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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 679 · 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 9 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  2. 2.Solve: 4x + 13 = 2x + 19. What is x?
  3. 3.Solve: 3(p − 2) = p + 14. What is p?
  4. 4.The length of a rectangle is 1 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  5. 5.The sum of three consecutive whole numbers is 57. What is the smallest of them?
  6. 6.Solve: 6p + 2 = 2p + 14. What is p?
  7. 7.Solve: p/4 + p/6 = 40. What is p?
  8. 8.Solve: 9m + 17 = m + 73. What is m?
  9. 9.The sum of four consecutive whole numbers is 78. What is the largest of them?
  10. 10.Solve: 8n + 10 = 2n + 22. What is n?
  11. 11.Solve: n/5 + n/3 = 40. What is n?
  12. 12.Solve: 3(y − 4) = y + 18. What is y?
  13. 13.Solve: t/6 + t/2 = 16. What is t?
  14. 14.The sum of two consecutive whole numbers is 29. What is the smallest of them?
  15. 15.The length of a rectangle is 4 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
  16. 16.Solve: n/4 + n/6 = 25. What is n?
  17. 17.The length of a rectangle is 13 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  18. 18.Solve: 4(m − 5) = 2m + 24. What is m?
  19. 19.Solve: p/4 + p/3 = 49. What is p?
  20. 20.The sum of two consecutive whole numbers is 17. What is the largest of them?
  21. 21.The length of a rectangle is 1 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  22. 22.Solve: 8y + 20 = 7y + 21. What is y?
  23. 23.The length of a rectangle is 15 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  24. 24.A father is 27 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  25. 25.A father is 19 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  26. 26.The sum of three consecutive whole numbers is 51. What is the smallest of them?
  27. 27.A father is 39 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  28. 28.Solve: 3(t − 1) = t + 5. What is t?
  29. 29.Solve: 3(x − 1) = x + 17. What is x?
  30. 30.Solve: 6(n − 2) = n + 58. What is n?
  31. 31.The length of a rectangle is 8 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  32. 32.Solve: p/4 + p/3 = 14. What is p?
  33. 33.Solve: 4(p − 1) = 3p + 3. What is p?
  34. 34.The length of a rectangle is 4 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  35. 35.Solve: 4(m − 4) = 3m + 10. What is m?
  36. 36.A father is 24 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  37. 37.Solve: 3(y − 1) = 2y + 10. What is y?
  38. 38.The sum of four consecutive whole numbers is 158. What is the smallest of them?
  39. 39.The sum of four consecutive whole numbers is 34. What is the smallest of them?
  40. 40.Solve: n/5 + n/3 = 8. What is n?

Answer key

  1. 13
  2. 3
  3. 10
  4. 13
  5. 18
  6. 3
  7. 96
  8. 7
  9. 21
  10. 2
  11. 75
  12. 15
  13. 24
  14. 14
  15. 28
  16. 60
  17. 3
  18. 22
  19. 84
  20. 9
  21. 24
  22. 1
  23. 2
  24. 7
  25. 11
  26. 16
  27. 12
  28. 4
  29. 10
  30. 14
  31. 23
  32. 24
  33. 7
  34. 5
  35. 26
  36. 4
  37. 13
  38. 38
  39. 7
  40. 15

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