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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 451 · 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 16 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  2. 2.Solve: p/5 + p/6 = 33. What is p?
  3. 3.Solve: 6t + 5 = 4t + 9. What is t?
  4. 4.Solve: p/4 + p/2 = 24. What is p?
  5. 5.A father is 12 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  6. 6.Solve: 6(p − 4) = 4p + 12. What is p?
  7. 7.A father is 10 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  8. 8.Solve: y/5 + y/4 = 27. What is y?
  9. 9.The sum of two consecutive whole numbers is 63. What is the smallest of them?
  10. 10.Solve: 6x + 10 = 3x + 55. What is x?
  11. 11.The length of a rectangle is 5 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
  12. 12.Solve: 6n + 10 = 4n + 36. What is n?
  13. 13.Solve: 6(t − 1) = 4t + 4. What is t?
  14. 14.The length of a rectangle is 5 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  15. 15.Solve: 6(t − 1) = 2t + 50. What is t?
  16. 16.Solve: x/4 + x/2 = 18. What is x?
  17. 17.Solve: p/3 + p/6 = 21. What is p?
  18. 18.Solve: 4n + 11 = 2n + 15. What is n?
  19. 19.A father is 14 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  20. 20.Solve: 3t + 11 = t + 15. What is t?
  21. 21.The length of a rectangle is 2 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  22. 22.A father is 14 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?
  23. 23.Solve: 5(n − 3) = 2n + 9. What is n?
  24. 24.The length of a rectangle is 1 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  25. 25.Solve: 4t + 6 = 2t + 24. What is t?
  26. 26.Solve: m/3 + m/4 = 21. What is m?
  27. 27.Solve: 6(p − 4) = 2p + 20. What is p?
  28. 28.Solve: x/4 + x/6 = 15. What is x?
  29. 29.Solve: 3(n − 4) = n + 8. What is n?
  30. 30.The length of a rectangle is 8 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  31. 31.The length of a rectangle is 4 cm more than its width. Its perimeter is 16 cm. What is its width (in cm)?
  32. 32.Solve: 8y + 7 = 7y + 13. What is y?
  33. 33.The length of a rectangle is 13 cm more than its width. Its perimeter is 146 cm. What is its width (in cm)?
  34. 34.Solve: 4(m − 4) = 2m + 26. What is m?
  35. 35.Solve: m/2 + m/6 = 16. What is m?
  36. 36.Solve: 4(t − 4) = 3t + 7. What is t?
  37. 37.Solve: 3(n − 1) = n + 23. What is n?
  38. 38.A father is 51 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?
  39. 39.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  40. 40.Solve: 5(y − 1) = 3y + 21. What is y?

Answer key

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

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