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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 404 · 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.The length of a rectangle is 5 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  2. 2.Solve: 4(m − 1) = 3m + 2. What is m?
  3. 3.The sum of two consecutive whole numbers is 11. What is the smallest of them?
  4. 4.Solve: 3(m − 3) = 2m + 6. What is m?
  5. 5.Solve: 4(p − 1) = 2p + 6. What is p?
  6. 6.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?
  7. 7.Solve: 6(x − 3) = x + 42. What is x?
  8. 8.The length of a rectangle is 7 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  9. 9.The length of a rectangle is 14 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  10. 10.Solve: 9t + 1 = 8t + 3. What is t?
  11. 11.Solve: 6(p − 4) = 5p + 8. What is p?
  12. 12.Solve: 5(n − 5) = n + 39. What is n?
  13. 13.Solve: y/2 + y/3 = 40. What is y?
  14. 14.A father is 24 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
  15. 15.A father is 30 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?
  16. 16.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?
  17. 17.The length of a rectangle is 12 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  18. 18.A father is 57 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?
  19. 19.The sum of two consecutive whole numbers is 27. What is the largest of them?
  20. 20.The length of a rectangle is 8 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  21. 21.A father is 12 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.The sum of three consecutive whole numbers is 165. What is the largest of them?
  23. 23.The sum of three consecutive whole numbers is 168. What is the largest of them?
  24. 24.Solve: 3(x − 5) = x + 5. What is x?
  25. 25.A father is 28 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?
  26. 26.The sum of four consecutive whole numbers is 130. What is the largest of them?
  27. 27.The sum of two consecutive whole numbers is 113. What is the smallest of them?
  28. 28.Solve: 9y + 6 = 5y + 62. What is y?
  29. 29.Solve: 9m + 2 = 5m + 54. What is m?
  30. 30.The length of a rectangle is 12 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  31. 31.The sum of four consecutive whole numbers is 86. What is the largest of them?
  32. 32.The sum of four consecutive whole numbers is 66. What is the largest of them?
  33. 33.Solve: 5(n − 4) = 2n + 13. What is n?
  34. 34.The length of a rectangle is 2 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  35. 35.A father is 38 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?
  36. 36.The length of a rectangle is 15 cm more than its width. Its perimeter is 146 cm. What is its width (in cm)?
  37. 37.Solve: 6(x − 2) = x + 28. What is x?
  38. 38.The length of a rectangle is 2 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  39. 39.Solve: m/3 + m/4 = 7. What is m?
  40. 40.Solve: y/6 + y/5 = 55. What is y?

Answer key

  1. 8
  2. 6
  3. 5
  4. 15
  5. 5
  6. 3
  7. 12
  8. 21
  9. 21
  10. 2
  11. 32
  12. 16
  13. 48
  14. 8
  15. 4
  16. 12
  17. 16
  18. 12
  19. 14
  20. 24
  21. 5
  22. 56
  23. 57
  24. 10
  25. 11
  26. 34
  27. 56
  28. 14
  29. 13
  30. 21
  31. 23
  32. 18
  33. 11
  34. 18
  35. 12
  36. 29
  37. 8
  38. 24
  39. 12
  40. 150

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