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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 540 · 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: 8n + 12 = 7n + 15. What is n?
  2. 2.The length of a rectangle is 10 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  3. 3.Solve: 6(n − 4) = 2n + 52. What is n?
  4. 4.The length of a rectangle is 4 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  5. 5.Solve: 4(t − 5) = 3t + 2. What is t?
  6. 6.Solve: n/6 + n/3 = 6. What is n?
  7. 7.A father is 39 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?
  8. 8.Solve: 3(n − 5) = n + 5. What is n?
  9. 9.Solve: 4(t − 3) = t + 9. What is t?
  10. 10.A father is 22 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?
  11. 11.Solve: 5x + 17 = 4x + 32. What is x?
  12. 12.Solve: 9y + 3 = 8y + 14. What is y?
  13. 13.A father is 5 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  14. 14.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?
  15. 15.The sum of two consecutive whole numbers is 69. What is the smallest of them?
  16. 16.Solve: x/4 + x/3 = 14. What is x?
  17. 17.Solve: m/3 + m/6 = 9. What is m?
  18. 18.Solve: 6(y − 4) = 3y + 27. What is y?
  19. 19.Solve: 6n + 17 = 3n + 47. What is n?
  20. 20.Solve: 3m + 11 = 2m + 18. What is m?
  21. 21.Solve: 5(p − 1) = 4p + 1. What is p?
  22. 22.A father is 21 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  23. 23.Solve: x/4 + x/3 = 49. What is x?
  24. 24.Solve: t/3 + t/4 = 42. What is t?
  25. 25.Solve: 7p + 13 = 6p + 26. What is p?
  26. 26.Solve: 6(p − 5) = 3p + 15. What is p?
  27. 27.Solve: 3(t − 5) = 2t + 7. What is t?
  28. 28.Solve: 7p + 3 = 5p + 11. What is p?
  29. 29.The sum of two consecutive whole numbers is 49. What is the smallest of them?
  30. 30.A father is 12 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  31. 31.The sum of three consecutive whole numbers is 171. What is the largest of them?
  32. 32.A father is 13 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  33. 33.Solve: 5(y − 2) = 4y + 4. What is y?
  34. 34.Solve: 5(p − 2) = 2p + 8. What is p?
  35. 35.Solve: n/3 + n/4 = 42. What is n?
  36. 36.Solve: 6(p − 3) = p + 42. What is p?
  37. 37.The length of a rectangle is 3 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
  38. 38.The length of a rectangle is 12 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  39. 39.A father is 9 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  40. 40.Solve: 8n + 7 = 6n + 31. What is n?

Answer key

  1. 3
  2. 20
  3. 19
  4. 7
  5. 22
  6. 12
  7. 5
  8. 10
  9. 7
  10. 7
  11. 15
  12. 11
  13. 4
  14. 10
  15. 34
  16. 24
  17. 18
  18. 17
  19. 10
  20. 7
  21. 6
  22. 2
  23. 84
  24. 72
  25. 13
  26. 15
  27. 22
  28. 4
  29. 24
  30. 10
  31. 58
  32. 7
  33. 14
  34. 6
  35. 72
  36. 12
  37. 4
  38. 14
  39. 5
  40. 12

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