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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 102 · 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: 3t + 17 = t + 33. What is t?
  2. 2.Solve: y/3 + y/2 = 10. What is y?
  3. 3.The length of a rectangle is 8 cm more than its width. Its perimeter is 72 cm. What is its width (in cm)?
  4. 4.The length of a rectangle is 13 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  5. 5.Solve: 6n + 1 = 3n + 34. What is n?
  6. 6.A father is 48 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
  7. 7.Solve: 3y + 16 = 2y + 30. What is y?
  8. 8.The sum of four consecutive whole numbers is 58. What is the smallest of them?
  9. 9.The sum of three consecutive whole numbers is 75. What is the largest of them?
  10. 10.Solve: n/2 + n/4 = 24. What is n?
  11. 11.The length of a rectangle is 2 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  12. 12.The length of a rectangle is 11 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  13. 13.Solve: 6t + 17 = t + 67. What is t?
  14. 14.The length of a rectangle is 2 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  15. 15.Solve: 6m + 9 = m + 14. What is m?
  16. 16.Solve: 5p + 8 = 3p + 20. What is p?
  17. 17.Solve: 4m + 5 = 2m + 11. What is m?
  18. 18.Solve: t/5 + t/4 = 27. What is t?
  19. 19.Solve: 6(y − 5) = 2y + 46. What is y?
  20. 20.The length of a rectangle is 11 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  21. 21.Solve: n/6 + n/3 = 21. What is n?
  22. 22.Solve: 4(p − 4) = 3p + 1. What is p?
  23. 23.The length of a rectangle is 8 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  24. 24.Solve: 5m + 20 = 3m + 22. What is m?
  25. 25.Solve: 5(x − 1) = 4x + 1. What is x?
  26. 26.Solve: 3(p − 1) = 2p + 12. What is p?
  27. 27.Solve: 6x + 3 = 4x + 21. What is x?
  28. 28.Solve: p/6 + p/4 = 10. What is p?
  29. 29.Solve: 3(t − 2) = 2t + 1. What is t?
  30. 30.The sum of two consecutive whole numbers is 97. What is the smallest of them?
  31. 31.The sum of two consecutive whole numbers is 23. What is the largest of them?
  32. 32.Solve: 5(p − 1) = 3p + 1. What is p?
  33. 33.The length of a rectangle is 13 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  34. 34.Solve: 5x + 15 = 3x + 33. What is x?
  35. 35.Solve: 6p + 2 = 5p + 6. What is p?
  36. 36.The length of a rectangle is 13 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  37. 37.Solve: t/5 + t/3 = 40. What is t?
  38. 38.Solve: 3p + 18 = 2p + 30. What is p?
  39. 39.The length of a rectangle is 12 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  40. 40.Solve: x/2 + x/4 = 9. What is x?

Answer key

  1. 8
  2. 12
  3. 14
  4. 19
  5. 11
  6. 10
  7. 14
  8. 13
  9. 26
  10. 32
  11. 26
  12. 29
  13. 10
  14. 28
  15. 1
  16. 6
  17. 3
  18. 60
  19. 19
  20. 18
  21. 42
  22. 17
  23. 16
  24. 1
  25. 6
  26. 15
  27. 9
  28. 24
  29. 7
  30. 48
  31. 12
  32. 3
  33. 9
  34. 9
  35. 4
  36. 16
  37. 75
  38. 12
  39. 8
  40. 12

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