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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 12 · 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.The length of a rectangle is 8 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  2. 2.Solve: 3(n − 2) = n + 18. What is n?
  3. 3.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?
  4. 4.The length of a rectangle is 13 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  5. 5.The sum of four consecutive whole numbers is 38. What is the smallest of them?
  6. 6.The length of a rectangle is 12 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  7. 7.Solve: 9n + 9 = 8n + 13. What is n?
  8. 8.Solve: 3(x − 2) = 2x + 7. What is x?
  9. 9.Solve: 6(n − 3) = 5n + 2. What is n?
  10. 10.The length of a rectangle is 5 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  11. 11.Solve: 4y + 17 = y + 38. What is y?
  12. 12.Solve: 5t + 1 = 2t + 34. What is t?
  13. 13.A father is 34 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
  14. 14.Solve: 5x + 2 = 4x + 10. What is x?
  15. 15.The length of a rectangle is 2 cm more than its width. Its perimeter is 12 cm. What is its width (in cm)?
  16. 16.Solve: 4(t − 1) = t + 14. What is t?
  17. 17.Solve: 4(x − 1) = x + 5. What is x?
  18. 18.The length of a rectangle is 14 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  19. 19.Solve: 7x + 14 = x + 80. What is x?
  20. 20.A father is 39 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?
  21. 21.Solve: 6(p − 1) = 2p + 26. What is p?
  22. 22.Solve: 7x + 4 = x + 28. What is x?
  23. 23.The sum of three consecutive whole numbers is 30. What is the largest of them?
  24. 24.Solve: 5y + 4 = 4y + 15. What is y?
  25. 25.A father is 39 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?
  26. 26.Solve: 4(m − 2) = m + 1. What is m?
  27. 27.Solve: 5(m − 4) = m + 44. What is m?
  28. 28.Solve: m/5 + m/2 = 56. What is m?
  29. 29.Solve: 5(t − 3) = 4t + 13. What is t?
  30. 30.Solve: 4(t − 5) = 2t + 4. What is t?
  31. 31.The length of a rectangle is 1 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  32. 32.Solve: y/4 + y/5 = 18. What is y?
  33. 33.Solve: x/6 + x/5 = 77. What is x?
  34. 34.Solve: t/3 + t/4 = 56. What is t?
  35. 35.Solve: 5y + 7 = 4y + 12. What is y?
  36. 36.Solve: 5x + 16 = 2x + 52. What is x?
  37. 37.Solve: 5(x − 3) = 2x + 33. What is x?
  38. 38.Solve: 3(y − 4) = 2y + 5. What is y?
  39. 39.The sum of three consecutive whole numbers is 33. What is the smallest of them?
  40. 40.Solve: m/2 + m/3 = 5. What is m?

Answer key

  1. 3
  2. 12
  3. 10
  4. 3
  5. 8
  6. 16
  7. 4
  8. 13
  9. 20
  10. 5
  11. 7
  12. 11
  13. 11
  14. 8
  15. 2
  16. 6
  17. 3
  18. 19
  19. 11
  20. 10
  21. 8
  22. 4
  23. 11
  24. 11
  25. 8
  26. 3
  27. 16
  28. 80
  29. 28
  30. 12
  31. 17
  32. 40
  33. 210
  34. 96
  35. 5
  36. 12
  37. 16
  38. 17
  39. 10
  40. 6

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