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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 534 · 40 sums
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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(t − 2) = t + 8. What is t?
  2. 2.A father is 22 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?
  3. 3.The sum of four consecutive whole numbers is 34. What is the smallest of them?
  4. 4.Solve: n/2 + n/4 = 21. What is n?
  5. 5.Solve: p/3 + p/2 = 25. What is p?
  6. 6.Solve: 5p + 1 = p + 33. What is p?
  7. 7.Solve: m/6 + m/3 = 24. What is m?
  8. 8.The length of a rectangle is 7 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  9. 9.A father is 20 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  10. 10.Solve: t/4 + t/5 = 9. What is t?
  11. 11.Solve: 4(p − 1) = p + 26. What is p?
  12. 12.Solve: n/5 + n/4 = 63. What is n?
  13. 13.The length of a rectangle is 5 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
  14. 14.Solve: n/3 + n/2 = 20. What is n?
  15. 15.The sum of four consecutive whole numbers is 102. What is the largest of them?
  16. 16.Solve: 3n + 2 = n + 26. What is n?
  17. 17.Solve: 9p + 1 = 7p + 7. What is p?
  18. 18.Solve: 8y + 3 = 2y + 45. What is y?
  19. 19.Solve: 4(x − 3) = x + 30. What is x?
  20. 20.Solve: 3(p − 3) = p + 1. What is p?
  21. 21.Solve: p/2 + p/5 = 14. What is p?
  22. 22.The length of a rectangle is 1 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  23. 23.A father is 27 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?
  24. 24.Solve: 3(p − 3) = 2p + 6. What is p?
  25. 25.Solve: 6p + 18 = 4p + 24. What is p?
  26. 26.A father is 45 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  27. 27.Solve: n/6 + n/2 = 12. What is n?
  28. 28.Solve: 4p + 16 = 2p + 30. What is p?
  29. 29.Solve: p/6 + p/5 = 11. What is p?
  30. 30.Solve: m/2 + m/3 = 35. What is m?
  31. 31.A father is 42 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  32. 32.The length of a rectangle is 1 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  33. 33.Solve: y/3 + y/6 = 6. What is y?
  34. 34.Solve: 5n + 7 = 2n + 16. What is n?
  35. 35.Solve: n/3 + n/2 = 10. What is n?
  36. 36.Solve: 5p + 11 = 3p + 13. What is p?
  37. 37.Solve: x/6 + x/4 = 5. What is x?
  38. 38.Solve: 5(p − 5) = 3p + 21. What is p?
  39. 39.Solve: 8y + 20 = 2y + 92. What is y?
  40. 40.The length of a rectangle is 1 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?

Answer key

  1. 7
  2. 3
  3. 7
  4. 28
  5. 30
  6. 8
  7. 48
  8. 19
  9. 12
  10. 20
  11. 10
  12. 140
  13. 18
  14. 24
  15. 27
  16. 12
  17. 3
  18. 7
  19. 14
  20. 5
  21. 20
  22. 22
  23. 6
  24. 15
  25. 3
  26. 7
  27. 18
  28. 7
  29. 30
  30. 42
  31. 7
  32. 23
  33. 12
  34. 3
  35. 12
  36. 1
  37. 12
  38. 23
  39. 12
  40. 7

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