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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 413 · 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.Solve: 5(n − 5) = 3n + 3. What is n?
  2. 2.A father is 13 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  3. 3.A father is 5 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  4. 4.The length of a rectangle is 13 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  5. 5.The sum of two consecutive whole numbers is 41. What is the largest of them?
  6. 6.Solve: 7x + 14 = x + 86. What is x?
  7. 7.The length of a rectangle is 13 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  8. 8.Solve: 6(x − 1) = 5x + 4. What is x?
  9. 9.A father is 11 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  10. 10.Solve: 5(n − 2) = 4n + 4. What is n?
  11. 11.Solve: p/3 + p/2 = 10. What is p?
  12. 12.The length of a rectangle is 11 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  13. 13.Solve: 3x + 5 = x + 7. What is x?
  14. 14.Solve: 4t + 8 = t + 50. What is t?
  15. 15.Solve: 5(t − 4) = 3t + 16. What is t?
  16. 16.A father is 33 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?
  17. 17.A father is 12 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  18. 18.Solve: t/2 + t/4 = 3. What is t?
  19. 19.Solve: 3(y − 3) = 2y + 3. What is y?
  20. 20.Solve: 4(y − 5) = y + 4. What is y?
  21. 21.Solve: 4(t − 3) = 2t + 24. What is t?
  22. 22.The length of a rectangle is 4 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  23. 23.Solve: 6(n − 2) = 5n + 8. What is n?
  24. 24.The length of a rectangle is 11 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  25. 25.Solve: 7t + 20 = 4t + 41. What is t?
  26. 26.Solve: 7m + 6 = 3m + 54. What is m?
  27. 27.Solve: 9t + 4 = 2t + 32. What is t?
  28. 28.Solve: n/5 + n/3 = 32. What is n?
  29. 29.Solve: 3(x − 5) = x + 15. What is x?
  30. 30.A father is 16 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  31. 31.Solve: 4(x − 5) = 2x + 4. What is x?
  32. 32.Solve: t/4 + t/6 = 5. What is t?
  33. 33.Solve: 4n + 3 = 3n + 17. What is n?
  34. 34.A father is 11 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  35. 35.The length of a rectangle is 10 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  36. 36.The sum of four consecutive whole numbers is 174. What is the largest of them?
  37. 37.Solve: 6(t − 2) = 2t + 28. What is t?
  38. 38.Solve: y/6 + y/3 = 15. What is y?
  39. 39.Solve: 6(n − 4) = 3n + 36. What is n?
  40. 40.The sum of two consecutive whole numbers is 109. What is the smallest of them?

Answer key

  1. 14
  2. 6
  3. 4
  4. 5
  5. 21
  6. 12
  7. 15
  8. 10
  9. 7
  10. 14
  11. 12
  12. 14
  13. 1
  14. 14
  15. 18
  16. 5
  17. 7
  18. 4
  19. 12
  20. 8
  21. 18
  22. 10
  23. 20
  24. 29
  25. 7
  26. 12
  27. 4
  28. 60
  29. 15
  30. 12
  31. 12
  32. 12
  33. 14
  34. 5
  35. 12
  36. 45
  37. 10
  38. 30
  39. 20
  40. 54

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