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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 46 · 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: 4(p − 4) = p + 32. What is p?
  2. 2.The sum of two consecutive whole numbers is 87. What is the largest of them?
  3. 3.Solve: t/4 + t/3 = 7. What is t?
  4. 4.Solve: p/5 + p/2 = 42. What is p?
  5. 5.The length of a rectangle is 11 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  6. 6.The length of a rectangle is 5 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
  7. 7.The length of a rectangle is 6 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  8. 8.The length of a rectangle is 3 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  9. 9.The length of a rectangle is 6 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  10. 10.Solve: 3y + 7 = 2y + 18. What is y?
  11. 11.Solve: t/5 + t/6 = 55. What is t?
  12. 12.A father is 24 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?
  13. 13.A father is 22 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  14. 14.Solve: m/5 + m/2 = 56. What is m?
  15. 15.The length of a rectangle is 9 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  16. 16.Solve: 6x + 7 = x + 57. What is x?
  17. 17.The sum of four consecutive whole numbers is 154. What is the largest of them?
  18. 18.The length of a rectangle is 3 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  19. 19.A father is 36 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
  20. 20.The sum of two consecutive whole numbers is 111. What is the smallest of them?
  21. 21.The length of a rectangle is 4 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
  22. 22.The length of a rectangle is 12 cm more than its width. Its perimeter is 144 cm. What is its width (in cm)?
  23. 23.Solve: 4x + 18 = x + 60. What is x?
  24. 24.The sum of four consecutive whole numbers is 238. What is the largest of them?
  25. 25.A father is 20 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  26. 26.A father is 57 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  27. 27.A father is 11 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  28. 28.Solve: 3n + 1 = n + 9. What is n?
  29. 29.Solve: n/4 + n/6 = 25. What is n?
  30. 30.Solve: 9m + 10 = 8m + 14. What is m?
  31. 31.Solve: t/2 + t/6 = 28. What is t?
  32. 32.Solve: 3(x − 2) = 2x + 1. What is x?
  33. 33.Solve: 4(y − 1) = y + 14. What is y?
  34. 34.A father is 17 years older than his son. In 6 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 2 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
  36. 36.Solve: 6(x − 5) = x + 15. What is x?
  37. 37.Solve: m/3 + m/2 = 10. What is m?
  38. 38.A father is 15 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  39. 39.The length of a rectangle is 10 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  40. 40.The length of a rectangle is 7 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?

Answer key

  1. 16
  2. 44
  3. 12
  4. 60
  5. 19
  6. 4
  7. 8
  8. 24
  9. 20
  10. 11
  11. 150
  12. 4
  13. 4
  14. 80
  15. 18
  16. 10
  17. 40
  18. 30
  19. 6
  20. 55
  21. 4
  22. 30
  23. 14
  24. 61
  25. 12
  26. 11
  27. 7
  28. 4
  29. 60
  30. 4
  31. 42
  32. 7
  33. 6
  34. 11
  35. 15
  36. 9
  37. 12
  38. 8
  39. 4
  40. 16

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