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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 583 · 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.Solve: 7t + 9 = 4t + 21. What is t?
  2. 2.Solve: 8n + 18 = n + 74. What is n?
  3. 3.The sum of four consecutive whole numbers is 82. What is the smallest of them?
  4. 4.The length of a rectangle is 4 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  5. 5.Solve: 3y + 14 = 2y + 19. What is y?
  6. 6.Solve: 4(p − 2) = 2p + 4. What is p?
  7. 7.The length of a rectangle is 10 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
  8. 8.The sum of four consecutive whole numbers is 82. What is the largest of them?
  9. 9.The sum of three consecutive whole numbers is 81. What is the largest of them?
  10. 10.Solve: 7p + 17 = 3p + 61. What is p?
  11. 11.Solve: 3(y − 1) = y + 23. What is y?
  12. 12.Solve: 7x + 12 = 4x + 15. What is x?
  13. 13.The length of a rectangle is 7 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  14. 14.The length of a rectangle is 7 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  15. 15.Solve: 3p + 6 = p + 32. What is p?
  16. 16.The length of a rectangle is 2 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  17. 17.Solve: y/5 + y/3 = 24. What is y?
  18. 18.The sum of three consecutive whole numbers is 168. What is the largest of them?
  19. 19.The sum of four consecutive whole numbers is 58. What is the largest of them?
  20. 20.Solve: 5n + 19 = 2n + 37. What is n?
  21. 21.Solve: m/4 + m/2 = 24. What is m?
  22. 22.Solve: 3(t − 1) = t + 13. What is t?
  23. 23.A father is 12 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  24. 24.The sum of two consecutive whole numbers is 47. What is the smallest of them?
  25. 25.Solve: 8p + 20 = 6p + 32. What is p?
  26. 26.Solve: 6m + 11 = 2m + 35. What is m?
  27. 27.Solve: 4(m − 5) = m + 25. What is m?
  28. 28.The length of a rectangle is 2 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  29. 29.Solve: 5n + 20 = 3n + 44. What is n?
  30. 30.Solve: p/6 + p/3 = 15. What is p?
  31. 31.Solve: 3(y − 5) = 2y + 10. What is y?
  32. 32.The sum of two consecutive whole numbers is 15. What is the largest of them?
  33. 33.The sum of two consecutive whole numbers is 73. What is the largest of them?
  34. 34.Solve: 3p + 5 = 2p + 19. What is p?
  35. 35.Solve: m/4 + m/6 = 30. What is m?
  36. 36.A father is 30 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?
  37. 37.Solve: x/4 + x/6 = 20. What is x?
  38. 38.Solve: 7p + 17 = 4p + 32. What is p?
  39. 39.Solve: y/2 + y/3 = 20. What is y?
  40. 40.Solve: 3t + 2 = t + 26. What is t?

Answer key

  1. 4
  2. 8
  3. 19
  4. 22
  5. 5
  6. 6
  7. 27
  8. 22
  9. 28
  10. 11
  11. 13
  12. 1
  13. 10
  14. 16
  15. 13
  16. 15
  17. 45
  18. 57
  19. 16
  20. 6
  21. 32
  22. 8
  23. 5
  24. 23
  25. 6
  26. 6
  27. 15
  28. 29
  29. 12
  30. 30
  31. 25
  32. 8
  33. 37
  34. 14
  35. 72
  36. 11
  37. 48
  38. 5
  39. 24
  40. 12

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