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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 37 · 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: 5(n − 5) = 4n + 10. What is n?
  2. 2.The sum of two consecutive whole numbers is 31. What is the largest of them?
  3. 3.Solve: 3(p − 2) = 2p + 1. What is p?
  4. 4.The length of a rectangle is 5 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
  5. 5.The length of a rectangle is 13 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  6. 6.The length of a rectangle is 8 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  7. 7.A father is 24 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?
  8. 8.Solve: 5x + 18 = 2x + 57. What is x?
  9. 9.Solve: 7x + 14 = 3x + 70. What is x?
  10. 10.A father is 28 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?
  11. 11.Solve: 3(y − 5) = y + 21. What is y?
  12. 12.Solve: 5(p − 1) = 2p + 4. What is p?
  13. 13.Solve: 5(n − 4) = 2n + 25. What is n?
  14. 14.Solve: 9n + 8 = 2n + 29. What is n?
  15. 15.Solve: y/6 + y/4 = 35. What is y?
  16. 16.Solve: p/4 + p/3 = 7. What is p?
  17. 17.Solve: y/6 + y/5 = 22. What is y?
  18. 18.Solve: 5p + 2 = 2p + 17. What is p?
  19. 19.The sum of four consecutive whole numbers is 70. What is the smallest of them?
  20. 20.Solve: 6(y − 2) = 3y + 39. What is y?
  21. 21.Solve: 7m + 18 = 2m + 73. What is m?
  22. 22.Solve: 8t + 1 = 2t + 85. What is t?
  23. 23.The length of a rectangle is 15 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  24. 24.Solve: y/5 + y/2 = 42. What is y?
  25. 25.Solve: 6(m − 2) = 2m + 36. What is m?
  26. 26.The length of a rectangle is 6 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  27. 27.Solve: 5(t − 2) = 2t + 11. What is t?
  28. 28.The sum of two consecutive whole numbers is 85. What is the smallest of them?
  29. 29.Solve: 5(m − 1) = m + 43. What is m?
  30. 30.A father is 20 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?
  31. 31.The length of a rectangle is 1 cm more than its width. Its perimeter is 14 cm. What is its width (in cm)?
  32. 32.Solve: 3(p − 3) = p + 9. What is p?
  33. 33.Solve: 3(x − 1) = 2x + 12. What is x?
  34. 34.Solve: p/2 + p/3 = 35. What is p?
  35. 35.Solve: t/6 + t/4 = 35. What is t?
  36. 36.The length of a rectangle is 15 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  37. 37.A father is 24 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?
  38. 38.A father is 12 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?
  39. 39.Solve: 6(m − 2) = 2m + 12. What is m?
  40. 40.The length of a rectangle is 2 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?

Answer key

  1. 35
  2. 16
  3. 7
  4. 3
  5. 19
  6. 25
  7. 7
  8. 13
  9. 14
  10. 12
  11. 18
  12. 3
  13. 15
  14. 3
  15. 84
  16. 12
  17. 60
  18. 5
  19. 16
  20. 17
  21. 11
  22. 14
  23. 8
  24. 60
  25. 12
  26. 17
  27. 7
  28. 42
  29. 12
  30. 2
  31. 3
  32. 9
  33. 15
  34. 42
  35. 84
  36. 18
  37. 9
  38. 3
  39. 6
  40. 16

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