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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 433 · 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: 3(x − 3) = x + 13. What is x?
  2. 2.The sum of two consecutive whole numbers is 49. What is the smallest of them?
  3. 3.Solve: 3(x − 2) = 2x + 5. What is x?
  4. 4.Solve: 4(x − 1) = 3x + 3. What is x?
  5. 5.Solve: 5(x − 3) = 3x + 17. What is x?
  6. 6.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?
  7. 7.Solve: x/3 + x/6 = 21. What is x?
  8. 8.A father is 42 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  9. 9.A father is 24 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  10. 10.Solve: 4(t − 1) = 2t + 22. What is t?
  11. 11.A father is 18 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  12. 12.A father is 14 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  13. 13.The length of a rectangle is 11 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  14. 14.Solve: 6m + 11 = 2m + 71. What is m?
  15. 15.Solve: 4(n − 2) = n + 22. What is n?
  16. 16.Solve: 4(t − 5) = t + 16. What is t?
  17. 17.The length of a rectangle is 1 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  18. 18.Solve: 5(y − 1) = 4y + 5. What is y?
  19. 19.Solve: 3(n − 5) = 2n + 1. What is n?
  20. 20.Solve: 6(y − 5) = 4y + 16. What is y?
  21. 21.Solve: 3n + 5 = 2n + 18. What is n?
  22. 22.Solve: 3(m − 3) = m + 19. What is m?
  23. 23.Solve: n/2 + n/6 = 20. What is n?
  24. 24.Solve: 3t + 6 = 2t + 13. What is t?
  25. 25.Solve: y/2 + y/6 = 16. What is y?
  26. 26.Solve: 4x + 6 = 3x + 20. What is x?
  27. 27.The length of a rectangle is 14 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
  28. 28.The sum of four consecutive whole numbers is 130. What is the largest of them?
  29. 29.Solve: 7n + 16 = n + 46. What is n?
  30. 30.The sum of three consecutive whole numbers is 180. What is the largest of them?
  31. 31.The sum of two consecutive whole numbers is 45. What is the smallest of them?
  32. 32.The length of a rectangle is 15 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  33. 33.The length of a rectangle is 1 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  34. 34.The length of a rectangle is 9 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
  35. 35.The sum of two consecutive whole numbers is 43. What is the largest of them?
  36. 36.Solve: x/4 + x/3 = 21. What is x?
  37. 37.The sum of two consecutive whole numbers is 57. What is the smallest of them?
  38. 38.Solve: 8x + 5 = 5x + 8. What is x?
  39. 39.The sum of two consecutive whole numbers is 93. What is the smallest of them?
  40. 40.The sum of three consecutive whole numbers is 33. What is the smallest of them?

Answer key

  1. 11
  2. 24
  3. 11
  4. 7
  5. 16
  6. 5
  7. 42
  8. 11
  9. 4
  10. 13
  11. 3
  12. 12
  13. 6
  14. 15
  15. 10
  16. 12
  17. 25
  18. 10
  19. 16
  20. 23
  21. 13
  22. 14
  23. 30
  24. 7
  25. 24
  26. 14
  27. 26
  28. 34
  29. 5
  30. 61
  31. 22
  32. 11
  33. 22
  34. 28
  35. 22
  36. 36
  37. 28
  38. 1
  39. 46
  40. 10

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