: 4(m − 4) = 2m + 6. What is m?
  4. 4.Solve: 3m + 20 = 2m + 32. What is m?
  5. 5.Solve: 9x + 11 = 3x + 59. What is x?
  6. 6.Solve: t/6 + t/2 = 20. What is t?
  7. 7.A father is 6 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  8. 8.The length of a rectangle is 14 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  9. 9.Solve: 4(n − 1) = 3n + 9. What is n?
  10. 10.A father is 27 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.The length of a rectangle is 8 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  12. 12.Solve: 7t + 11 = t + 17. What is t?
  13. 13.Solve: 6(n − 4) = 2n + 24. What is n?
  14. 14.Solve: 6y + 3 = 3y + 24. What is y?
  15. 15.A father is 36 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  16. 16.Solve: n/5 + n/2 = 28. What is n?
  17. 17.Solve: 6n + 19 = n + 54. What is n?
  18. 18.Solve: 5(x − 1) = 3x + 17. What is x?
  19. 19.Solve: p/5 + p/2 = 35. What is p?
  20. 20.Solve: 3(y − 3) = y + 13. What is y?
  21. 21.The length of a rectangle is 10 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  22. 22.The sum of four consecutive whole numbers is 66. What is the smallest of them?
  23. 23.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?
  24. 24.The sum of three consecutive whole numbers is 120. What is the smallest of them?
  25. 25.The sum of two consecutive whole numbers is 113. What is the largest of them?
  26. 26.A father is 10 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?
  27. 27.Solve: 5(y − 2) = y + 42. What is y?
  28. 28.Solve: 8y + 3 = 2y + 33. What is y?
  29. 29.Solve: n/5 + n/2 = 21. What is n?
  30. 30.Solve: y/2 + y/6 = 4. What is y?
  31. 31.Solve: 5(n − 1) = 2n + 13. What is n?
  32. 32.Solve: 7t + 10 = 5t + 38. What is t?
  33. 33.The sum of two consecutive whole numbers is 37. What is the largest of them?
  34. 34.Solve: n/2 + n/5 = 49. What is n?
  35. 35.A father is 14 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?
  36. 36.The length of a rectangle is 8 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  37. 37.Solve: 5n + 6 = n + 18. What is n?
  38. 38.The length of a rectangle is 8 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  39. 39.The sum of two consecutive whole numbers is 41. What is the smallest of them?
  40. 40.The length of a rectangle is 6 cm more than its width. Its perimeter is 72 cm. What is its width (in cm)?

Answer key

  1. 12
  2. 8
  3. 11
  4. 12
  5. 8
  6. 30
  7. 5
  8. 6
  9. 13
  10. 4
  11. 18
  12. 1
  13. 12
  14. 7
  15. 10
  16. 40
  17. 7
  18. 11
  19. 50
  20. 11
  21. 20
  22. 15
  23. 11
  24. 39
  25. 57
  26. 3
  27. 13
  28. 5
  29. 30
  30. 6
  31. 6
  32. 14
  33. 19
  34. 70
  35. 3
  36. 23
  37. 3
  38. 17
  39. 20
  40. 15

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