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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 55 · 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: 4(y − 3) = 2y + 26. What is y?
  2. 2.Solve: m/4 + m/3 = 56. What is m?
  3. 3.Solve: 9m + 12 = 8m + 15. What is m?
  4. 4.Solve: 3(n − 5) = n + 5. What is n?
  5. 5.Solve: 6(x − 2) = 4x + 10. What is x?
  6. 6.Solve: y/2 + y/6 = 12. What is y?
  7. 7.Solve: n/6 + n/4 = 25. What is n?
  8. 8.The sum of four consecutive whole numbers is 194. What is the largest of them?
  9. 9.Solve: 6(p − 1) = 4p + 16. What is p?
  10. 10.A father is 17 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  11. 11.Solve: n/4 + n/3 = 21. What is n?
  12. 12.Solve: y/2 + y/5 = 28. What is y?
  13. 13.The sum of three consecutive whole numbers is 162. What is the smallest of them?
  14. 14.The length of a rectangle is 1 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  15. 15.Solve: 6m + 4 = m + 49. What is m?
  16. 16.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?
  17. 17.The sum of two consecutive whole numbers is 45. What is the smallest of them?
  18. 18.A father is 42 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  19. 19.The sum of four consecutive whole numbers is 30. What is the smallest of them?
  20. 20.The sum of four consecutive whole numbers is 34. What is the largest of them?
  21. 21.The sum of three consecutive whole numbers is 93. What is the smallest of them?
  22. 22.Solve: 9n + 3 = 2n + 24. What is n?
  23. 23.The length of a rectangle is 8 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  24. 24.Solve: 6(y − 4) = 5y + 2. What is y?
  25. 25.Solve: y/6 + y/3 = 18. What is y?
  26. 26.The sum of two consecutive whole numbers is 35. What is the smallest of them?
  27. 27.Solve: 4(y − 4) = 3y + 10. What is y?
  28. 28.Solve: 6(n − 3) = 4n + 14. What is n?
  29. 29.The length of a rectangle is 6 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  30. 30.Solve: 3(m − 4) = 2m + 4. What is m?
  31. 31.A father is 42 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  32. 32.Solve: 3n + 4 = 2n + 18. What is n?
  33. 33.Solve: y/4 + y/6 = 25. What is y?
  34. 34.Solve: 3(t − 1) = 2t + 13. What is t?
  35. 35.A father is 40 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
  36. 36.The sum of four consecutive whole numbers is 206. What is the largest of them?
  37. 37.Solve: x/2 + x/6 = 28. What is x?
  38. 38.The sum of two consecutive whole numbers is 73. What is the smallest of them?
  39. 39.The sum of four consecutive whole numbers is 66. What is the smallest of them?
  40. 40.A father is 36 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?

Answer key

  1. 19
  2. 96
  3. 3
  4. 10
  5. 11
  6. 18
  7. 60
  8. 50
  9. 11
  10. 12
  11. 36
  12. 40
  13. 53
  14. 18
  15. 9
  16. 11
  17. 22
  18. 7
  19. 6
  20. 10
  21. 30
  22. 3
  23. 26
  24. 26
  25. 36
  26. 17
  27. 26
  28. 16
  29. 20
  30. 16
  31. 10
  32. 14
  33. 60
  34. 16
  35. 12
  36. 53
  37. 42
  38. 36
  39. 15
  40. 11

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