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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 493 · 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: n/5 + n/4 = 63. What is n?
  2. 2.Solve: y/2 + y/3 = 35. What is y?
  3. 3.Solve: 6n + 20 = 2n + 48. What is n?
  4. 4.A father is 22 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 sum of three consecutive whole numbers is 48. What is the largest of them?
  6. 6.The sum of three consecutive whole numbers is 174. What is the largest of them?
  7. 7.Solve: 3(y − 1) = 2y + 5. What is y?
  8. 8.Solve: x/2 + x/3 = 40. What is x?
  9. 9.A father is 14 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?
  10. 10.Solve: p/5 + p/2 = 14. What is p?
  11. 11.The length of a rectangle is 8 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  12. 12.The sum of three consecutive whole numbers is 165. What is the largest of them?
  13. 13.Solve: n/2 + n/5 = 49. What is n?
  14. 14.The sum of two consecutive whole numbers is 19. What is the smallest of them?
  15. 15.Solve: 3(y − 1) = y + 19. What is y?
  16. 16.Solve: 6(x − 5) = 2x + 26. What is x?
  17. 17.Solve: 6(p − 3) = 3p + 3. What is p?
  18. 18.Solve: t/2 + t/3 = 20. What is t?
  19. 19.Solve: 3(t − 5) = 2t + 5. What is t?
  20. 20.A father is 42 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  21. 21.The sum of two consecutive whole numbers is 79. What is the smallest of them?
  22. 22.A father is 10 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  23. 23.A father is 36 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?
  24. 24.The sum of two consecutive whole numbers is 17. What is the smallest of them?
  25. 25.Solve: 9t + 13 = 6t + 58. What is t?
  26. 26.Solve: 6x + 6 = x + 71. What is x?
  27. 27.Solve: 6(n − 1) = n + 19. What is n?
  28. 28.The length of a rectangle is 12 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  29. 29.Solve: 4(p − 5) = 3p + 10. What is p?
  30. 30.Solve: 6(m − 5) = 5m + 11. What is m?
  31. 31.The length of a rectangle is 3 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  32. 32.A father is 10 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  33. 33.Solve: n/4 + n/2 = 21. What is n?
  34. 34.Solve: 4(y − 5) = y + 4. What is y?
  35. 35.The length of a rectangle is 1 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  36. 36.Solve: 7y + 16 = 5y + 22. What is y?
  37. 37.Solve: x/5 + x/6 = 44. What is x?
  38. 38.Solve: 9p + 16 = 7p + 36. What is p?
  39. 39.A father is 14 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  40. 40.The length of a rectangle is 12 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?

Answer key

  1. 140
  2. 42
  3. 7
  4. 5
  5. 17
  6. 59
  7. 8
  8. 48
  9. 5
  10. 20
  11. 7
  12. 56
  13. 70
  14. 9
  15. 11
  16. 14
  17. 7
  18. 24
  19. 20
  20. 11
  21. 39
  22. 8
  23. 4
  24. 8
  25. 15
  26. 13
  27. 5
  28. 4
  29. 30
  30. 41
  31. 15
  32. 3
  33. 28
  34. 8
  35. 29
  36. 3
  37. 120
  38. 10
  39. 10
  40. 11

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