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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 53 · 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: 3(n − 1) = 2n + 8. What is n?
  2. 2.Solve: 3n + 14 = 2n + 24. What is n?
  3. 3.The sum of two consecutive whole numbers is 43. What is the largest of them?
  4. 4.Solve: p/4 + p/5 = 54. What is p?
  5. 5.The length of a rectangle is 15 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  6. 6.Solve: 5(y − 2) = 4y + 11. What is y?
  7. 7.Solve: 5(y − 5) = y + 19. What is y?
  8. 8.A father is 4 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  9. 9.Solve: 5t + 2 = 4t + 9. What is t?
  10. 10.The sum of three consecutive whole numbers is 165. What is the largest of them?
  11. 11.Solve: 5x + 6 = 3x + 32. What is x?
  12. 12.Solve: 6(t − 3) = 2t + 2. What is t?
  13. 13.The sum of three consecutive whole numbers is 96. What is the smallest of them?
  14. 14.Solve: 9t + 9 = 3t + 81. What is t?
  15. 15.Solve: m/2 + m/4 = 15. What is m?
  16. 16.A father is 24 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  17. 17.Solve: 5(m − 2) = 2m + 8. What is m?
  18. 18.Solve: x/2 + x/3 = 35. What is x?
  19. 19.The length of a rectangle is 4 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  20. 20.A father is 42 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?
  21. 21.The length of a rectangle is 2 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  22. 22.Solve: 5(y − 1) = 4y + 9. What is y?
  23. 23.Solve: 3(x − 2) = 2x + 5. What is x?
  24. 24.Solve: 7p + 3 = 4p + 9. What is p?
  25. 25.Solve: 3(m − 3) = 2m + 2. What is m?
  26. 26.Solve: 3(m − 1) = m + 25. What is m?
  27. 27.The length of a rectangle is 3 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  28. 28.Solve: 7m + 4 = 3m + 20. What is m?
  29. 29.Solve: t/4 + t/3 = 21. What is t?
  30. 30.Solve: 3p + 13 = p + 41. What is p?
  31. 31.Solve: 9n + 16 = n + 128. What is n?
  32. 32.Solve: 6y + 18 = y + 88. What is y?
  33. 33.The length of a rectangle is 13 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
  34. 34.A father is 11 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  35. 35.Solve: 6(m − 1) = 2m + 10. What is m?
  36. 36.The length of a rectangle is 9 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  37. 37.A father is 22 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  38. 38.Solve: 3y + 14 = y + 32. What is y?
  39. 39.Solve: 4(n − 2) = 3n + 7. What is n?
  40. 40.Solve: 4(t − 1) = 3t + 1. What is t?

Answer key

  1. 11
  2. 10
  3. 22
  4. 120
  5. 14
  6. 21
  7. 11
  8. 3
  9. 7
  10. 56
  11. 13
  12. 5
  13. 31
  14. 12
  15. 20
  16. 11
  17. 6
  18. 42
  19. 19
  20. 12
  21. 8
  22. 14
  23. 11
  24. 2
  25. 11
  26. 14
  27. 30
  28. 4
  29. 36
  30. 14
  31. 14
  32. 14
  33. 14
  34. 10
  35. 4
  36. 27
  37. 8
  38. 9
  39. 15
  40. 5

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