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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 993 · 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.A father is 17 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  2. 2.The sum of two consecutive whole numbers is 17. What is the smallest of them?
  3. 3.The sum of two consecutive whole numbers is 95. What is the largest of them?
  4. 4.Solve: y/5 + y/4 = 45. What is y?
  5. 5.The length of a rectangle is 15 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  6. 6.Solve: 6(m − 2) = 2m + 40. What is m?
  7. 7.Solve: 7p + 9 = p + 51. What is p?
  8. 8.Solve: 6(n − 3) = 3n + 27. What is n?
  9. 9.The sum of two consecutive whole numbers is 55. What is the largest of them?
  10. 10.Solve: 9x + 15 = 3x + 69. What is x?
  11. 11.A father is 21 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  12. 12.The length of a rectangle is 7 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  13. 13.The length of a rectangle is 4 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  14. 14.Solve: 3x + 2 = x + 12. What is x?
  15. 15.Solve: 9m + 16 = 2m + 79. What is m?
  16. 16.A father is 45 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?
  17. 17.A father is 11 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  18. 18.The length of a rectangle is 1 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  19. 19.The length of a rectangle is 5 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
  20. 20.The length of a rectangle is 1 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
  21. 21.The length of a rectangle is 3 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  22. 22.Solve: 3y + 17 = y + 41. What is y?
  23. 23.A father is 7 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  24. 24.The sum of two consecutive whole numbers is 63. What is the smallest of them?
  25. 25.The sum of two consecutive whole numbers is 15. What is the largest of them?
  26. 26.Solve: n/3 + n/5 = 56. What is n?
  27. 27.Solve: 6(p − 3) = 2p + 10. What is p?
  28. 28.A father is 12 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  29. 29.The length of a rectangle is 12 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  30. 30.The sum of four consecutive whole numbers is 42. What is the smallest of them?
  31. 31.Solve: 3p + 15 = p + 19. What is p?
  32. 32.The length of a rectangle is 9 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  33. 33.Solve: 9n + 9 = 7n + 21. What is n?
  34. 34.Solve: 5(y − 1) = 2y + 25. What is y?
  35. 35.The sum of two consecutive whole numbers is 99. What is the largest of them?
  36. 36.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?
  37. 37.Solve: 3(x − 3) = x + 15. What is x?
  38. 38.Solve: 6(t − 1) = 4t + 4. What is t?
  39. 39.The length of a rectangle is 4 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  40. 40.The sum of two consecutive whole numbers is 29. What is the smallest of them?

Answer key

  1. 12
  2. 8
  3. 48
  4. 100
  5. 4
  6. 13
  7. 7
  8. 15
  9. 28
  10. 9
  11. 2
  12. 27
  13. 23
  14. 5
  15. 9
  16. 12
  17. 8
  18. 19
  19. 3
  20. 4
  21. 7
  22. 12
  23. 3
  24. 31
  25. 8
  26. 105
  27. 7
  28. 10
  29. 20
  30. 9
  31. 2
  32. 17
  33. 6
  34. 10
  35. 50
  36. 7
  37. 12
  38. 5
  39. 29
  40. 14

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