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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 415 · 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: 3(n − 2) = 2n + 2. What is n?
  2. 2.Solve: 4(m − 2) = 3m + 10. What is m?
  3. 3.Solve: 3n + 2 = 2n + 14. What is n?
  4. 4.Solve: 3(t − 3) = t + 7. What is t?
  5. 5.The sum of three consecutive whole numbers is 81. What is the smallest of them?
  6. 6.Solve: y/5 + y/6 = 33. What is y?
  7. 7.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?
  8. 8.The sum of four consecutive whole numbers is 74. What is the largest of them?
  9. 9.Solve: 4(n − 1) = 2n + 4. What is n?
  10. 10.Solve: 6n + 6 = 4n + 24. What is n?
  11. 11.The sum of three consecutive whole numbers is 117. What is the largest of them?
  12. 12.Solve: 6p + 3 = 3p + 42. What is p?
  13. 13.The length of a rectangle is 4 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  14. 14.Solve: 8t + 4 = 4t + 32. What is t?
  15. 15.A father is 18 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  16. 16.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  17. 17.Solve: 8x + 5 = 6x + 29. What is x?
  18. 18.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?
  19. 19.The sum of four consecutive whole numbers is 94. What is the largest of them?
  20. 20.A father is 14 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  21. 21.Solve: y/4 + y/5 = 27. What is y?
  22. 22.The length of a rectangle is 2 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  23. 23.A father is 24 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?
  24. 24.Solve: 8y + 7 = 4y + 51. What is y?
  25. 25.Solve: 9m + 8 = 7m + 32. What is m?
  26. 26.Solve: 6(t − 4) = 4t + 16. What is t?
  27. 27.Solve: 3(n − 2) = 2n + 8. What is n?
  28. 28.The sum of three consecutive whole numbers is 99. What is the largest of them?
  29. 29.The length of a rectangle is 13 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  30. 30.Solve: 6(n − 2) = 4n + 12. What is n?
  31. 31.The length of a rectangle is 10 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  32. 32.Solve: p/6 + p/3 = 18. What is p?
  33. 33.The sum of four consecutive whole numbers is 166. What is the largest of them?
  34. 34.Solve: m/6 + m/5 = 22. What is m?
  35. 35.Solve: 7y + 2 = 5y + 32. What is y?
  36. 36.A father is 22 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?
  37. 37.The sum of two consecutive whole numbers is 119. What is the smallest of them?
  38. 38.The length of a rectangle is 1 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  39. 39.Solve: 5(n − 4) = 4n + 8. What is n?
  40. 40.Solve: y/3 + y/5 = 56. What is y?

Answer key

  1. 8
  2. 18
  3. 12
  4. 8
  5. 26
  6. 90
  7. 9
  8. 20
  9. 4
  10. 9
  11. 40
  12. 13
  13. 9
  14. 7
  15. 5
  16. 6
  17. 12
  18. 3
  19. 25
  20. 10
  21. 60
  22. 8
  23. 6
  24. 11
  25. 12
  26. 20
  27. 14
  28. 34
  29. 13
  30. 12
  31. 22
  32. 36
  33. 43
  34. 60
  35. 15
  36. 3
  37. 59
  38. 17
  39. 28
  40. 105

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