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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 104 · 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 20 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  2. 2.A father is 17 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  3. 3.Solve: 6n + 17 = 2n + 49. What is n?
  4. 4.A father is 26 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  5. 5.A father is 10 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?
  6. 6.Solve: 5(p − 3) = p + 9. What is p?
  7. 7.Solve: x/4 + x/2 = 24. What is x?
  8. 8.A father is 36 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?
  9. 9.The length of a rectangle is 8 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  10. 10.Solve: y/3 + y/6 = 3. What is y?
  11. 11.The sum of three consecutive whole numbers is 42. What is the largest of them?
  12. 12.The length of a rectangle is 8 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  13. 13.The sum of four consecutive whole numbers is 146. What is the smallest of them?
  14. 14.The sum of two consecutive whole numbers is 29. What is the smallest of them?
  15. 15.The length of a rectangle is 9 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  16. 16.The sum of three consecutive whole numbers is 123. What is the largest of them?
  17. 17.The sum of three consecutive whole numbers is 66. What is the largest of them?
  18. 18.Solve: 6t + 7 = t + 47. What is t?
  19. 19.Solve: p/2 + p/6 = 20. What is p?
  20. 20.The length of a rectangle is 2 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  21. 21.The length of a rectangle is 4 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  22. 22.Solve: p/6 + p/4 = 10. What is p?
  23. 23.Solve: 3x + 12 = x + 36. What is x?
  24. 24.Solve: 9y + 10 = y + 26. What is y?
  25. 25.Solve: 6x + 3 = 3x + 21. What is x?
  26. 26.Solve: 5(x − 3) = x + 9. What is x?
  27. 27.Solve: 4(x − 5) = 3x + 9. What is x?
  28. 28.Solve: 6x + 19 = 4x + 39. What is x?
  29. 29.The sum of two consecutive whole numbers is 89. What is the largest of them?
  30. 30.Solve: 4(n − 2) = 3n + 12. What is n?
  31. 31.The length of a rectangle is 14 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  32. 32.A father is 16 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  33. 33.Solve: x/4 + x/6 = 5. What is x?
  34. 34.Solve: n/5 + n/4 = 45. What is n?
  35. 35.Solve: 8m + 19 = 2m + 79. What is m?
  36. 36.Solve: x/6 + x/3 = 9. What is x?
  37. 37.Solve: 9p + 18 = 6p + 30. What is p?
  38. 38.Solve: y/6 + y/3 = 21. What is y?
  39. 39.Solve: t/3 + t/2 = 5. What is t?
  40. 40.A father is 22 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?

Answer key

  1. 9
  2. 12
  3. 8
  4. 12
  5. 2
  6. 6
  7. 32
  8. 11
  9. 26
  10. 6
  11. 15
  12. 10
  13. 35
  14. 14
  15. 19
  16. 42
  17. 23
  18. 8
  19. 30
  20. 20
  21. 13
  22. 24
  23. 12
  24. 2
  25. 6
  26. 6
  27. 29
  28. 10
  29. 45
  30. 20
  31. 5
  32. 9
  33. 12
  34. 100
  35. 10
  36. 18
  37. 4
  38. 42
  39. 6
  40. 8

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