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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 127 · 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 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?
  2. 2.The sum of three consecutive whole numbers is 111. What is the smallest of them?
  3. 3.Solve: t/6 + t/4 = 5. What is t?
  4. 4.Solve: 6(x − 4) = x + 26. What is x?
  5. 5.The sum of four consecutive whole numbers is 86. What is the smallest of them?
  6. 6.Solve: 6y + 4 = 5y + 12. What is y?
  7. 7.The length of a rectangle is 10 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  8. 8.The length of a rectangle is 1 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  9. 9.Solve: p/5 + p/6 = 66. What is p?
  10. 10.A father is 28 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  11. 11.Solve: p/4 + p/3 = 21. What is p?
  12. 12.Solve: 4y + 8 = y + 14. What is y?
  13. 13.A father is 6 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  14. 14.A father is 30 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
  15. 15.Solve: 4(n − 2) = n + 28. What is n?
  16. 16.The sum of two consecutive whole numbers is 117. What is the largest of them?
  17. 17.Solve: y/5 + y/4 = 45. What is y?
  18. 18.A father is 8 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  19. 19.Solve: 4(t − 3) = t + 30. What is t?
  20. 20.Solve: 8x + 18 = 3x + 48. What is x?
  21. 21.Solve: y/4 + y/5 = 63. What is y?
  22. 22.A father is 7 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  23. 23.The sum of two consecutive whole numbers is 95. What is the smallest of them?
  24. 24.A father is 28 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?
  25. 25.The sum of four consecutive whole numbers is 54. What is the largest of them?
  26. 26.Solve: 4n + 4 = 2n + 6. What is n?
  27. 27.Solve: y/5 + y/6 = 88. What is y?
  28. 28.Solve: x/3 + x/2 = 15. What is x?
  29. 29.Solve: x/5 + x/6 = 33. What is x?
  30. 30.The length of a rectangle is 4 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  31. 31.Solve: 7y + 4 = 5y + 12. What is y?
  32. 32.Solve: 6t + 9 = 3t + 21. What is t?
  33. 33.A father is 11 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  34. 34.A father is 12 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  35. 35.The length of a rectangle is 11 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  36. 36.The sum of two consecutive whole numbers is 67. What is the largest of them?
  37. 37.The length of a rectangle is 3 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  38. 38.The length of a rectangle is 13 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  39. 39.The length of a rectangle is 5 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  40. 40.The length of a rectangle is 12 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?

Answer key

  1. 5
  2. 36
  3. 12
  4. 10
  5. 20
  6. 8
  7. 26
  8. 8
  9. 180
  10. 11
  11. 36
  12. 2
  13. 3
  14. 9
  15. 12
  16. 59
  17. 100
  18. 7
  19. 14
  20. 6
  21. 140
  22. 4
  23. 47
  24. 10
  25. 15
  26. 1
  27. 240
  28. 18
  29. 90
  30. 7
  31. 4
  32. 4
  33. 3
  34. 8
  35. 20
  36. 34
  37. 25
  38. 25
  39. 8
  40. 20

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