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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 739 · 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: p/3 + p/2 = 15. What is p?
  2. 2.Solve: 3y + 5 = y + 35. What is y?
  3. 3.The sum of two consecutive whole numbers is 37. What is the largest of them?
  4. 4.A father is 9 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  5. 5.Solve: 4y + 12 = 2y + 24. What is y?
  6. 6.Solve: 9m + 17 = 3m + 77. What is m?
  7. 7.A father is 36 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  8. 8.Solve: 5(n − 3) = 2n + 6. What is n?
  9. 9.Solve: 4n + 3 = 2n + 31. What is n?
  10. 10.A father is 15 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  11. 11.The length of a rectangle is 1 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  12. 12.Solve: 3(x − 3) = x + 21. What is x?
  13. 13.Solve: 3y + 3 = y + 5. What is y?
  14. 14.The sum of two consecutive whole numbers is 115. What is the smallest of them?
  15. 15.Solve: m/3 + m/2 = 10. What is m?
  16. 16.Solve: 5(x − 3) = 2x + 27. What is x?
  17. 17.Solve: n/2 + n/6 = 8. What is n?
  18. 18.The length of a rectangle is 5 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  19. 19.The length of a rectangle is 12 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  20. 20.The sum of two consecutive whole numbers is 73. What is the smallest of them?
  21. 21.The length of a rectangle is 3 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  22. 22.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?
  23. 23.Solve: 6(p − 1) = 5p + 7. What is p?
  24. 24.Solve: 6n + 19 = 5n + 21. What is n?
  25. 25.Solve: 9x + 19 = 3x + 43. What is x?
  26. 26.Solve: 8x + 6 = 2x + 36. What is x?
  27. 27.The sum of four consecutive whole numbers is 218. What is the smallest of them?
  28. 28.The sum of two consecutive whole numbers is 81. What is the smallest of them?
  29. 29.Solve: 4p + 13 = p + 16. What is p?
  30. 30.Solve: 4(x − 1) = 3x + 8. What is x?
  31. 31.Solve: n/6 + n/5 = 55. What is n?
  32. 32.Solve: x/6 + x/5 = 88. What is x?
  33. 33.The sum of two consecutive whole numbers is 23. What is the smallest of them?
  34. 34.Solve: 6(y − 4) = 2y + 20. What is y?
  35. 35.Solve: p/4 + p/3 = 35. What is p?
  36. 36.A father is 3 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  37. 37.A father is 16 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
  38. 38.Solve: 4(y − 2) = 2y + 12. What is y?
  39. 39.The sum of two consecutive whole numbers is 19. What is the largest of them?
  40. 40.Solve: 6m + 1 = 5m + 10. What is m?

Answer key

  1. 18
  2. 15
  3. 19
  4. 4
  5. 6
  6. 10
  7. 11
  8. 7
  9. 14
  10. 7
  11. 10
  12. 15
  13. 1
  14. 57
  15. 12
  16. 14
  17. 12
  18. 20
  19. 10
  20. 36
  21. 25
  22. 8
  23. 13
  24. 2
  25. 4
  26. 5
  27. 53
  28. 40
  29. 1
  30. 12
  31. 150
  32. 240
  33. 11
  34. 11
  35. 60
  36. 2
  37. 3
  38. 10
  39. 10
  40. 9

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