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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 883 · 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.A father is 14 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  2. 2.The sum of three consecutive whole numbers is 78. What is the smallest of them?
  3. 3.Solve: y/3 + y/4 = 7. What is y?
  4. 4.Solve: 5y + 16 = y + 28. What is y?
  5. 5.Solve: 5(y − 4) = 3y + 6. What is y?
  6. 6.The length of a rectangle is 3 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  7. 7.The length of a rectangle is 3 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  8. 8.A father is 28 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
  9. 9.A father is 18 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  10. 10.The sum of two consecutive whole numbers is 37. What is the largest of them?
  11. 11.A father is 15 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  12. 12.Solve: y/5 + y/2 = 14. What is y?
  13. 13.Solve: 5(m − 2) = 2m + 2. What is m?
  14. 14.The sum of three consecutive whole numbers is 42. What is the smallest of them?
  15. 15.The length of a rectangle is 4 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  16. 16.Solve: 8x + 18 = 3x + 63. What is x?
  17. 17.The length of a rectangle is 7 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  18. 18.Solve: 6x + 11 = 5x + 26. What is x?
  19. 19.Solve: 5n + 16 = 4n + 22. What is n?
  20. 20.The length of a rectangle is 2 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
  21. 21.Solve: 3p + 7 = p + 31. What is p?
  22. 22.The length of a rectangle is 4 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  23. 23.The sum of four consecutive whole numbers is 130. What is the largest of them?
  24. 24.Solve: t/3 + t/6 = 24. What is t?
  25. 25.Solve: 3y + 5 = y + 27. What is y?
  26. 26.The sum of three consecutive whole numbers is 48. What is the smallest of them?
  27. 27.Solve: t/2 + t/5 = 42. What is t?
  28. 28.Solve: y/6 + y/4 = 30. What is y?
  29. 29.The sum of two consecutive whole numbers is 71. What is the smallest of them?
  30. 30.Solve: 3(x − 1) = 2x + 5. What is x?
  31. 31.Solve: 4(n − 2) = 2n + 14. What is n?
  32. 32.The length of a rectangle is 8 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  33. 33.Solve: m/4 + m/6 = 30. What is m?
  34. 34.The length of a rectangle is 5 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
  35. 35.Solve: 4x + 5 = 3x + 9. What is x?
  36. 36.Solve: 5(y − 1) = y + 51. What is y?
  37. 37.Solve: 4n + 13 = 3n + 20. What is n?
  38. 38.Solve: 7t + 4 = 5t + 20. What is t?
  39. 39.The sum of four consecutive whole numbers is 202. What is the smallest of them?
  40. 40.Solve: t/6 + t/3 = 15. What is t?

Answer key

  1. 9
  2. 25
  3. 12
  4. 3
  5. 13
  6. 15
  7. 21
  8. 9
  9. 5
  10. 19
  11. 7
  12. 20
  13. 4
  14. 13
  15. 8
  16. 9
  17. 28
  18. 15
  19. 6
  20. 5
  21. 12
  22. 14
  23. 34
  24. 48
  25. 11
  26. 15
  27. 60
  28. 72
  29. 35
  30. 8
  31. 11
  32. 15
  33. 72
  34. 18
  35. 4
  36. 14
  37. 7
  38. 8
  39. 49
  40. 30

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