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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 119 · 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 1 cm more than its width. Its perimeter is 10 cm. What is its width (in cm)?
  2. 2.Solve: 5x + 20 = 2x + 47. What is x?
  3. 3.Solve: 9y + 1 = 2y + 36. What is y?
  4. 4.Solve: y/2 + y/6 = 8. What is y?
  5. 5.Solve: 5(t − 1) = 4t + 12. What is t?
  6. 6.Solve: y/3 + y/2 = 30. What is y?
  7. 7.The sum of four consecutive whole numbers is 202. What is the largest of them?
  8. 8.Solve: 4n + 5 = 3n + 7. What is n?
  9. 9.Solve: n/4 + n/6 = 20. What is n?
  10. 10.Solve: 7y + 3 = 5y + 31. What is y?
  11. 11.Solve: 6(y − 3) = y + 62. What is y?
  12. 12.Solve: 4(p − 2) = p + 4. What is p?
  13. 13.Solve: 5(x − 2) = 3x + 18. What is x?
  14. 14.Solve: 6(m − 4) = 3m + 33. What is m?
  15. 15.Solve: x/3 + x/2 = 40. What is x?
  16. 16.Solve: 5y + 7 = y + 67. What is y?
  17. 17.The sum of four consecutive whole numbers is 230. What is the largest of them?
  18. 18.A father is 26 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
  19. 19.A father is 9 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  20. 20.The sum of two consecutive whole numbers is 67. What is the largest of them?
  21. 21.The length of a rectangle is 11 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  22. 22.Solve: 6p + 9 = p + 44. What is p?
  23. 23.Solve: 4p + 8 = p + 50. What is p?
  24. 24.Solve: 4y + 17 = 3y + 26. What is y?
  25. 25.Solve: 7p + 17 = 4p + 32. What is p?
  26. 26.Solve: p/3 + p/6 = 15. What is p?
  27. 27.Solve: 4(y − 1) = 2y + 8. What is y?
  28. 28.Solve: t/2 + t/3 = 5. What is t?
  29. 29.The length of a rectangle is 8 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  30. 30.Solve: x/5 + x/6 = 33. What is x?
  31. 31.The length of a rectangle is 10 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  32. 32.The length of a rectangle is 11 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  33. 33.The sum of four consecutive whole numbers is 46. What is the smallest of them?
  34. 34.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?
  35. 35.The sum of three consecutive whole numbers is 132. What is the largest of them?
  36. 36.A father is 54 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  37. 37.The sum of two consecutive whole numbers is 21. What is the largest of them?
  38. 38.Solve: 3t + 10 = t + 14. What is t?
  39. 39.Solve: 6m + 19 = 3m + 31. What is m?
  40. 40.The sum of four consecutive whole numbers is 46. What is the largest of them?

Answer key

  1. 2
  2. 9
  3. 5
  4. 12
  5. 17
  6. 36
  7. 52
  8. 2
  9. 48
  10. 14
  11. 16
  12. 4
  13. 14
  14. 19
  15. 48
  16. 15
  17. 59
  18. 5
  19. 5
  20. 34
  21. 16
  22. 7
  23. 14
  24. 9
  25. 5
  26. 30
  27. 6
  28. 6
  29. 24
  30. 90
  31. 14
  32. 7
  33. 10
  34. 11
  35. 45
  36. 11
  37. 11
  38. 2
  39. 4
  40. 13

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