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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 597 · 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(t − 2) = t + 63. What is t?
  2. 2.Solve: 3x + 11 = 2x + 20. What is x?
  3. 3.Solve: p/5 + p/2 = 21. What is p?
  4. 4.Solve: 4y + 6 = 2y + 22. What is y?
  5. 5.The length of a rectangle is 7 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  6. 6.The length of a rectangle is 15 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  7. 7.A father is 24 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?
  8. 8.Solve: y/3 + y/5 = 40. What is y?
  9. 9.Solve: y/3 + y/2 = 10. What is y?
  10. 10.Solve: 7t + 14 = 4t + 44. What is t?
  11. 11.Solve: 6(p − 2) = 4p + 2. What is p?
  12. 12.Solve: n/3 + n/6 = 3. What is n?
  13. 13.Solve: p/2 + p/3 = 15. What is p?
  14. 14.Solve: x/6 + x/4 = 35. What is x?
  15. 15.The length of a rectangle is 9 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  16. 16.The sum of four consecutive whole numbers is 190. What is the largest of them?
  17. 17.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  18. 18.Solve: 4x + 3 = x + 24. What is x?
  19. 19.The sum of four consecutive whole numbers is 158. What is the smallest of them?
  20. 20.Solve: 5(p − 4) = 2p + 34. What is p?
  21. 21.A father is 14 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  22. 22.The length of a rectangle is 2 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
  23. 23.The length of a rectangle is 6 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  24. 24.Solve: 8t + 14 = 2t + 56. What is t?
  25. 25.The length of a rectangle is 3 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  26. 26.Solve: 5(p − 2) = 3p + 14. What is p?
  27. 27.The sum of two consecutive whole numbers is 59. What is the largest of them?
  28. 28.A father is 26 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?
  29. 29.The length of a rectangle is 5 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  30. 30.The sum of three consecutive whole numbers is 138. What is the smallest of them?
  31. 31.The sum of three consecutive whole numbers is 21. What is the smallest of them?
  32. 32.The sum of two consecutive whole numbers is 33. What is the smallest of them?
  33. 33.Solve: 8y + 2 = 2y + 50. What is y?
  34. 34.Solve: 3p + 12 = 2p + 24. What is p?
  35. 35.Solve: 3(x − 2) = x + 18. What is x?
  36. 36.A father is 15 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  37. 37.Solve: x/3 + x/4 = 56. What is x?
  38. 38.Solve: n/4 + n/5 = 72. What is n?
  39. 39.Solve: n/4 + n/2 = 24. What is n?
  40. 40.Solve: 4p + 8 = 2p + 38. What is p?

Answer key

  1. 15
  2. 9
  3. 30
  4. 8
  5. 9
  6. 24
  7. 11
  8. 75
  9. 12
  10. 10
  11. 7
  12. 6
  13. 18
  14. 84
  15. 7
  16. 49
  17. 2
  18. 7
  19. 38
  20. 18
  21. 4
  22. 5
  23. 21
  24. 7
  25. 24
  26. 12
  27. 30
  28. 6
  29. 9
  30. 45
  31. 6
  32. 16
  33. 8
  34. 12
  35. 12
  36. 7
  37. 96
  38. 160
  39. 32
  40. 15

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