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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 350 · 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 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?
  2. 2.The length of a rectangle is 1 cm more than its width. Its perimeter is 10 cm. What is its width (in cm)?
  3. 3.A father is 51 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
  4. 4.The length of a rectangle is 3 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  5. 5.The sum of two consecutive whole numbers is 25. What is the smallest of them?
  6. 6.The sum of two consecutive whole numbers is 13. What is the largest of them?
  7. 7.The sum of four consecutive whole numbers is 66. What is the smallest of them?
  8. 8.The sum of three consecutive whole numbers is 168. What is the largest of them?
  9. 9.The length of a rectangle is 14 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  10. 10.The sum of two consecutive whole numbers is 15. What is the smallest of them?
  11. 11.Solve: y/2 + y/6 = 32. What is y?
  12. 12.A father is 14 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  13. 13.Solve: 9p + 9 = 4p + 29. What is p?
  14. 14.The sum of two consecutive whole numbers is 59. What is the smallest of them?
  15. 15.The length of a rectangle is 1 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  16. 16.Solve: 3m + 1 = m + 23. What is m?
  17. 17.Solve: 7y + 20 = y + 38. What is y?
  18. 18.A father is 13 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  19. 19.A father is 12 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  20. 20.Solve: 3n + 12 = n + 16. What is n?
  21. 21.The sum of two consecutive whole numbers is 11. What is the smallest of them?
  22. 22.Solve: 4(y − 2) = 2y + 14. What is y?
  23. 23.Solve: 9m + 9 = m + 89. What is m?
  24. 24.The length of a rectangle is 8 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  25. 25.The length of a rectangle is 5 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
  26. 26.Solve: 6n + 15 = 5n + 29. What is n?
  27. 27.Solve: 5x + 6 = 3x + 8. What is x?
  28. 28.The length of a rectangle is 2 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  29. 29.The sum of two consecutive whole numbers is 47. What is the largest of them?
  30. 30.Solve: 5(x − 3) = 4x + 4. What is x?
  31. 31.The sum of three consecutive whole numbers is 75. What is the smallest of them?
  32. 32.The sum of four consecutive whole numbers is 38. What is the smallest of them?
  33. 33.Solve: 6p + 2 = 3p + 17. What is p?
  34. 34.Solve: y/5 + y/2 = 56. What is y?
  35. 35.The length of a rectangle is 10 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  36. 36.A father is 36 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?
  37. 37.Solve: m/3 + m/4 = 35. What is m?
  38. 38.Solve: 4(t − 5) = 2t + 6. What is t?
  39. 39.The length of a rectangle is 4 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  40. 40.The length of a rectangle is 12 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?

Answer key

  1. 5
  2. 2
  3. 11
  4. 12
  5. 12
  6. 7
  7. 15
  8. 57
  9. 2
  10. 7
  11. 48
  12. 4
  13. 4
  14. 29
  15. 8
  16. 11
  17. 3
  18. 8
  19. 3
  20. 2
  21. 5
  22. 11
  23. 10
  24. 8
  25. 30
  26. 14
  27. 1
  28. 16
  29. 24
  30. 19
  31. 24
  32. 8
  33. 5
  34. 80
  35. 21
  36. 12
  37. 60
  38. 13
  39. 25
  40. 22

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