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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 820 · 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 four consecutive whole numbers is 246. What is the smallest of them?
  2. 2.The sum of two consecutive whole numbers is 63. What is the smallest of them?
  3. 3.Solve: 4(y − 5) = 3y + 13. What is y?
  4. 4.Solve: 9x + 6 = 7x + 24. What is x?
  5. 5.Solve: 8p + 1 = 3p + 21. What is p?
  6. 6.Solve: 4(y − 1) = 3y + 13. What is y?
  7. 7.Solve: 5y + 20 = 4y + 27. What is y?
  8. 8.Solve: 5p + 14 = 4p + 16. What is p?
  9. 9.The sum of two consecutive whole numbers is 121. What is the smallest of them?
  10. 10.Solve: 8x + 15 = 4x + 23. What is x?
  11. 11.The sum of four consecutive whole numbers is 58. What is the smallest of them?
  12. 12.Solve: 3(y − 2) = 2y + 5. What is y?
  13. 13.Solve: 6(y − 4) = 4y + 2. What is y?
  14. 14.Solve: x/2 + x/4 = 24. What is x?
  15. 15.Solve: t/5 + t/3 = 64. What is t?
  16. 16.The length of a rectangle is 1 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  17. 17.Solve: 9x + 10 = 4x + 20. What is x?
  18. 18.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?
  19. 19.Solve: y/6 + y/4 = 20. What is y?
  20. 20.Solve: x/2 + x/3 = 15. What is x?
  21. 21.The sum of two consecutive whole numbers is 27. What is the smallest of them?
  22. 22.Solve: 5n + 2 = n + 6. What is n?
  23. 23.The sum of two consecutive whole numbers is 79. What is the smallest of them?
  24. 24.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?
  25. 25.Solve: 4n + 19 = 2n + 33. What is n?
  26. 26.The sum of two consecutive whole numbers is 97. What is the largest of them?
  27. 27.Solve: 5n + 2 = n + 54. What is n?
  28. 28.The sum of three consecutive whole numbers is 147. What is the smallest of them?
  29. 29.Solve: m/5 + m/2 = 7. What is m?
  30. 30.Solve: 7y + 16 = 3y + 44. What is y?
  31. 31.Solve: n/5 + n/6 = 77. What is n?
  32. 32.Solve: 4y + 2 = 2y + 14. What is y?
  33. 33.Solve: p/2 + p/6 = 8. What is p?
  34. 34.Solve: 5n + 9 = 4n + 12. What is n?
  35. 35.Solve: 5y + 19 = 2y + 52. What is y?
  36. 36.The length of a rectangle is 15 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  37. 37.The length of a rectangle is 2 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  38. 38.The length of a rectangle is 11 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  39. 39.Solve: 4(t − 3) = 2t + 24. What is t?
  40. 40.A father is 51 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?

Answer key

  1. 60
  2. 31
  3. 33
  4. 9
  5. 4
  6. 17
  7. 7
  8. 2
  9. 60
  10. 2
  11. 13
  12. 11
  13. 13
  14. 32
  15. 120
  16. 30
  17. 2
  18. 3
  19. 48
  20. 18
  21. 13
  22. 1
  23. 39
  24. 3
  25. 7
  26. 49
  27. 13
  28. 48
  29. 10
  30. 7
  31. 210
  32. 6
  33. 12
  34. 3
  35. 11
  36. 2
  37. 12
  38. 23
  39. 18
  40. 10

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