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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 314 · 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 65. What is the largest of them?
  2. 2.The sum of three consecutive whole numbers is 90. What is the smallest of them?
  3. 3.The sum of two consecutive whole numbers is 27. What is the smallest of them?
  4. 4.The length of a rectangle is 10 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  5. 5.The length of a rectangle is 1 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  6. 6.Solve: t/4 + t/5 = 54. What is t?
  7. 7.Solve: 3p + 13 = 2p + 17. What is p?
  8. 8.Solve: 5(m − 4) = 3m + 12. What is m?
  9. 9.Solve: m/5 + m/4 = 45. What is m?
  10. 10.A father is 17 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  11. 11.Solve: 9n + 9 = 3n + 45. What is n?
  12. 12.A father is 9 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  13. 13.A father is 48 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  14. 14.Solve: 6(n − 3) = 5n + 7. What is n?
  15. 15.Solve: y/3 + y/5 = 64. What is y?
  16. 16.The length of a rectangle is 12 cm more than its width. Its perimeter is 144 cm. What is its width (in cm)?
  17. 17.A father is 16 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?
  18. 18.A father is 40 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?
  19. 19.Solve: 4m + 5 = 3m + 10. What is m?
  20. 20.Solve: 8y + 16 = 7y + 29. What is y?
  21. 21.Solve: 5(t − 5) = 2t + 2. What is t?
  22. 22.Solve: x/3 + x/4 = 28. What is x?
  23. 23.Solve: m/2 + m/3 = 35. What is m?
  24. 24.A father is 30 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?
  25. 25.The length of a rectangle is 13 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  26. 26.A father is 16 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  27. 27.The length of a rectangle is 15 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  28. 28.Solve: 6(y − 5) = 2y + 30. What is y?
  29. 29.Solve: t/5 + t/6 = 77. What is t?
  30. 30.The sum of two consecutive whole numbers is 105. What is the largest of them?
  31. 31.Solve: 9m + 6 = 6m + 51. What is m?
  32. 32.The length of a rectangle is 7 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  33. 33.The sum of three consecutive whole numbers is 36. What is the largest of them?
  34. 34.The length of a rectangle is 9 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  35. 35.The sum of four consecutive whole numbers is 170. What is the largest of them?
  36. 36.The sum of three consecutive whole numbers is 84. What is the smallest of them?
  37. 37.A father is 18 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  38. 38.Solve: 4y + 15 = 2y + 43. What is y?
  39. 39.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?
  40. 40.Solve: t/6 + t/4 = 15. What is t?

Answer key

  1. 33
  2. 29
  3. 13
  4. 21
  5. 9
  6. 120
  7. 4
  8. 16
  9. 100
  10. 12
  11. 6
  12. 4
  13. 8
  14. 25
  15. 120
  16. 30
  17. 3
  18. 12
  19. 5
  20. 13
  21. 9
  22. 48
  23. 42
  24. 8
  25. 4
  26. 8
  27. 16
  28. 15
  29. 210
  30. 53
  31. 15
  32. 28
  33. 13
  34. 24
  35. 44
  36. 27
  37. 10
  38. 14
  39. 4
  40. 36

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