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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 111 · 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.A father is 36 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?
  2. 2.A father is 28 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?
  3. 3.The sum of three consecutive whole numbers is 150. What is the largest of them?
  4. 4.Solve: 5x + 4 = 2x + 49. What is x?
  5. 5.The sum of two consecutive whole numbers is 37. What is the smallest of them?
  6. 6.A father is 33 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?
  7. 7.The length of a rectangle is 9 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  8. 8.Solve: 7p + 14 = p + 86. What is p?
  9. 9.Solve: n/5 + n/6 = 55. What is n?
  10. 10.The length of a rectangle is 5 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  11. 11.The length of a rectangle is 11 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  12. 12.The length of a rectangle is 11 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  13. 13.Solve: 6(p − 1) = 5p + 6. What is p?
  14. 14.The length of a rectangle is 14 cm more than its width. Its perimeter is 140 cm. What is its width (in cm)?
  15. 15.Solve: x/2 + x/4 = 15. What is x?
  16. 16.Solve: 6n + 16 = 4n + 30. What is n?
  17. 17.Solve: x/3 + x/5 = 40. What is x?
  18. 18.Solve: 4m + 3 = m + 21. What is m?
  19. 19.Solve: 4(n − 5) = n + 37. What is n?
  20. 20.Solve: 4m + 5 = 2m + 31. What is m?
  21. 21.The sum of two consecutive whole numbers is 79. What is the largest of them?
  22. 22.Solve: n/4 + n/5 = 54. What is n?
  23. 23.Solve: 6x + 20 = x + 65. What is x?
  24. 24.Solve: 4(t − 4) = 2t + 12. What is t?
  25. 25.A father is 12 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?
  26. 26.Solve: 4p + 4 = 2p + 28. What is p?
  27. 27.Solve: 6(n − 3) = 2n + 26. What is n?
  28. 28.Solve: 4x + 17 = 3x + 28. What is x?
  29. 29.Solve: 3(m − 4) = 2m + 7. What is m?
  30. 30.The sum of two consecutive whole numbers is 17. What is the largest of them?
  31. 31.Solve: t/4 + t/3 = 35. What is t?
  32. 32.Solve: 8y + 11 = 2y + 83. What is y?
  33. 33.A father is 26 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
  34. 34.A father is 10 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  35. 35.Solve: n/3 + n/2 = 5. What is n?
  36. 36.The length of a rectangle is 10 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  37. 37.The sum of three consecutive whole numbers is 117. What is the smallest of them?
  38. 38.The sum of four consecutive whole numbers is 134. What is the largest of them?
  39. 39.Solve: 5p + 18 = 3p + 42. What is p?
  40. 40.Solve: 8m + 3 = 5m + 18. What is m?

Answer key

  1. 10
  2. 10
  3. 51
  4. 15
  5. 18
  6. 9
  7. 15
  8. 12
  9. 150
  10. 10
  11. 29
  12. 18
  13. 12
  14. 28
  15. 20
  16. 7
  17. 75
  18. 6
  19. 19
  20. 13
  21. 40
  22. 120
  23. 9
  24. 14
  25. 2
  26. 12
  27. 11
  28. 11
  29. 19
  30. 9
  31. 60
  32. 12
  33. 7
  34. 8
  35. 6
  36. 17
  37. 38
  38. 35
  39. 12
  40. 5

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