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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 536 · 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 42 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  2. 2.The sum of four consecutive whole numbers is 242. What is the smallest of them?
  3. 3.Solve: 8p + 8 = 5p + 14. What is p?
  4. 4.Solve: 8p + 15 = 5p + 27. What is p?
  5. 5.A father is 30 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?
  6. 6.Solve: 3m + 3 = 2m + 5. What is m?
  7. 7.The length of a rectangle is 2 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  8. 8.The length of a rectangle is 7 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  9. 9.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?
  10. 10.The length of a rectangle is 4 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  11. 11.The sum of three consecutive whole numbers is 162. What is the smallest of them?
  12. 12.The sum of four consecutive whole numbers is 26. What is the smallest of them?
  13. 13.Solve: 5(p − 5) = p + 39. What is p?
  14. 14.The sum of two consecutive whole numbers is 59. What is the largest of them?
  15. 15.Solve: 3(n − 5) = 2n + 9. What is n?
  16. 16.The length of a rectangle is 12 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  17. 17.Solve: 5(t − 4) = t + 16. What is t?
  18. 18.Solve: x/2 + x/5 = 35. What is x?
  19. 19.The sum of four consecutive whole numbers is 178. What is the largest of them?
  20. 20.A father is 32 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?
  21. 21.Solve: 5(y − 3) = 4y + 10. What is y?
  22. 22.A father is 3 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  23. 23.Solve: 5(n − 2) = n + 50. What is n?
  24. 24.Solve: 8m + 18 = 7m + 27. What is m?
  25. 25.The length of a rectangle is 15 cm more than its width. Its perimeter is 142 cm. What is its width (in cm)?
  26. 26.The length of a rectangle is 15 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  27. 27.Solve: 3(n − 2) = 2n + 3. What is n?
  28. 28.The sum of four consecutive whole numbers is 62. What is the largest of them?
  29. 29.Solve: y/6 + y/2 = 24. What is y?
  30. 30.Solve: 5(y − 1) = y + 47. What is y?
  31. 31.A father is 30 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?
  32. 32.Solve: 6x + 18 = 4x + 30. What is x?
  33. 33.Solve: p/3 + p/6 = 6. What is p?
  34. 34.The length of a rectangle is 10 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  35. 35.The sum of three consecutive whole numbers is 30. What is the largest of them?
  36. 36.A father is 9 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  37. 37.A father is 34 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?
  38. 38.Solve: y/2 + y/6 = 28. What is y?
  39. 39.The length of a rectangle is 9 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  40. 40.Solve: 5(t − 2) = 2t + 14. What is t?

Answer key

  1. 9
  2. 59
  3. 2
  4. 4
  5. 8
  6. 2
  7. 21
  8. 4
  9. 5
  10. 11
  11. 53
  12. 5
  13. 16
  14. 30
  15. 24
  16. 7
  17. 9
  18. 50
  19. 46
  20. 8
  21. 25
  22. 2
  23. 15
  24. 9
  25. 28
  26. 27
  27. 9
  28. 17
  29. 36
  30. 13
  31. 8
  32. 6
  33. 12
  34. 12
  35. 11
  36. 8
  37. 11
  38. 42
  39. 5
  40. 8

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