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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 214 · 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.A father is 51 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?
  2. 2.Solve: 4(t − 2) = 3t + 8. What is t?
  3. 3.Solve: 3(n − 2) = n + 24. What is n?
  4. 4.Solve: 3(n − 1) = n + 23. What is n?
  5. 5.Solve: x/4 + x/3 = 28. What is x?
  6. 6.Solve: 3t + 8 = t + 10. What is t?
  7. 7.Solve: 7n + 4 = 2n + 74. What is n?
  8. 8.Solve: 9y + 20 = 4y + 70. What is y?
  9. 9.Solve: 4(x − 2) = x + 13. What is x?
  10. 10.Solve: y/4 + y/3 = 21. What is y?
  11. 11.Solve: 3(n − 3) = n + 9. What is n?
  12. 12.Solve: 6(x − 5) = x + 25. What is x?
  13. 13.Solve: 4n + 2 = 3n + 4. What is n?
  14. 14.Solve: 3m + 11 = 2m + 20. What is m?
  15. 15.Solve: n/4 + n/5 = 72. What is n?
  16. 16.The sum of three consecutive whole numbers is 33. What is the largest of them?
  17. 17.The length of a rectangle is 10 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  18. 18.A father is 22 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?
  19. 19.The length of a rectangle is 7 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  20. 20.A father is 16 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  21. 21.Solve: 6(m − 4) = 5m + 12. What is m?
  22. 22.Solve: y/6 + y/2 = 12. What is y?
  23. 23.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?
  24. 24.The sum of four consecutive whole numbers is 66. What is the largest of them?
  25. 25.Solve: x/3 + x/5 = 24. What is x?
  26. 26.Solve: 3(x − 5) = 2x + 2. What is x?
  27. 27.Solve: 6t + 2 = t + 67. What is t?
  28. 28.The length of a rectangle is 1 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  29. 29.Solve: 4(x − 2) = 3x + 2. What is x?
  30. 30.Solve: 3(m − 2) = 2m + 10. What is m?
  31. 31.A father is 18 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  32. 32.Solve: 6m + 16 = 5m + 30. What is m?
  33. 33.Solve: 3(y − 3) = y + 21. What is y?
  34. 34.A father is 28 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?
  35. 35.The length of a rectangle is 4 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  36. 36.Solve: 9x + 7 = 7x + 31. What is x?
  37. 37.Solve: 8x + 19 = x + 124. What is x?
  38. 38.Solve: 4p + 13 = 2p + 21. What is p?
  39. 39.Solve: 6(p − 1) = 3p + 6. What is p?
  40. 40.Solve: 7x + 5 = x + 23. What is x?

Answer key

  1. 11
  2. 16
  3. 15
  4. 13
  5. 48
  6. 1
  7. 14
  8. 10
  9. 7
  10. 36
  11. 9
  12. 11
  13. 2
  14. 9
  15. 160
  16. 12
  17. 18
  18. 3
  19. 8
  20. 6
  21. 36
  22. 18
  23. 7
  24. 18
  25. 45
  26. 17
  27. 13
  28. 21
  29. 10
  30. 16
  31. 10
  32. 14
  33. 15
  34. 7
  35. 17
  36. 12
  37. 15
  38. 4
  39. 4
  40. 3

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