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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 176 · 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 14 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  2. 2.The sum of three consecutive whole numbers is 51. What is the largest of them?
  3. 3.Solve: 9n + 13 = 7n + 17. What is n?
  4. 4.Solve: m/5 + m/6 = 66. What is m?
  5. 5.Solve: 5(n − 1) = 2n + 4. What is n?
  6. 6.Solve: n/2 + n/5 = 7. What is n?
  7. 7.The length of a rectangle is 3 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  8. 8.The length of a rectangle is 10 cm more than its width. Its perimeter is 136 cm. What is its width (in cm)?
  9. 9.The length of a rectangle is 1 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  10. 10.Solve: p/3 + p/2 = 30. What is p?
  11. 11.Solve: n/2 + n/3 = 40. What is n?
  12. 12.Solve: 4(x − 5) = 2x + 8. What is x?
  13. 13.Solve: 8y + 20 = 7y + 35. What is y?
  14. 14.Solve: 5(p − 2) = 3p + 24. What is p?
  15. 15.Solve: 5(m − 4) = m + 44. What is m?
  16. 16.Solve: 3(t − 3) = 2t + 3. What is t?
  17. 17.The sum of four consecutive whole numbers is 170. What is the smallest of them?
  18. 18.The sum of two consecutive whole numbers is 13. What is the smallest of them?
  19. 19.The sum of four consecutive whole numbers is 102. What is the smallest of them?
  20. 20.A father is 9 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  21. 21.Solve: 9p + 2 = 4p + 12. What is p?
  22. 22.The sum of two consecutive whole numbers is 119. What is the smallest of them?
  23. 23.The length of a rectangle is 8 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  24. 24.The sum of three consecutive whole numbers is 54. What is the largest of them?
  25. 25.Solve: 8p + 13 = 3p + 73. What is p?
  26. 26.Solve: 7y + 4 = 3y + 48. What is y?
  27. 27.Solve: 5(n − 3) = n + 1. What is n?
  28. 28.The length of a rectangle is 1 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  29. 29.Solve: 4(n − 4) = 3n + 11. What is n?
  30. 30.Solve: 5x + 7 = 4x + 15. What is x?
  31. 31.Solve: 8t + 5 = 4t + 61. What is t?
  32. 32.Solve: 9x + 4 = x + 100. What is x?
  33. 33.Solve: n/2 + n/4 = 12. What is n?
  34. 34.Solve: 8x + 6 = 5x + 30. What is x?
  35. 35.The length of a rectangle is 5 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
  36. 36.Solve: 4x + 11 = 3x + 23. What is x?
  37. 37.A father is 24 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  38. 38.A father is 14 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?
  39. 39.The sum of three consecutive whole numbers is 72. What is the largest of them?
  40. 40.The sum of three consecutive whole numbers is 126. What is the largest of them?

Answer key

  1. 15
  2. 18
  3. 2
  4. 180
  5. 3
  6. 10
  7. 29
  8. 29
  9. 21
  10. 36
  11. 48
  12. 14
  13. 15
  14. 17
  15. 16
  16. 12
  17. 41
  18. 6
  19. 24
  20. 3
  21. 2
  22. 59
  23. 18
  24. 19
  25. 12
  26. 11
  27. 4
  28. 18
  29. 27
  30. 8
  31. 14
  32. 12
  33. 16
  34. 8
  35. 30
  36. 12
  37. 6
  38. 3
  39. 25
  40. 43

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