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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 43 · 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 15 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
  2. 2.The sum of three consecutive whole numbers is 141. What is the smallest of them?
  3. 3.The sum of two consecutive whole numbers is 95. What is the smallest of them?
  4. 4.Solve: y/2 + y/3 = 15. What is y?
  5. 5.Solve: 4y + 10 = y + 22. What is y?
  6. 6.Solve: 3(x − 3) = 2x + 13. What is x?
  7. 7.The sum of four consecutive whole numbers is 182. What is the smallest of them?
  8. 8.The sum of two consecutive whole numbers is 117. What is the smallest of them?
  9. 9.A father is 13 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  10. 10.Solve: p/6 + p/5 = 66. What is p?
  11. 11.Solve: 3(n − 1) = 2n + 6. What is n?
  12. 12.Solve: 6(m − 1) = 3m + 12. What is m?
  13. 13.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  14. 14.The length of a rectangle is 1 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
  15. 15.Solve: 5(t − 2) = 4t + 4. What is t?
  16. 16.Solve: 4(n − 5) = 3n + 8. What is n?
  17. 17.A father is 12 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?
  18. 18.Solve: 7m + 18 = m + 84. What is m?
  19. 19.Solve: 5t + 12 = t + 52. What is t?
  20. 20.The sum of two consecutive whole numbers is 65. What is the smallest of them?
  21. 21.The sum of two consecutive whole numbers is 73. What is the smallest of them?
  22. 22.Solve: m/2 + m/3 = 40. What is m?
  23. 23.Solve: 4(n − 1) = 3n + 12. What is n?
  24. 24.The sum of two consecutive whole numbers is 21. What is the largest of them?
  25. 25.A father is 14 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 two consecutive whole numbers is 11. What is the smallest of them?
  27. 27.The length of a rectangle is 2 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  28. 28.The sum of two consecutive whole numbers is 105. What is the largest of them?
  29. 29.Solve: 4(x − 2) = x + 31. What is x?
  30. 30.Solve: t/3 + t/4 = 14. What is t?
  31. 31.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?
  32. 32.Solve: 4m + 3 = m + 48. What is m?
  33. 33.Solve: 5(y − 2) = 4y + 4. What is y?
  34. 34.The length of a rectangle is 8 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
  35. 35.The length of a rectangle is 1 cm more than its width. Its perimeter is 14 cm. What is its width (in cm)?
  36. 36.The length of a rectangle is 9 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  37. 37.Solve: 8m + 18 = m + 60. What is m?
  38. 38.Solve: 9y + 18 = 6y + 63. What is y?
  39. 39.Solve: 3(m − 1) = m + 5. What is m?
  40. 40.Solve: 6(p − 4) = 4p + 16. What is p?

Answer key

  1. 13
  2. 46
  3. 47
  4. 18
  5. 4
  6. 22
  7. 44
  8. 58
  9. 12
  10. 180
  11. 9
  12. 6
  13. 6
  14. 4
  15. 14
  16. 28
  17. 3
  18. 11
  19. 10
  20. 32
  21. 36
  22. 48
  23. 16
  24. 11
  25. 4
  26. 5
  27. 26
  28. 53
  29. 13
  30. 24
  31. 5
  32. 15
  33. 14
  34. 29
  35. 3
  36. 21
  37. 6
  38. 15
  39. 4
  40. 20

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