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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 35 · 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 82 cm. What is its width (in cm)?
  2. 2.A father is 10 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  3. 3.Solve: 9x + 5 = 3x + 29. What is x?
  4. 4.Solve: 9p + 12 = 2p + 47. What is p?
  5. 5.The sum of four consecutive whole numbers is 218. What is the smallest of them?
  6. 6.Solve: m/2 + m/6 = 4. What is m?
  7. 7.Solve: 4(n − 3) = 3n + 4. What is n?
  8. 8.Solve: y/6 + y/5 = 55. What is y?
  9. 9.Solve: 9p + 12 = 6p + 48. What is p?
  10. 10.The length of a rectangle is 4 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  11. 11.Solve: 7n + 19 = 2n + 24. What is n?
  12. 12.The length of a rectangle is 7 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  13. 13.The sum of four consecutive whole numbers is 218. What is the largest of them?
  14. 14.Solve: y/3 + y/2 = 35. What is y?
  15. 15.Solve: 4p + 2 = p + 44. What is p?
  16. 16.A father is 13 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  17. 17.Solve: 5(y − 4) = 4y + 2. What is y?
  18. 18.The length of a rectangle is 1 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  19. 19.Solve: p/5 + p/2 = 21. What is p?
  20. 20.Solve: 9y + 4 = 8y + 7. What is y?
  21. 21.Solve: 8t + 16 = 4t + 48. What is t?
  22. 22.Solve: 6(m − 4) = 5m + 7. What is m?
  23. 23.A father is 11 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  24. 24.Solve: t/3 + t/2 = 5. What is t?
  25. 25.Solve: 9t + 13 = 2t + 76. What is t?
  26. 26.Solve: 6(y − 5) = 3y + 33. What is y?
  27. 27.Solve: m/3 + m/2 = 25. What is m?
  28. 28.Solve: 4m + 8 = m + 23. What is m?
  29. 29.The sum of two consecutive whole numbers is 111. What is the smallest of them?
  30. 30.Solve: x/6 + x/4 = 25. What is x?
  31. 31.Solve: 8y + 6 = 2y + 12. What is y?
  32. 32.Solve: 5p + 6 = 2p + 39. What is p?
  33. 33.The sum of two consecutive whole numbers is 55. What is the smallest of them?
  34. 34.Solve: 5y + 13 = y + 45. What is y?
  35. 35.The length of a rectangle is 1 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  36. 36.Solve: 3n + 13 = n + 17. What is n?
  37. 37.The length of a rectangle is 2 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
  38. 38.Solve: 6y + 1 = 2y + 37. What is y?
  39. 39.A father is 18 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?
  40. 40.Solve: 6(n − 4) = n + 11. What is n?

Answer key

  1. 20
  2. 3
  3. 4
  4. 5
  5. 53
  6. 6
  7. 16
  8. 150
  9. 12
  10. 5
  11. 1
  12. 22
  13. 56
  14. 42
  15. 14
  16. 8
  17. 22
  18. 12
  19. 30
  20. 3
  21. 8
  22. 31
  23. 5
  24. 6
  25. 9
  26. 21
  27. 30
  28. 5
  29. 55
  30. 60
  31. 1
  32. 11
  33. 27
  34. 8
  35. 22
  36. 2
  37. 7
  38. 9
  39. 2
  40. 7

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