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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 317 · 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.The sum of three consecutive whole numbers is 21. What is the smallest of them?
  2. 2.A father is 9 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  3. 3.Solve: n/3 + n/2 = 5. What is n?
  4. 4.The length of a rectangle is 10 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  5. 5.Solve: 3p + 4 = p + 32. What is p?
  6. 6.A father is 30 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?
  7. 7.Solve: 5(t − 1) = 2t + 7. What is t?
  8. 8.Solve: 5(y − 2) = 3y + 2. What is y?
  9. 9.The length of a rectangle is 1 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
  10. 10.A father is 30 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?
  11. 11.Solve: 3(x − 3) = x + 17. What is x?
  12. 12.Solve: 5n + 3 = 3n + 9. What is n?
  13. 13.The length of a rectangle is 10 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  14. 14.Solve: 6(x − 4) = x + 51. What is x?
  15. 15.Solve: x/5 + x/6 = 11. What is x?
  16. 16.The length of a rectangle is 1 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  17. 17.A father is 28 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?
  18. 18.Solve: 4(p − 5) = 2p + 2. What is p?
  19. 19.Solve: x/3 + x/4 = 21. What is x?
  20. 20.Solve: y/4 + y/3 = 14. What is y?
  21. 21.The sum of four consecutive whole numbers is 190. What is the smallest of them?
  22. 22.Solve: 4t + 20 = 3t + 26. What is t?
  23. 23.Solve: 6(p − 5) = p + 25. What is p?
  24. 24.Solve: n/4 + n/5 = 54. What is n?
  25. 25.Solve: 7t + 6 = t + 66. What is t?
  26. 26.The sum of three consecutive whole numbers is 99. What is the largest of them?
  27. 27.The sum of three consecutive whole numbers is 156. What is the smallest of them?
  28. 28.Solve: m/4 + m/6 = 15. What is m?
  29. 29.Solve: 3(m − 4) = 2m + 3. What is m?
  30. 30.The length of a rectangle is 6 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  31. 31.The sum of four consecutive whole numbers is 70. What is the smallest of them?
  32. 32.Solve: 6n + 10 = 5n + 15. What is n?
  33. 33.Solve: 4(y − 1) = 2y + 4. What is y?
  34. 34.The length of a rectangle is 13 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  35. 35.Solve: 9n + 2 = n + 66. What is n?
  36. 36.A father is 12 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  37. 37.Solve: 3(t − 4) = 2t + 10. What is t?
  38. 38.The sum of two consecutive whole numbers is 73. What is the smallest of them?
  39. 39.Solve: 3(p − 2) = p + 12. What is p?
  40. 40.Solve: p/4 + p/6 = 5. What is p?

Answer key

  1. 6
  2. 6
  3. 6
  4. 8
  5. 14
  6. 9
  7. 4
  8. 6
  9. 4
  10. 10
  11. 13
  12. 3
  13. 5
  14. 15
  15. 30
  16. 19
  17. 10
  18. 11
  19. 36
  20. 24
  21. 46
  22. 6
  23. 11
  24. 120
  25. 10
  26. 34
  27. 51
  28. 36
  29. 15
  30. 8
  31. 16
  32. 5
  33. 4
  34. 17
  35. 8
  36. 5
  37. 22
  38. 36
  39. 9
  40. 12

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