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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 522 · 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 2 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  2. 2.The length of a rectangle is 6 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
  3. 3.The length of a rectangle is 6 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  4. 4.Solve: 3(y − 2) = 2y + 9. What is y?
  5. 5.Solve: 5n + 9 = n + 13. What is n?
  6. 6.A father is 28 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?
  7. 7.Solve: 4n + 16 = 3n + 23. What is n?
  8. 8.A father is 16 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  9. 9.Solve: 3(n − 1) = 2n + 9. What is n?
  10. 10.Solve: 6(p − 2) = 5p + 1. What is p?
  11. 11.The sum of four consecutive whole numbers is 190. What is the largest of them?
  12. 12.Solve: p/5 + p/2 = 35. What is p?
  13. 13.Solve: y/4 + y/2 = 18. What is y?
  14. 14.The length of a rectangle is 2 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  15. 15.Solve: 5(m − 3) = 4m + 8. What is m?
  16. 16.Solve: 3(x − 2) = 2x + 7. What is x?
  17. 17.The length of a rectangle is 13 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  18. 18.Solve: 7x + 12 = 5x + 34. What is x?
  19. 19.The sum of two consecutive whole numbers is 45. What is the largest of them?
  20. 20.Solve: 3x + 15 = 2x + 18. What is x?
  21. 21.Solve: m/4 + m/5 = 9. What is m?
  22. 22.The sum of two consecutive whole numbers is 31. What is the smallest of them?
  23. 23.Solve: 3(x − 2) = x + 24. What is x?
  24. 24.A father is 22 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?
  25. 25.The length of a rectangle is 6 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
  26. 26.Solve: 3(y − 4) = 2y + 4. What is y?
  27. 27.Solve: 4x + 18 = x + 48. What is x?
  28. 28.Solve: 4(x − 5) = x + 19. What is x?
  29. 29.Solve: 6n + 2 = n + 12. What is n?
  30. 30.Solve: m/4 + m/3 = 21. What is m?
  31. 31.A father is 33 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?
  32. 32.Solve: 3t + 14 = 2t + 26. What is t?
  33. 33.Solve: p/5 + p/4 = 9. What is p?
  34. 34.Solve: 3p + 1 = p + 21. What is p?
  35. 35.Solve: 5(t − 5) = 2t + 8. What is t?
  36. 36.The sum of four consecutive whole numbers is 26. What is the largest of them?
  37. 37.The length of a rectangle is 13 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  38. 38.Solve: 4(x − 5) = 3x + 13. What is x?
  39. 39.Solve: 5(y − 2) = 2y + 11. What is y?
  40. 40.The sum of two consecutive whole numbers is 85. What is the largest of them?

Answer key

  1. 14
  2. 3
  3. 28
  4. 15
  5. 1
  6. 8
  7. 7
  8. 9
  9. 12
  10. 13
  11. 49
  12. 50
  13. 24
  14. 25
  15. 23
  16. 13
  17. 15
  18. 11
  19. 23
  20. 3
  21. 20
  22. 15
  23. 15
  24. 3
  25. 24
  26. 16
  27. 10
  28. 13
  29. 2
  30. 36
  31. 5
  32. 12
  33. 20
  34. 10
  35. 11
  36. 8
  37. 23
  38. 33
  39. 7
  40. 43

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