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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 747 · 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: 4(n − 5) = n + 4. What is n?
  2. 2.Solve: x/4 + x/2 = 12. What is x?
  3. 3.The sum of four consecutive whole numbers is 106. What is the largest of them?
  4. 4.Solve: 4(t − 4) = 3t + 3. What is t?
  5. 5.Solve: 3m + 7 = 2m + 16. What is m?
  6. 6.The sum of three consecutive whole numbers is 87. What is the smallest of them?
  7. 7.The sum of three consecutive whole numbers is 177. What is the smallest of them?
  8. 8.Solve: 4n + 8 = 3n + 11. What is n?
  9. 9.Solve: 6(x − 2) = x + 33. What is x?
  10. 10.The length of a rectangle is 6 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  11. 11.The sum of two consecutive whole numbers is 85. What is the largest of them?
  12. 12.Solve: 3y + 15 = y + 23. What is y?
  13. 13.The sum of three consecutive whole numbers is 30. What is the smallest of them?
  14. 14.The length of a rectangle is 9 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  15. 15.Solve: t/2 + t/4 = 9. What is t?
  16. 16.A father is 42 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?
  17. 17.Solve: x/6 + x/5 = 22. What is x?
  18. 18.Solve: 6(p − 1) = p + 4. What is p?
  19. 19.Solve: 6(x − 3) = x + 32. What is x?
  20. 20.Solve: 6(m − 2) = 3m + 3. What is m?
  21. 21.Solve: p/2 + p/5 = 21. What is p?
  22. 22.A father is 33 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  23. 23.Solve: 8n + 18 = 7n + 31. What is n?
  24. 24.Solve: 5(p − 4) = p + 8. What is p?
  25. 25.Solve: 3(x − 5) = 2x + 4. What is x?
  26. 26.Solve: 6(y − 4) = 3y + 3. What is y?
  27. 27.The sum of two consecutive whole numbers is 111. What is the largest of them?
  28. 28.Solve: 8y + 9 = 2y + 87. What is y?
  29. 29.A father is 39 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?
  30. 30.Solve: 5(m − 3) = m + 41. What is m?
  31. 31.A father is 24 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?
  32. 32.The sum of four consecutive whole numbers is 114. What is the smallest of them?
  33. 33.Solve: 5(m − 1) = 4m + 1. What is m?
  34. 34.Solve: 3y + 8 = 2y + 14. What is y?
  35. 35.Solve: 4(t − 1) = 2t + 14. What is t?
  36. 36.Solve: p/4 + p/6 = 25. What is p?
  37. 37.Solve: 3(t − 1) = t + 5. What is t?
  38. 38.A father is 22 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  39. 39.A father is 12 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?
  40. 40.Solve: 3x + 5 = x + 13. What is x?

Answer key

  1. 8
  2. 16
  3. 28
  4. 19
  5. 9
  6. 28
  7. 58
  8. 3
  9. 9
  10. 20
  11. 43
  12. 4
  13. 9
  14. 9
  15. 12
  16. 12
  17. 60
  18. 2
  19. 10
  20. 5
  21. 30
  22. 7
  23. 13
  24. 7
  25. 19
  26. 9
  27. 56
  28. 13
  29. 10
  30. 14
  31. 4
  32. 27
  33. 6
  34. 6
  35. 9
  36. 60
  37. 4
  38. 4
  39. 2
  40. 4

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