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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 640 · 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 length of a rectangle is 3 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  2. 2.A father is 20 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  3. 3.Solve: 4(y − 2) = 3y + 12. What is y?
  4. 4.A father is 4 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  5. 5.Solve: 3(p − 1) = p + 11. What is p?
  6. 6.Solve: 8m + 17 = 6m + 41. What is m?
  7. 7.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?
  8. 8.The length of a rectangle is 13 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  9. 9.Solve: 8y + 11 = 6y + 17. What is y?
  10. 10.Solve: 7y + 13 = y + 55. What is y?
  11. 11.Solve: 4(t − 2) = 3t + 1. What is t?
  12. 12.Solve: y/4 + y/3 = 49. What is y?
  13. 13.Solve: y/3 + y/2 = 35. What is y?
  14. 14.Solve: 4y + 11 = y + 44. What is y?
  15. 15.The length of a rectangle is 2 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  16. 16.Solve: 3t + 4 = 2t + 10. What is t?
  17. 17.The length of a rectangle is 4 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  18. 18.The sum of two consecutive whole numbers is 111. What is the largest of them?
  19. 19.Solve: 4(m − 4) = 2m + 16. What is m?
  20. 20.Solve: y/5 + y/2 = 35. What is y?
  21. 21.Solve: t/2 + t/6 = 32. What is t?
  22. 22.The sum of three consecutive whole numbers is 105. What is the largest of them?
  23. 23.Solve: 3(y − 2) = 2y + 8. What is y?
  24. 24.Solve: m/4 + m/2 = 12. What is m?
  25. 25.The sum of three consecutive whole numbers is 57. What is the smallest of them?
  26. 26.Solve: 3y + 5 = y + 7. What is y?
  27. 27.Solve: p/6 + p/3 = 3. What is p?
  28. 28.A father is 21 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?
  29. 29.Solve: y/5 + y/6 = 44. What is y?
  30. 30.Solve: 4(p − 3) = 2p + 10. What is p?
  31. 31.Solve: 4y + 5 = y + 32. What is y?
  32. 32.The length of a rectangle is 2 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  33. 33.Solve: 6(n − 5) = n + 10. What is n?
  34. 34.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?
  35. 35.The length of a rectangle is 10 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  36. 36.Solve: 5p + 10 = p + 70. What is p?
  37. 37.Solve: 5(y − 3) = y + 1. What is y?
  38. 38.Solve: 3(p − 2) = p + 2. What is p?
  39. 39.A father is 5 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  40. 40.Solve: 7t + 12 = 4t + 30. What is t?

Answer key

  1. 11
  2. 12
  3. 20
  4. 3
  5. 7
  6. 12
  7. 2
  8. 24
  9. 3
  10. 7
  11. 9
  12. 84
  13. 42
  14. 11
  15. 8
  16. 6
  17. 24
  18. 56
  19. 16
  20. 50
  21. 48
  22. 36
  23. 14
  24. 16
  25. 18
  26. 1
  27. 6
  28. 2
  29. 120
  30. 11
  31. 9
  32. 26
  33. 8
  34. 8
  35. 4
  36. 15
  37. 4
  38. 4
  39. 2
  40. 6

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