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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 40 · 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: 4(x − 1) = x + 8. What is x?
  2. 2.Solve: 6(t − 3) = t + 47. What is t?
  3. 3.Solve: t/3 + t/6 = 18. What is t?
  4. 4.Solve: 6x + 20 = 2x + 72. What is x?
  5. 5.Solve: 5(y − 4) = 4y + 9. What is y?
  6. 6.Solve: 6n + 3 = 5n + 17. What is n?
  7. 7.A father is 51 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?
  8. 8.Solve: 9y + 6 = 4y + 21. What is y?
  9. 9.Solve: 6(n − 1) = 2n + 14. What is n?
  10. 10.The length of a rectangle is 7 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  11. 11.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?
  12. 12.The length of a rectangle is 1 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  13. 13.Solve: y/5 + y/2 = 56. What is y?
  14. 14.The length of a rectangle is 5 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  15. 15.Solve: 7n + 6 = 4n + 42. What is n?
  16. 16.Solve: 9t + 6 = 5t + 38. What is t?
  17. 17.Solve: 8t + 8 = 7t + 20. What is t?
  18. 18.Solve: 5(y − 3) = y + 17. What is y?
  19. 19.Solve: 3(x − 2) = 2x + 2. What is x?
  20. 20.Solve: 6(m − 5) = 2m + 14. What is m?
  21. 21.Solve: 5p + 17 = 2p + 56. What is p?
  22. 22.The sum of two consecutive whole numbers is 19. What is the largest of them?
  23. 23.The length of a rectangle is 2 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  24. 24.Solve: 5(t − 3) = t + 37. What is t?
  25. 25.Solve: p/3 + p/6 = 6. What is p?
  26. 26.A father is 14 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  27. 27.The sum of three consecutive whole numbers is 57. What is the largest of them?
  28. 28.Solve: 9y + 1 = 8y + 12. What is y?
  29. 29.The length of a rectangle is 1 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  30. 30.Solve: 4n + 12 = 2n + 42. What is n?
  31. 31.Solve: 4(n − 4) = 2n + 4. What is n?
  32. 32.Solve: 9p + 5 = p + 29. What is p?
  33. 33.Solve: 4t + 1 = t + 10. What is t?
  34. 34.The sum of four consecutive whole numbers is 90. What is the smallest of them?
  35. 35.Solve: t/2 + t/6 = 8. What is t?
  36. 36.Solve: 3x + 12 = 2x + 18. What is x?
  37. 37.A father is 24 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
  38. 38.The length of a rectangle is 8 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
  39. 39.Solve: t/2 + t/4 = 24. What is t?
  40. 40.Solve: p/3 + p/2 = 35. What is p?

Answer key

  1. 4
  2. 13
  3. 36
  4. 13
  5. 29
  6. 14
  7. 9
  8. 3
  9. 5
  10. 15
  11. 7
  12. 24
  13. 80
  14. 22
  15. 12
  16. 8
  17. 12
  18. 8
  19. 8
  20. 11
  21. 13
  22. 10
  23. 25
  24. 13
  25. 12
  26. 8
  27. 20
  28. 11
  29. 28
  30. 15
  31. 10
  32. 3
  33. 3
  34. 21
  35. 12
  36. 6
  37. 8
  38. 28
  39. 32
  40. 42

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