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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 878 · 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.Solve: 5(x − 1) = x + 31. What is x?
  2. 2.A father is 10 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  3. 3.The sum of three consecutive whole numbers is 159. What is the smallest of them?
  4. 4.Solve: 4(n − 3) = 3n + 2. What is n?
  5. 5.A father is 11 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  6. 6.The length of a rectangle is 8 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  7. 7.Solve: 3t + 13 = 2t + 16. What is t?
  8. 8.Solve: 6y + 13 = 2y + 29. What is y?
  9. 9.Solve: p/3 + p/5 = 32. What is p?
  10. 10.Solve: t/2 + t/5 = 21. What is t?
  11. 11.The sum of three consecutive whole numbers is 51. What is the largest of them?
  12. 12.The sum of four consecutive whole numbers is 50. What is the smallest of them?
  13. 13.The sum of two consecutive whole numbers is 27. What is the smallest of them?
  14. 14.Solve: 5(p − 3) = 4p + 1. What is p?
  15. 15.The sum of two consecutive whole numbers is 57. What is the largest of them?
  16. 16.Solve: 5(m − 3) = 2m + 18. What is m?
  17. 17.The length of a rectangle is 3 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  18. 18.The sum of three consecutive whole numbers is 102. What is the largest of them?
  19. 19.Solve: 4(p − 2) = p + 1. What is p?
  20. 20.Solve: t/2 + t/6 = 16. What is t?
  21. 21.Solve: 5p + 17 = p + 21. What is p?
  22. 22.A father is 15 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  23. 23.The length of a rectangle is 3 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  24. 24.Solve: 9x + 13 = 7x + 41. What is x?
  25. 25.A father is 57 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?
  26. 26.Solve: y/4 + y/3 = 42. What is y?
  27. 27.Solve: 6n + 18 = 2n + 54. What is n?
  28. 28.Solve: 3(x − 2) = x + 20. What is x?
  29. 29.Solve: 6(y − 2) = 4y + 22. What is y?
  30. 30.The sum of two consecutive whole numbers is 77. What is the smallest of them?
  31. 31.A father is 6 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  32. 32.Solve: y/5 + y/3 = 56. What is y?
  33. 33.Solve: 6(x − 5) = 2x + 42. What is x?
  34. 34.Solve: 5(y − 2) = 2y + 32. What is y?
  35. 35.The length of a rectangle is 4 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  36. 36.The sum of three consecutive whole numbers is 72. What is the largest of them?
  37. 37.The length of a rectangle is 11 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  38. 38.Solve: m/3 + m/4 = 56. What is m?
  39. 39.Solve: p/4 + p/5 = 36. What is p?
  40. 40.Solve: 5(n − 5) = 3n + 3. What is n?

Answer key

  1. 9
  2. 4
  3. 52
  4. 14
  5. 6
  6. 12
  7. 3
  8. 4
  9. 60
  10. 30
  11. 18
  12. 11
  13. 13
  14. 16
  15. 29
  16. 11
  17. 18
  18. 35
  19. 3
  20. 24
  21. 1
  22. 11
  23. 23
  24. 14
  25. 11
  26. 72
  27. 9
  28. 13
  29. 17
  30. 38
  31. 2
  32. 105
  33. 18
  34. 14
  35. 10
  36. 25
  37. 14
  38. 96
  39. 80
  40. 14

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