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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 166 · 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: 6(x − 5) = 2x + 6. What is x?
  2. 2.Solve: 9m + 3 = 7m + 29. What is m?
  3. 3.Solve: 5m + 2 = 2m + 14. What is m?
  4. 4.The length of a rectangle is 5 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  5. 5.Solve: 3y + 11 = y + 29. What is y?
  6. 6.The length of a rectangle is 6 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  7. 7.Solve: 6(x − 1) = 4x + 6. What is x?
  8. 8.The sum of two consecutive whole numbers is 21. What is the largest of them?
  9. 9.Solve: 9p + 2 = 7p + 8. What is p?
  10. 10.The length of a rectangle is 10 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  11. 11.Solve: 5n + 2 = 4n + 7. What is n?
  12. 12.Solve: 3(m − 3) = m + 19. What is m?
  13. 13.Solve: 5(y − 1) = 4y + 7. What is y?
  14. 14.The length of a rectangle is 12 cm more than its width. Its perimeter is 72 cm. What is its width (in cm)?
  15. 15.Solve: 3m + 14 = 2m + 22. What is m?
  16. 16.A father is 16 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  17. 17.Solve: x/6 + x/4 = 35. What is x?
  18. 18.Solve: n/4 + n/6 = 30. What is n?
  19. 19.Solve: 3x + 6 = x + 30. What is x?
  20. 20.The sum of two consecutive whole numbers is 11. What is the smallest of them?
  21. 21.Solve: y/4 + y/2 = 9. What is y?
  22. 22.The length of a rectangle is 1 cm more than its width. Its perimeter is 10 cm. What is its width (in cm)?
  23. 23.Solve: 4(x − 5) = x + 31. What is x?
  24. 24.A father is 9 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  25. 25.The sum of three consecutive whole numbers is 48. What is the largest of them?
  26. 26.Solve: 4(y − 1) = y + 11. What is y?
  27. 27.Solve: 5(x − 1) = 4x + 1. What is x?
  28. 28.Solve: x/6 + x/2 = 32. What is x?
  29. 29.A father is 18 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?
  30. 30.The length of a rectangle is 6 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  31. 31.Solve: t/5 + t/3 = 16. What is t?
  32. 32.The sum of three consecutive whole numbers is 177. What is the smallest of them?
  33. 33.Solve: y/2 + y/4 = 15. What is y?
  34. 34.The sum of four consecutive whole numbers is 166. What is the largest of them?
  35. 35.The length of a rectangle is 15 cm more than its width. Its perimeter is 146 cm. What is its width (in cm)?
  36. 36.Solve: n/5 + n/4 = 45. What is n?
  37. 37.A father is 34 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?
  38. 38.Solve: 4(t − 3) = 3t + 4. What is t?
  39. 39.The sum of two consecutive whole numbers is 113. What is the smallest of them?
  40. 40.The sum of three consecutive whole numbers is 78. What is the largest of them?

Answer key

  1. 9
  2. 13
  3. 4
  4. 5
  5. 9
  6. 17
  7. 6
  8. 11
  9. 3
  10. 5
  11. 5
  12. 14
  13. 12
  14. 12
  15. 8
  16. 10
  17. 84
  18. 72
  19. 12
  20. 5
  21. 12
  22. 2
  23. 17
  24. 6
  25. 17
  26. 5
  27. 6
  28. 48
  29. 8
  30. 24
  31. 30
  32. 58
  33. 20
  34. 43
  35. 29
  36. 100
  37. 12
  38. 16
  39. 56
  40. 27

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