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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 96 · 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: 3(m − 1) = m + 9. What is m?
  2. 2.Solve: 6(x − 3) = 4x + 18. What is x?
  3. 3.The sum of two consecutive whole numbers is 115. What is the smallest of them?
  4. 4.Solve: 3(n − 2) = 2n + 8. What is n?
  5. 5.The length of a rectangle is 9 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  6. 6.Solve: 7y + 14 = 5y + 26. What is y?
  7. 7.The length of a rectangle is 2 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  8. 8.Solve: p/3 + p/6 = 6. What is p?
  9. 9.The length of a rectangle is 9 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  10. 10.A father is 28 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?
  11. 11.Solve: 3(y − 2) = 2y + 13. What is y?
  12. 12.Solve: 5m + 1 = 3m + 17. What is m?
  13. 13.The length of a rectangle is 4 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  14. 14.The sum of three consecutive whole numbers is 138. What is the smallest of them?
  15. 15.Solve: 5(m − 1) = m + 27. What is m?
  16. 16.A father is 13 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  17. 17.Solve: 5(n − 5) = 4n + 7. What is n?
  18. 18.Solve: 3p + 18 = 2p + 22. What is p?
  19. 19.Solve: 6y + 3 = 5y + 17. What is y?
  20. 20.The sum of four consecutive whole numbers is 94. What is the largest of them?
  21. 21.A father is 13 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  22. 22.A father is 24 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?
  23. 23.The sum of two consecutive whole numbers is 109. What is the largest of them?
  24. 24.Solve: 4(y − 1) = y + 8. What is y?
  25. 25.Solve: y/6 + y/4 = 30. What is y?
  26. 26.Solve: 6y + 14 = 4y + 36. What is y?
  27. 27.Solve: 9n + 2 = 5n + 50. What is n?
  28. 28.Solve: 9n + 15 = 2n + 29. What is n?
  29. 29.Solve: 6x + 2 = 5x + 15. What is x?
  30. 30.Solve: y/4 + y/2 = 18. What is y?
  31. 31.Solve: p/2 + p/5 = 49. What is p?
  32. 32.The sum of three consecutive whole numbers is 27. What is the smallest of them?
  33. 33.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?
  34. 34.Solve: 3(t − 2) = 2t + 10. What is t?
  35. 35.A father is 26 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?
  36. 36.Solve: 9t + 5 = t + 77. What is t?
  37. 37.Solve: 3(p − 3) = 2p + 1. What is p?
  38. 38.Solve: 9m + 1 = 5m + 25. What is m?
  39. 39.The length of a rectangle is 11 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  40. 40.Solve: y/4 + y/3 = 28. What is y?

Answer key

  1. 6
  2. 18
  3. 57
  4. 14
  5. 19
  6. 6
  7. 19
  8. 12
  9. 3
  10. 9
  11. 19
  12. 8
  13. 25
  14. 45
  15. 8
  16. 10
  17. 32
  18. 4
  19. 14
  20. 25
  21. 12
  22. 10
  23. 55
  24. 4
  25. 72
  26. 11
  27. 12
  28. 2
  29. 13
  30. 24
  31. 70
  32. 8
  33. 6
  34. 16
  35. 5
  36. 9
  37. 10
  38. 6
  39. 7
  40. 48

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