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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 971 · 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 12 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  2. 2.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?
  3. 3.Solve: 3t + 16 = 2t + 18. What is t?
  4. 4.Solve: 5(y − 4) = 2y + 31. What is y?
  5. 5.Solve: 6(t − 1) = t + 44. What is t?
  6. 6.Solve: 3(p − 2) = 2p + 5. What is p?
  7. 7.Solve: 5x + 5 = x + 17. What is x?
  8. 8.Solve: 6y + 2 = 4y + 18. What is y?
  9. 9.Solve: 7x + 17 = 6x + 24. What is x?
  10. 10.Solve: 8p + 6 = 6p + 12. What is p?
  11. 11.Solve: 7y + 5 = 4y + 14. What is y?
  12. 12.The sum of two consecutive whole numbers is 69. What is the smallest of them?
  13. 13.Solve: 4m + 13 = 3m + 16. What is m?
  14. 14.Solve: 3(m − 1) = 2m + 8. What is m?
  15. 15.Solve: 7p + 14 = 4p + 59. What is p?
  16. 16.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?
  17. 17.Solve: 7n + 13 = 3n + 45. What is n?
  18. 18.A father is 11 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  19. 19.Solve: 3m + 20 = m + 30. What is m?
  20. 20.The length of a rectangle is 10 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
  21. 21.Solve: 3(y − 2) = y + 16. What is y?
  22. 22.Solve: m/2 + m/6 = 20. What is m?
  23. 23.A father is 4 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  24. 24.Solve: 8m + 5 = m + 96. What is m?
  25. 25.Solve: p/6 + p/2 = 12. What is p?
  26. 26.The length of a rectangle is 1 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  27. 27.Solve: 6(m − 1) = m + 44. What is m?
  28. 28.The length of a rectangle is 5 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  29. 29.The sum of three consecutive whole numbers is 147. What is the smallest of them?
  30. 30.Solve: 8x + 12 = 6x + 32. What is x?
  31. 31.Solve: 7p + 17 = 4p + 41. What is p?
  32. 32.Solve: 6(m − 1) = 3m + 27. What is m?
  33. 33.A father is 14 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  34. 34.The sum of three consecutive whole numbers is 51. What is the smallest of them?
  35. 35.Solve: m/4 + m/5 = 18. What is m?
  36. 36.Solve: 3t + 17 = 2t + 26. What is t?
  37. 37.A father is 16 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  38. 38.The sum of three consecutive whole numbers is 123. What is the largest of them?
  39. 39.Solve: 4m + 10 = 2m + 26. What is m?
  40. 40.The sum of two consecutive whole numbers is 105. What is the smallest of them?

Answer key

  1. 9
  2. 10
  3. 2
  4. 17
  5. 10
  6. 11
  7. 3
  8. 8
  9. 7
  10. 3
  11. 3
  12. 34
  13. 3
  14. 11
  15. 15
  16. 8
  17. 8
  18. 10
  19. 5
  20. 28
  21. 11
  22. 30
  23. 2
  24. 13
  25. 18
  26. 15
  27. 10
  28. 8
  29. 48
  30. 10
  31. 8
  32. 11
  33. 5
  34. 16
  35. 40
  36. 9
  37. 12
  38. 42
  39. 8
  40. 52

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