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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 286 · 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 sum of three consecutive whole numbers is 99. What is the smallest of them?
  2. 2.Solve: x/2 + x/3 = 40. What is x?
  3. 3.The length of a rectangle is 15 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  4. 4.The length of a rectangle is 15 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  5. 5.Solve: 9y + 18 = 8y + 22. What is y?
  6. 6.Solve: 3t + 18 = 2t + 33. What is t?
  7. 7.Solve: t/6 + t/5 = 33. What is t?
  8. 8.Solve: x/3 + x/2 = 10. What is x?
  9. 9.Solve: 6(t − 1) = t + 29. What is t?
  10. 10.A father is 13 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  11. 11.The sum of four consecutive whole numbers is 174. What is the smallest of them?
  12. 12.The length of a rectangle is 1 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  13. 13.The sum of three consecutive whole numbers is 177. What is the smallest of them?
  14. 14.Solve: 5t + 10 = t + 66. What is t?
  15. 15.A father is 20 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?
  16. 16.Solve: 9n + 12 = 8n + 20. What is n?
  17. 17.Solve: 6(t − 5) = 4t + 16. What is t?
  18. 18.Solve: 5(y − 3) = 3y + 3. What is y?
  19. 19.A father is 16 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
  20. 20.Solve: 5(n − 5) = n + 11. What is n?
  21. 21.A father is 33 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  22. 22.Solve: 5(t − 3) = t + 49. What is t?
  23. 23.Solve: p/5 + p/3 = 8. What is p?
  24. 24.Solve: x/5 + x/3 = 56. What is x?
  25. 25.Solve: 3y + 20 = y + 22. What is y?
  26. 26.Solve: p/3 + p/2 = 35. What is p?
  27. 27.Solve: 4y + 3 = 2y + 29. What is y?
  28. 28.Solve: x/2 + x/4 = 24. What is x?
  29. 29.The length of a rectangle is 1 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
  30. 30.Solve: 4(n − 2) = 3n + 13. What is n?
  31. 31.The sum of three consecutive whole numbers is 138. What is the largest of them?
  32. 32.The length of a rectangle is 13 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  33. 33.Solve: 9t + 16 = t + 136. What is t?
  34. 34.Solve: p/2 + p/3 = 10. What is p?
  35. 35.Solve: 6(p − 2) = 5p + 1. What is p?
  36. 36.The sum of two consecutive whole numbers is 75. What is the smallest of them?
  37. 37.A father is 10 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  38. 38.Solve: 8t + 14 = 3t + 54. What is t?
  39. 39.Solve: n/3 + n/6 = 18. What is n?
  40. 40.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?

Answer key

  1. 32
  2. 48
  3. 18
  4. 24
  5. 4
  6. 15
  7. 90
  8. 12
  9. 7
  10. 7
  11. 42
  12. 15
  13. 58
  14. 14
  15. 6
  16. 8
  17. 23
  18. 9
  19. 3
  20. 9
  21. 8
  22. 16
  23. 15
  24. 105
  25. 1
  26. 42
  27. 13
  28. 32
  29. 5
  30. 21
  31. 47
  32. 22
  33. 15
  34. 12
  35. 13
  36. 37
  37. 2
  38. 8
  39. 36
  40. 2

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