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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 326 · 40 sums
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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: t/5 + t/4 = 36. What is t?
  2. 2.Solve: 5(m − 4) = 2m + 10. What is m?
  3. 3.Solve: n/4 + n/3 = 56. What is n?
  4. 4.Solve: 6(m − 2) = 3m + 9. What is m?
  5. 5.The sum of four consecutive whole numbers is 70. What is the smallest of them?
  6. 6.Solve: 6p + 8 = 3p + 50. What is p?
  7. 7.A father is 12 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  8. 8.Solve: y/4 + y/5 = 63. What is y?
  9. 9.Solve: 4(t − 3) = t + 27. What is t?
  10. 10.Solve: 6(n − 4) = 5n + 13. What is n?
  11. 11.Solve: n/5 + n/2 = 28. What is n?
  12. 12.Solve: 5(y − 1) = y + 35. What is y?
  13. 13.Solve: 3(x − 1) = 2x + 11. What is x?
  14. 14.Solve: 4n + 17 = n + 50. What is n?
  15. 15.Solve: 5(n − 5) = n + 11. What is n?
  16. 16.Solve: 9x + 3 = 7x + 11. What is x?
  17. 17.A father is 26 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  18. 18.Solve: 6(x − 4) = x + 26. What is x?
  19. 19.A father is 12 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  20. 20.Solve: x/4 + x/6 = 25. What is x?
  21. 21.Solve: n/4 + n/5 = 36. What is n?
  22. 22.Solve: 7x + 13 = 5x + 33. What is x?
  23. 23.The length of a rectangle is 2 cm more than its width. Its perimeter is 12 cm. What is its width (in cm)?
  24. 24.Solve: 3(x − 4) = 2x + 5. What is x?
  25. 25.Solve: 6(t − 3) = 3t + 27. What is t?
  26. 26.The length of a rectangle is 13 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  27. 27.The length of a rectangle is 5 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  28. 28.Solve: 6(m − 2) = 5m + 8. What is m?
  29. 29.The length of a rectangle is 5 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  30. 30.The sum of four consecutive whole numbers is 218. What is the largest of them?
  31. 31.The length of a rectangle is 7 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  32. 32.The length of a rectangle is 14 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  33. 33.Solve: 6(n − 1) = 4n + 18. What is n?
  34. 34.Solve: t/4 + t/6 = 15. What is t?
  35. 35.A father is 10 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  36. 36.Solve: 8m + 4 = 7m + 8. What is m?
  37. 37.Solve: 8t + 3 = t + 17. What is t?
  38. 38.Solve: 6m + 6 = 4m + 8. What is m?
  39. 39.Solve: 6n + 2 = 2n + 14. What is n?
  40. 40.Solve: 3(m − 3) = m + 17. What is m?

Answer key

  1. 80
  2. 10
  3. 96
  4. 7
  5. 16
  6. 14
  7. 8
  8. 140
  9. 13
  10. 37
  11. 40
  12. 10
  13. 14
  14. 11
  15. 9
  16. 4
  17. 12
  18. 10
  19. 5
  20. 60
  21. 80
  22. 10
  23. 2
  24. 17
  25. 15
  26. 23
  27. 19
  28. 20
  29. 27
  30. 56
  31. 20
  32. 3
  33. 12
  34. 36
  35. 5
  36. 4
  37. 2
  38. 1
  39. 3
  40. 13

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