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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 489 · 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 length of a rectangle is 8 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  2. 2.The length of a rectangle is 9 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  3. 3.The length of a rectangle is 11 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  4. 4.The sum of three consecutive whole numbers is 24. What is the smallest of them?
  5. 5.Solve: 4(x − 1) = x + 14. What is x?
  6. 6.The length of a rectangle is 10 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  7. 7.Solve: 5(p − 4) = p + 8. What is p?
  8. 8.The length of a rectangle is 3 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  9. 9.Solve: 3y + 20 = 2y + 28. What is y?
  10. 10.Solve: n/2 + n/3 = 15. What is n?
  11. 11.The length of a rectangle is 2 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  12. 12.The sum of three consecutive whole numbers is 84. What is the largest of them?
  13. 13.Solve: 3n + 7 = n + 17. What is n?
  14. 14.Solve: t/2 + t/6 = 20. What is t?
  15. 15.A father is 27 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?
  16. 16.The sum of two consecutive whole numbers is 35. What is the largest of them?
  17. 17.Solve: y/3 + y/4 = 56. What is y?
  18. 18.Solve: 5(y − 5) = 2y + 2. What is y?
  19. 19.Solve: 5m + 15 = 2m + 45. What is m?
  20. 20.Solve: t/5 + t/3 = 24. What is t?
  21. 21.Solve: 5t + 4 = 4t + 19. What is t?
  22. 22.Solve: m/5 + m/2 = 7. What is m?
  23. 23.Solve: 4(y − 2) = 3y + 1. What is y?
  24. 24.Solve: 4x + 15 = 3x + 23. What is x?
  25. 25.The length of a rectangle is 8 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  26. 26.The sum of two consecutive whole numbers is 87. What is the largest of them?
  27. 27.Solve: 4(n − 2) = 3n + 1. What is n?
  28. 28.The sum of four consecutive whole numbers is 66. What is the smallest of them?
  29. 29.Solve: 9n + 10 = 3n + 16. What is n?
  30. 30.The length of a rectangle is 1 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  31. 31.Solve: 6(x − 3) = 5x + 6. What is x?
  32. 32.Solve: p/5 + p/3 = 8. What is p?
  33. 33.The sum of two consecutive whole numbers is 115. What is the largest of them?
  34. 34.Solve: 3(p − 2) = 2p + 7. What is p?
  35. 35.The sum of three consecutive whole numbers is 123. What is the largest of them?
  36. 36.A father is 30 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?
  37. 37.Solve: 7p + 6 = 5p + 18. What is p?
  38. 38.Solve: 6x + 9 = x + 34. What is x?
  39. 39.The sum of four consecutive whole numbers is 170. What is the smallest of them?
  40. 40.Solve: 3(p − 2) = 2p + 12. What is p?

Answer key

  1. 15
  2. 26
  3. 11
  4. 7
  5. 6
  6. 7
  7. 7
  8. 17
  9. 8
  10. 18
  11. 12
  12. 29
  13. 5
  14. 30
  15. 8
  16. 18
  17. 96
  18. 9
  19. 10
  20. 45
  21. 15
  22. 10
  23. 9
  24. 8
  25. 6
  26. 44
  27. 9
  28. 15
  29. 1
  30. 17
  31. 24
  32. 15
  33. 58
  34. 13
  35. 42
  36. 12
  37. 6
  38. 5
  39. 41
  40. 18

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