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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 38 · 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: 8n + 4 = 5n + 31. What is n?
  2. 2.A father is 15 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  3. 3.A father is 19 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  4. 4.The length of a rectangle is 4 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  5. 5.Solve: t/2 + t/4 = 6. What is t?
  6. 6.Solve: 7n + 13 = 6n + 14. What is n?
  7. 7.The length of a rectangle is 11 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  8. 8.A father is 27 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
  9. 9.Solve: 9m + 3 = 3m + 45. What is m?
  10. 10.The sum of two consecutive whole numbers is 97. What is the largest of them?
  11. 11.A father is 33 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?
  12. 12.Solve: 6(m − 1) = m + 44. What is m?
  13. 13.Solve: 4(x − 1) = 2x + 4. What is x?
  14. 14.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?
  15. 15.Solve: 3(x − 3) = x + 5. What is x?
  16. 16.The sum of three consecutive whole numbers is 42. What is the largest of them?
  17. 17.Solve: t/3 + t/6 = 3. What is t?
  18. 18.Solve: y/5 + y/2 = 21. What is y?
  19. 19.The length of a rectangle is 14 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  20. 20.Solve: 6(m − 5) = 5m + 2. What is m?
  21. 21.Solve: 5(y − 5) = y + 3. What is y?
  22. 22.Solve: 8p + 10 = 7p + 13. What is p?
  23. 23.The length of a rectangle is 6 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  24. 24.Solve: t/2 + t/3 = 30. What is t?
  25. 25.Solve: 4(x − 3) = 3x + 11. What is x?
  26. 26.Solve: 5x + 3 = 3x + 27. What is x?
  27. 27.The sum of three consecutive whole numbers is 48. What is the largest of them?
  28. 28.The length of a rectangle is 8 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  29. 29.The sum of four consecutive whole numbers is 186. What is the smallest of them?
  30. 30.The length of a rectangle is 4 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  31. 31.Solve: 4(t − 1) = 3t + 5. What is t?
  32. 32.Solve: 4(x − 2) = x + 1. What is x?
  33. 33.A father is 18 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  34. 34.Solve: 6(p − 3) = 4p + 22. What is p?
  35. 35.The length of a rectangle is 13 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  36. 36.Solve: 3(t − 5) = 2t + 7. What is t?
  37. 37.Solve: 9n + 14 = n + 22. What is n?
  38. 38.Solve: 5(x − 3) = 3x + 5. What is x?
  39. 39.Solve: n/6 + n/3 = 18. What is n?
  40. 40.A father is 24 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?

Answer key

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

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