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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 71 · 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: 6p + 13 = 3p + 49. What is p?
  2. 2.The length of a rectangle is 4 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  3. 3.Solve: 9m + 10 = 7m + 20. What is m?
  4. 4.Solve: 4(y − 1) = 2y + 22. What is y?
  5. 5.Solve: 6(m − 1) = 3m + 36. What is m?
  6. 6.The length of a rectangle is 13 cm more than its width. Its perimeter is 146 cm. What is its width (in cm)?
  7. 7.Solve: 9n + 5 = 2n + 33. What is n?
  8. 8.Solve: 7y + 3 = y + 75. What is y?
  9. 9.Solve: 3(x − 3) = 2x + 6. What is x?
  10. 10.Solve: y/2 + y/3 = 10. What is y?
  11. 11.A father is 8 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?
  12. 12.Solve: 4t + 2 = 3t + 8. What is t?
  13. 13.Solve: 6(y − 3) = 4y + 14. What is y?
  14. 14.Solve: 3(x − 1) = 2x + 8. What is x?
  15. 15.Solve: 4p + 7 = 2p + 23. What is p?
  16. 16.The length of a rectangle is 15 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  17. 17.Solve: x/2 + x/4 = 12. What is x?
  18. 18.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?
  19. 19.Solve: 3(y − 2) = y + 4. What is y?
  20. 20.The sum of three consecutive whole numbers is 36. What is the largest of them?
  21. 21.A father is 8 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?
  22. 22.A father is 16 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?
  23. 23.Solve: p/4 + p/5 = 54. What is p?
  24. 24.Solve: 4(m − 4) = m + 32. What is m?
  25. 25.Solve: 5(x − 2) = 2x + 32. What is x?
  26. 26.A father is 30 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  27. 27.The sum of three consecutive whole numbers is 54. What is the smallest of them?
  28. 28.The sum of four consecutive whole numbers is 86. What is the largest of them?
  29. 29.The length of a rectangle is 13 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  30. 30.Solve: 6(p − 4) = 3p + 30. What is p?
  31. 31.A father is 45 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  32. 32.Solve: 4x + 13 = 2x + 41. What is x?
  33. 33.The length of a rectangle is 4 cm more than its width. Its perimeter is 72 cm. What is its width (in cm)?
  34. 34.Solve: t/2 + t/3 = 35. What is t?
  35. 35.The length of a rectangle is 15 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  36. 36.Solve: 5(m − 2) = m + 14. What is m?
  37. 37.The sum of two consecutive whole numbers is 63. What is the largest of them?
  38. 38.Solve: 5(x − 2) = 4x + 6. What is x?
  39. 39.Solve: 5(y − 2) = y + 18. What is y?
  40. 40.A father is 9 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?

Answer key

  1. 12
  2. 23
  3. 5
  4. 13
  5. 14
  6. 30
  7. 4
  8. 12
  9. 15
  10. 12
  11. 2
  12. 6
  13. 16
  14. 11
  15. 8
  16. 18
  17. 16
  18. 5
  19. 5
  20. 13
  21. 3
  22. 5
  23. 120
  24. 16
  25. 14
  26. 3
  27. 17
  28. 23
  29. 3
  30. 18
  31. 11
  32. 14
  33. 16
  34. 42
  35. 5
  36. 6
  37. 32
  38. 16
  39. 7
  40. 7

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