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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 719 · 40 sums
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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 length of a rectangle is 11 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  2. 2.The sum of three consecutive whole numbers is 69. What is the largest of them?
  3. 3.Solve: n/3 + n/2 = 30. What is n?
  4. 4.Solve: 3(t − 4) = t + 24. What is t?
  5. 5.The sum of three consecutive whole numbers is 129. What is the smallest of them?
  6. 6.The length of a rectangle is 11 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  7. 7.The length of a rectangle is 3 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  8. 8.The sum of three consecutive whole numbers is 72. What is the smallest of them?
  9. 9.Solve: 5(t − 3) = 3t + 3. What is t?
  10. 10.Solve: 3n + 13 = n + 37. What is n?
  11. 11.Solve: 8x + 1 = 4x + 21. What is x?
  12. 12.Solve: x/6 + x/5 = 55. What is x?
  13. 13.Solve: 5x + 9 = 2x + 45. What is x?
  14. 14.Solve: 7x + 11 = 4x + 14. What is x?
  15. 15.Solve: 5(x − 2) = 4x + 3. What is x?
  16. 16.A father is 18 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?
  17. 17.The sum of two consecutive whole numbers is 99. What is the smallest of them?
  18. 18.Solve: 5n + 15 = 2n + 24. What is n?
  19. 19.The length of a rectangle is 2 cm more than its width. Its perimeter is 16 cm. What is its width (in cm)?
  20. 20.Solve: 5p + 8 = 2p + 47. What is p?
  21. 21.Solve: 8m + 11 = 3m + 86. What is m?
  22. 22.Solve: 7t + 9 = t + 63. What is t?
  23. 23.Solve: 4n + 19 = 3n + 23. What is n?
  24. 24.A father is 60 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?
  25. 25.The sum of four consecutive whole numbers is 94. What is the largest of them?
  26. 26.A father is 26 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  27. 27.Solve: 9n + 7 = 4n + 27. What is n?
  28. 28.Solve: 6(y − 1) = 3y + 15. What is y?
  29. 29.Solve: 6(m − 2) = m + 8. What is m?
  30. 30.Solve: t/4 + t/2 = 12. What is t?
  31. 31.A father is 36 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  32. 32.The sum of three consecutive whole numbers is 39. What is the smallest of them?
  33. 33.The length of a rectangle is 4 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  34. 34.Solve: t/2 + t/4 = 6. What is t?
  35. 35.Solve: m/2 + m/5 = 14. What is m?
  36. 36.Solve: 5y + 14 = 4y + 19. What is y?
  37. 37.Solve: 3(t − 3) = t + 5. What is t?
  38. 38.Solve: 4(n − 5) = n + 4. What is n?
  39. 39.The length of a rectangle is 4 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  40. 40.The sum of three consecutive whole numbers is 174. What is the smallest of them?

Answer key

  1. 12
  2. 24
  3. 36
  4. 18
  5. 42
  6. 2
  7. 29
  8. 23
  9. 9
  10. 12
  11. 5
  12. 150
  13. 12
  14. 1
  15. 13
  16. 3
  17. 49
  18. 3
  19. 3
  20. 13
  21. 15
  22. 9
  23. 4
  24. 12
  25. 25
  26. 6
  27. 4
  28. 7
  29. 4
  30. 16
  31. 11
  32. 12
  33. 24
  34. 8
  35. 20
  36. 5
  37. 7
  38. 8
  39. 10
  40. 57

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