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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 662 · 40 sums
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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 8 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  2. 2.Solve: 8y + 20 = 4y + 40. What is y?
  3. 3.The sum of four consecutive whole numbers is 202. What is the smallest of them?
  4. 4.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?
  5. 5.Solve: 6(n − 1) = 3n + 33. What is n?
  6. 6.Solve: 6(x − 2) = 3x + 3. What is x?
  7. 7.Solve: m/4 + m/3 = 14. What is m?
  8. 8.The length of a rectangle is 12 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  9. 9.A father is 60 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?
  10. 10.Solve: m/5 + m/3 = 24. What is m?
  11. 11.Solve: 7x + 8 = x + 26. What is x?
  12. 12.Solve: 5(n − 4) = 3n + 20. What is n?
  13. 13.Solve: 7p + 4 = p + 64. What is p?
  14. 14.Solve: x/2 + x/6 = 12. What is x?
  15. 15.A father is 54 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?
  16. 16.Solve: m/5 + m/4 = 36. What is m?
  17. 17.The length of a rectangle is 3 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  18. 18.The sum of two consecutive whole numbers is 25. What is the largest of them?
  19. 19.Solve: 6(m − 2) = 5m + 11. What is m?
  20. 20.Solve: 8n + 2 = 7n + 4. What is n?
  21. 21.Solve: 6p + 5 = p + 60. What is p?
  22. 22.Solve: x/4 + x/5 = 18. What is x?
  23. 23.Solve: 6(m − 4) = 2m + 32. What is m?
  24. 24.A father is 16 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  25. 25.Solve: 5y + 7 = 3y + 31. What is y?
  26. 26.Solve: 6t + 14 = 4t + 30. What is t?
  27. 27.Solve: x/3 + x/2 = 5. What is x?
  28. 28.The sum of four consecutive whole numbers is 158. What is the largest of them?
  29. 29.Solve: 6(y − 3) = y + 57. What is y?
  30. 30.Solve: 7y + 6 = 3y + 10. What is y?
  31. 31.The sum of four consecutive whole numbers is 90. What is the largest of them?
  32. 32.Solve: 7p + 1 = 6p + 4. What is p?
  33. 33.The length of a rectangle is 10 cm more than its width. Its perimeter is 140 cm. What is its width (in cm)?
  34. 34.The length of a rectangle is 2 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  35. 35.The length of a rectangle is 5 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  36. 36.The sum of two consecutive whole numbers is 25. What is the smallest of them?
  37. 37.The sum of four consecutive whole numbers is 174. What is the smallest of them?
  38. 38.Solve: 8n + 16 = 4n + 32. What is n?
  39. 39.The sum of four consecutive whole numbers is 118. What is the largest of them?
  40. 40.Solve: x/3 + x/6 = 18. What is x?

Answer key

  1. 21
  2. 5
  3. 49
  4. 11
  5. 13
  6. 5
  7. 24
  8. 21
  9. 12
  10. 45
  11. 3
  12. 20
  13. 10
  14. 18
  15. 10
  16. 80
  17. 8
  18. 13
  19. 23
  20. 2
  21. 11
  22. 40
  23. 14
  24. 10
  25. 12
  26. 8
  27. 6
  28. 41
  29. 15
  30. 1
  31. 24
  32. 3
  33. 30
  34. 8
  35. 8
  36. 12
  37. 42
  38. 4
  39. 31
  40. 36

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