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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 142 · 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 four consecutive whole numbers is 210. What is the largest of them?
  2. 2.Solve: 9t + 5 = 3t + 17. What is t?
  3. 3.Solve: 3n + 13 = n + 27. What is n?
  4. 4.A father is 14 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  5. 5.Solve: 3x + 9 = x + 29. What is x?
  6. 6.The length of a rectangle is 14 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  7. 7.The sum of three consecutive whole numbers is 21. What is the largest of them?
  8. 8.Solve: 4(p − 3) = 2p + 22. What is p?
  9. 9.The length of a rectangle is 12 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  10. 10.Solve: 6y + 16 = 2y + 40. What is y?
  11. 11.The length of a rectangle is 4 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  12. 12.Solve: 6(x − 2) = 5x + 11. What is x?
  13. 13.Solve: x/5 + x/3 = 56. What is x?
  14. 14.Solve: t/6 + t/2 = 4. What is t?
  15. 15.Solve: 3(n − 2) = n + 18. What is n?
  16. 16.The sum of two consecutive whole numbers is 31. What is the smallest of them?
  17. 17.The sum of two consecutive whole numbers is 101. What is the smallest of them?
  18. 18.Solve: 4(p − 5) = 2p + 20. What is p?
  19. 19.Solve: y/2 + y/5 = 21. What is y?
  20. 20.Solve: 6(y − 2) = y + 63. What is y?
  21. 21.Solve: 6y + 1 = 2y + 61. What is y?
  22. 22.The sum of two consecutive whole numbers is 85. What is the largest of them?
  23. 23.The length of a rectangle is 5 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  24. 24.Solve: 4(p − 2) = 3p + 10. What is p?
  25. 25.The sum of three consecutive whole numbers is 159. What is the smallest of them?
  26. 26.The sum of three consecutive whole numbers is 99. What is the smallest of them?
  27. 27.Solve: p/6 + p/2 = 20. What is p?
  28. 28.Solve: 5m + 13 = 2m + 22. What is m?
  29. 29.A father is 36 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?
  30. 30.A father is 14 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?
  31. 31.Solve: 6(t − 2) = t + 8. What is t?
  32. 32.A father is 7 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  33. 33.Solve: 7x + 15 = 5x + 23. What is x?
  34. 34.The length of a rectangle is 2 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  35. 35.The sum of three consecutive whole numbers is 24. What is the smallest of them?
  36. 36.The sum of three consecutive whole numbers is 165. What is the largest of them?
  37. 37.A father is 24 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?
  38. 38.Solve: 4x + 18 = 3x + 27. What is x?
  39. 39.A father is 27 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?
  40. 40.Solve: p/5 + p/6 = 44. What is p?

Answer key

  1. 54
  2. 2
  3. 7
  4. 11
  5. 10
  6. 2
  7. 8
  8. 17
  9. 15
  10. 6
  11. 15
  12. 23
  13. 105
  14. 6
  15. 12
  16. 15
  17. 50
  18. 20
  19. 30
  20. 15
  21. 15
  22. 43
  23. 8
  24. 18
  25. 52
  26. 32
  27. 30
  28. 3
  29. 6
  30. 2
  31. 4
  32. 6
  33. 4
  34. 16
  35. 7
  36. 56
  37. 5
  38. 9
  39. 3
  40. 120

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