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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 646 · 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.The length of a rectangle is 1 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  2. 2.Solve: x/6 + x/5 = 44. What is x?
  3. 3.Solve: 8n + 9 = 2n + 99. What is n?
  4. 4.The length of a rectangle is 8 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  5. 5.Solve: 3x + 7 = 2x + 8. What is x?
  6. 6.A father is 18 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?
  7. 7.Solve: 3y + 11 = 2y + 25. What is y?
  8. 8.Solve: 6(t − 4) = t + 16. What is t?
  9. 9.Solve: 5(p − 1) = 3p + 13. What is p?
  10. 10.Solve: 6y + 12 = 2y + 20. What is y?
  11. 11.Solve: 4p + 9 = 2p + 21. What is p?
  12. 12.A father is 30 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  13. 13.A father is 36 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?
  14. 14.Solve: 5(m − 2) = m + 30. What is m?
  15. 15.Solve: 3t + 17 = 2t + 27. What is t?
  16. 16.Solve: y/6 + y/2 = 12. What is y?
  17. 17.Solve: 5(p − 2) = p + 22. What is p?
  18. 18.Solve: 3n + 17 = 2n + 27. What is n?
  19. 19.Solve: m/4 + m/5 = 18. What is m?
  20. 20.The length of a rectangle is 5 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
  21. 21.The sum of four consecutive whole numbers is 218. What is the largest of them?
  22. 22.Solve: n/3 + n/2 = 35. What is n?
  23. 23.A father is 33 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  24. 24.Solve: t/4 + t/6 = 10. What is t?
  25. 25.Solve: 3t + 17 = 2t + 20. What is t?
  26. 26.The sum of four consecutive whole numbers is 66. What is the smallest of them?
  27. 27.The sum of three consecutive whole numbers is 27. What is the smallest of them?
  28. 28.Solve: n/3 + n/6 = 6. What is n?
  29. 29.Solve: 4n + 14 = 2n + 30. What is n?
  30. 30.Solve: n/2 + n/3 = 5. What is n?
  31. 31.Solve: 7n + 13 = n + 49. What is n?
  32. 32.Solve: 9p + 5 = 4p + 25. What is p?
  33. 33.Solve: t/4 + t/5 = 18. What is t?
  34. 34.The length of a rectangle is 5 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  35. 35.Solve: 6t + 13 = 4t + 21. What is t?
  36. 36.A father is 24 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?
  37. 37.The sum of two consecutive whole numbers is 111. What is the smallest of them?
  38. 38.Solve: 5(y − 5) = 4y + 6. What is y?
  39. 39.The sum of four consecutive whole numbers is 130. What is the smallest of them?
  40. 40.The sum of two consecutive whole numbers is 73. What is the smallest of them?

Answer key

  1. 17
  2. 120
  3. 15
  4. 16
  5. 1
  6. 4
  7. 14
  8. 8
  9. 9
  10. 2
  11. 6
  12. 9
  13. 9
  14. 10
  15. 10
  16. 18
  17. 8
  18. 10
  19. 40
  20. 3
  21. 56
  22. 42
  23. 10
  24. 24
  25. 3
  26. 15
  27. 8
  28. 12
  29. 8
  30. 6
  31. 6
  32. 4
  33. 40
  34. 23
  35. 4
  36. 4
  37. 55
  38. 31
  39. 31
  40. 36

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