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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 374 · 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 30 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?
  2. 2.Solve: 3(n − 3) = n + 3. What is n?
  3. 3.Solve: 9p + 16 = p + 72. What is p?
  4. 4.The length of a rectangle is 7 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
  5. 5.The length of a rectangle is 13 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  6. 6.A father is 9 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  7. 7.The sum of two consecutive whole numbers is 17. What is the largest of them?
  8. 8.Solve: 5t + 9 = 3t + 23. What is t?
  9. 9.Solve: 5y + 4 = y + 44. What is y?
  10. 10.The sum of four consecutive whole numbers is 246. What is the smallest of them?
  11. 11.The sum of two consecutive whole numbers is 41. What is the largest of them?
  12. 12.Solve: 6(m − 2) = 4m + 18. What is m?
  13. 13.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?
  14. 14.The length of a rectangle is 1 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
  15. 15.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?
  16. 16.Solve: x/3 + x/5 = 56. What is x?
  17. 17.Solve: p/6 + p/4 = 35. What is p?
  18. 18.Solve: m/5 + m/6 = 55. What is m?
  19. 19.Solve: 6(y − 1) = 5y + 10. What is y?
  20. 20.Solve: t/5 + t/3 = 48. What is t?
  21. 21.The length of a rectangle is 13 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  22. 22.Solve: y/2 + y/3 = 5. What is y?
  23. 23.Solve: 7y + 12 = 6y + 27. What is y?
  24. 24.Solve: t/4 + t/3 = 7. What is t?
  25. 25.Solve: n/6 + n/4 = 5. What is n?
  26. 26.The length of a rectangle is 8 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
  27. 27.Solve: 8x + 17 = 7x + 28. What is x?
  28. 28.The length of a rectangle is 7 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  29. 29.Solve: 5n + 3 = n + 47. What is n?
  30. 30.The sum of two consecutive whole numbers is 95. What is the smallest of them?
  31. 31.Solve: 4n + 20 = 3n + 26. What is n?
  32. 32.A father is 39 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?
  33. 33.The length of a rectangle is 10 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  34. 34.Solve: 9y + 3 = 6y + 15. What is y?
  35. 35.A father is 11 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  36. 36.Solve: x/6 + x/5 = 44. What is x?
  37. 37.Solve: 8m + 3 = 7m + 18. What is m?
  38. 38.Solve: 5(y − 4) = 2y + 34. What is y?
  39. 39.Solve: 9x + 20 = 4x + 65. What is x?
  40. 40.A father is 17 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?

Answer key

  1. 2
  2. 6
  3. 7
  4. 3
  5. 10
  6. 7
  7. 9
  8. 7
  9. 10
  10. 60
  11. 21
  12. 15
  13. 3
  14. 5
  15. 3
  16. 105
  17. 84
  18. 150
  19. 16
  20. 90
  21. 16
  22. 6
  23. 15
  24. 12
  25. 12
  26. 2
  27. 11
  28. 10
  29. 11
  30. 47
  31. 6
  32. 10
  33. 10
  34. 4
  35. 8
  36. 120
  37. 15
  38. 18
  39. 9
  40. 9

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