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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 406 · 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.A father is 22 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?
  2. 2.Solve: 6p + 14 = 4p + 16. What is p?
  3. 3.Solve: 3(x − 1) = x + 13. What is x?
  4. 4.Solve: 5(t − 1) = t + 19. What is t?
  5. 5.Solve: 4(y − 5) = 2y + 8. What is y?
  6. 6.A father is 26 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
  7. 7.Solve: t/4 + t/3 = 42. What is t?
  8. 8.A father is 32 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?
  9. 9.Solve: 5x + 18 = x + 50. What is x?
  10. 10.A father is 8 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: 3p + 8 = p + 20. What is p?
  12. 12.Solve: 4(x − 2) = x + 34. What is x?
  13. 13.The sum of three consecutive whole numbers is 99. What is the smallest of them?
  14. 14.The length of a rectangle is 3 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  15. 15.The length of a rectangle is 4 cm more than its width. Its perimeter is 72 cm. What is its width (in cm)?
  16. 16.A father is 12 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  17. 17.Solve: 8m + 17 = 2m + 101. What is m?
  18. 18.Solve: 6(n − 4) = n + 31. What is n?
  19. 19.Solve: 3(x − 3) = x + 21. What is x?
  20. 20.A father is 39 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  21. 21.Solve: 5y + 6 = 3y + 14. What is y?
  22. 22.The sum of four consecutive whole numbers is 86. What is the largest of them?
  23. 23.A father is 14 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  24. 24.The sum of two consecutive whole numbers is 35. What is the smallest of them?
  25. 25.Solve: 9y + 9 = 7y + 19. What is y?
  26. 26.The sum of two consecutive whole numbers is 51. What is the largest of them?
  27. 27.Solve: y/6 + y/5 = 22. What is y?
  28. 28.Solve: 6m + 6 = m + 11. What is m?
  29. 29.Solve: y/4 + y/3 = 56. What is y?
  30. 30.Solve: 6(n − 3) = n + 32. What is n?
  31. 31.The sum of three consecutive whole numbers is 27. What is the smallest of them?
  32. 32.Solve: y/3 + y/5 = 48. What is y?
  33. 33.Solve: x/4 + x/3 = 42. What is x?
  34. 34.Solve: t/3 + t/2 = 20. What is t?
  35. 35.The length of a rectangle is 15 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  36. 36.The sum of three consecutive whole numbers is 129. What is the smallest of them?
  37. 37.A father is 19 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  38. 38.Solve: 7y + 5 = 5y + 27. What is y?
  39. 39.Solve: 3(m − 2) = m + 16. What is m?
  40. 40.The sum of four consecutive whole numbers is 222. What is the smallest of them?

Answer key

  1. 5
  2. 1
  3. 8
  4. 6
  5. 14
  6. 9
  7. 72
  8. 8
  9. 8
  10. 3
  11. 6
  12. 14
  13. 32
  14. 14
  15. 16
  16. 9
  17. 14
  18. 11
  19. 15
  20. 10
  21. 4
  22. 23
  23. 7
  24. 17
  25. 5
  26. 26
  27. 60
  28. 1
  29. 96
  30. 10
  31. 8
  32. 90
  33. 72
  34. 24
  35. 17
  36. 42
  37. 11
  38. 11
  39. 11
  40. 54

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