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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 450 · 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 6 years, the father will be four times as old as his son. How old is the son now?
  2. 2.Solve: 3t + 15 = t + 21. What is t?
  3. 3.Solve: n/2 + n/3 = 5. What is n?
  4. 4.Solve: 7y + 7 = 6y + 17. What is y?
  5. 5.Solve: 3(n − 5) = n + 19. What is n?
  6. 6.The sum of four consecutive whole numbers is 218. What is the smallest of them?
  7. 7.The length of a rectangle is 12 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  8. 8.Solve: 6(t − 1) = t + 59. What is t?
  9. 9.The length of a rectangle is 15 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
  10. 10.The length of a rectangle is 9 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  11. 11.The length of a rectangle is 12 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
  12. 12.A father is 13 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  13. 13.Solve: 4(x − 5) = 2x + 20. What is x?
  14. 14.Solve: 6(n − 3) = 4n + 26. What is n?
  15. 15.The sum of two consecutive whole numbers is 35. What is the smallest of them?
  16. 16.Solve: x/5 + x/3 = 64. What is x?
  17. 17.Solve: p/2 + p/6 = 12. What is p?
  18. 18.The sum of four consecutive whole numbers is 62. What is the smallest of them?
  19. 19.The sum of two consecutive whole numbers is 59. What is the smallest of them?
  20. 20.Solve: 6(p − 5) = 4p + 4. What is p?
  21. 21.Solve: 3(y − 5) = y + 17. What is y?
  22. 22.Solve: m/3 + m/5 = 24. What is m?
  23. 23.Solve: 6(x − 5) = 5x + 9. What is x?
  24. 24.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?
  25. 25.The sum of two consecutive whole numbers is 101. What is the smallest of them?
  26. 26.The length of a rectangle is 8 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  27. 27.Solve: 5(n − 5) = 4n + 4. What is n?
  28. 28.The sum of two consecutive whole numbers is 45. What is the largest of them?
  29. 29.Solve: 8y + 4 = 7y + 9. What is y?
  30. 30.The sum of three consecutive whole numbers is 114. What is the largest of them?
  31. 31.The length of a rectangle is 1 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  32. 32.The sum of two consecutive whole numbers is 53. What is the largest of them?
  33. 33.A father is 51 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?
  34. 34.The sum of three consecutive whole numbers is 21. What is the smallest of them?
  35. 35.Solve: 7y + 13 = 5y + 23. What is y?
  36. 36.The sum of three consecutive whole numbers is 21. What is the largest of them?
  37. 37.Solve: 6n + 7 = 3n + 40. What is n?
  38. 38.Solve: 6(p − 1) = p + 44. What is p?
  39. 39.Solve: 8y + 1 = 7y + 5. What is y?
  40. 40.The sum of two consecutive whole numbers is 95. What is the largest of them?

Answer key

  1. 8
  2. 3
  3. 6
  4. 10
  5. 17
  6. 53
  7. 19
  8. 13
  9. 26
  10. 24
  11. 2
  12. 7
  13. 20
  14. 22
  15. 17
  16. 120
  17. 18
  18. 14
  19. 29
  20. 17
  21. 16
  22. 45
  23. 39
  24. 4
  25. 50
  26. 23
  27. 29
  28. 23
  29. 5
  30. 39
  31. 7
  32. 27
  33. 11
  34. 6
  35. 5
  36. 8
  37. 11
  38. 10
  39. 4
  40. 48

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