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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 308 · 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.Solve: n/4 + n/6 = 30. What is n?
  2. 2.Solve: 7y + 2 = 4y + 17. What is y?
  3. 3.A father is 24 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  4. 4.Solve: 3m + 12 = 2m + 27. What is m?
  5. 5.The length of a rectangle is 14 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  6. 6.The sum of three consecutive whole numbers is 180. What is the smallest of them?
  7. 7.Solve: 6(y − 3) = 4y + 2. What is y?
  8. 8.Solve: 5p + 5 = 4p + 14. What is p?
  9. 9.The length of a rectangle is 12 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  10. 10.Solve: y/4 + y/6 = 20. What is y?
  11. 11.A father is 30 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?
  12. 12.Solve: 3p + 18 = p + 32. What is p?
  13. 13.The length of a rectangle is 14 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  14. 14.Solve: 3x + 14 = 2x + 19. What is x?
  15. 15.The sum of four consecutive whole numbers is 94. What is the smallest of them?
  16. 16.The length of a rectangle is 11 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  17. 17.Solve: 4n + 19 = 3n + 33. What is n?
  18. 18.Solve: 3p + 7 = p + 29. What is p?
  19. 19.The sum of two consecutive whole numbers is 59. What is the largest of them?
  20. 20.The sum of three consecutive whole numbers is 27. What is the largest of them?
  21. 21.The sum of three consecutive whole numbers is 96. What is the largest of them?
  22. 22.Solve: 6n + 15 = 4n + 43. What is n?
  23. 23.The sum of two consecutive whole numbers is 79. What is the largest of them?
  24. 24.Solve: m/4 + m/6 = 25. What is m?
  25. 25.Solve: y/6 + y/3 = 24. What is y?
  26. 26.Solve: 4(t − 1) = 2t + 26. What is t?
  27. 27.The length of a rectangle is 3 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  28. 28.Solve: x/2 + x/4 = 3. What is x?
  29. 29.The length of a rectangle is 15 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  30. 30.Solve: 7y + 5 = 5y + 13. What is y?
  31. 31.A father is 15 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?
  32. 32.Solve: 9m + 5 = m + 61. What is m?
  33. 33.Solve: 6y + 15 = y + 20. What is y?
  34. 34.Solve: 3(p − 4) = 2p + 10. What is p?
  35. 35.The length of a rectangle is 4 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  36. 36.Solve: 7t + 7 = 2t + 37. What is t?
  37. 37.The length of a rectangle is 6 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  38. 38.The sum of three consecutive whole numbers is 39. What is the smallest of them?
  39. 39.Solve: 4x + 7 = x + 10. What is x?
  40. 40.The sum of two consecutive whole numbers is 83. What is the smallest of them?

Answer key

  1. 72
  2. 5
  3. 6
  4. 15
  5. 19
  6. 59
  7. 10
  8. 9
  9. 5
  10. 48
  11. 9
  12. 7
  13. 20
  14. 5
  15. 22
  16. 14
  17. 14
  18. 11
  19. 30
  20. 10
  21. 33
  22. 14
  23. 40
  24. 60
  25. 48
  26. 15
  27. 16
  28. 4
  29. 12
  30. 4
  31. 4
  32. 7
  33. 1
  34. 22
  35. 13
  36. 6
  37. 25
  38. 12
  39. 1
  40. 41

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