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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 774 · 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: 3y + 7 = y + 35. What is y?
  2. 2.Solve: 8t + 10 = 6t + 16. What is t?
  3. 3.Solve: 4(p − 4) = 3p + 9. What is p?
  4. 4.Solve: 3x + 3 = 2x + 6. What is x?
  5. 5.The length of a rectangle is 5 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  6. 6.A father is 39 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  7. 7.The length of a rectangle is 6 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  8. 8.The length of a rectangle is 14 cm more than its width. Its perimeter is 136 cm. What is its width (in cm)?
  9. 9.The sum of three consecutive whole numbers is 30. What is the largest of them?
  10. 10.The length of a rectangle is 6 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
  11. 11.Solve: 3(n − 1) = n + 5. What is n?
  12. 12.The sum of two consecutive whole numbers is 93. What is the smallest of them?
  13. 13.Solve: 3n + 10 = n + 28. What is n?
  14. 14.Solve: 5(y − 5) = 4y + 10. What is y?
  15. 15.Solve: 3(x − 3) = 2x + 3. What is x?
  16. 16.The sum of four consecutive whole numbers is 146. What is the smallest of them?
  17. 17.Solve: 3p + 12 = 2p + 15. What is p?
  18. 18.Solve: 9x + 12 = 5x + 40. What is x?
  19. 19.Solve: 3(n − 5) = 2n + 8. What is n?
  20. 20.A father is 14 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  21. 21.Solve: m/3 + m/6 = 18. What is m?
  22. 22.Solve: 4(p − 1) = p + 11. What is p?
  23. 23.The length of a rectangle is 11 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  24. 24.Solve: 4(t − 5) = t + 4. What is t?
  25. 25.Solve: n/5 + n/3 = 16. What is n?
  26. 26.Solve: 9t + 18 = t + 74. What is t?
  27. 27.The length of a rectangle is 8 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  28. 28.Solve: t/4 + t/5 = 18. What is t?
  29. 29.The sum of three consecutive whole numbers is 105. What is the largest of them?
  30. 30.The sum of two consecutive whole numbers is 111. What is the smallest of them?
  31. 31.The length of a rectangle is 12 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  32. 32.Solve: 6x + 12 = x + 77. What is x?
  33. 33.The sum of two consecutive whole numbers is 51. What is the smallest of them?
  34. 34.Solve: y/2 + y/5 = 42. What is y?
  35. 35.Solve: x/4 + x/3 = 56. What is x?
  36. 36.The sum of three consecutive whole numbers is 48. What is the largest of them?
  37. 37.The length of a rectangle is 6 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  38. 38.The length of a rectangle is 14 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  39. 39.The length of a rectangle is 15 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
  40. 40.Solve: t/6 + t/3 = 21. What is t?

Answer key

  1. 14
  2. 3
  3. 25
  4. 3
  5. 15
  6. 11
  7. 17
  8. 27
  9. 11
  10. 2
  11. 4
  12. 46
  13. 9
  14. 35
  15. 12
  16. 35
  17. 3
  18. 7
  19. 23
  20. 6
  21. 36
  22. 5
  23. 20
  24. 8
  25. 30
  26. 7
  27. 16
  28. 40
  29. 36
  30. 55
  31. 24
  32. 13
  33. 25
  34. 60
  35. 96
  36. 17
  37. 13
  38. 23
  39. 13
  40. 42

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