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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 122 · 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.A father is 26 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?
  2. 2.Solve: 5(x − 5) = 3x + 17. What is x?
  3. 3.Solve: 7m + 2 = 6m + 15. What is m?
  4. 4.Solve: x/5 + x/6 = 33. What is x?
  5. 5.The length of a rectangle is 2 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  6. 6.Solve: 3(n − 3) = 2n + 1. What is n?
  7. 7.The length of a rectangle is 4 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
  8. 8.Solve: 6(x − 2) = x + 3. What is x?
  9. 9.Solve: 3m + 12 = 2m + 13. What is m?
  10. 10.The length of a rectangle is 9 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  11. 11.Solve: 3(m − 2) = m + 20. What is m?
  12. 12.Solve: n/2 + n/4 = 6. What is n?
  13. 13.The sum of four consecutive whole numbers is 206. What is the smallest of them?
  14. 14.Solve: 5(p − 5) = 4p + 8. What is p?
  15. 15.Solve: 9n + 2 = 3n + 38. What is n?
  16. 16.The sum of two consecutive whole numbers is 103. What is the smallest of them?
  17. 17.Solve: 6x + 9 = 2x + 21. What is x?
  18. 18.The length of a rectangle is 11 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  19. 19.Solve: 3x + 1 = x + 9. What is x?
  20. 20.Solve: 3(p − 4) = 2p + 2. What is p?
  21. 21.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?
  22. 22.The sum of three consecutive whole numbers is 87. What is the smallest of them?
  23. 23.A father is 27 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?
  24. 24.Solve: 6y + 5 = 5y + 11. What is y?
  25. 25.Solve: x/5 + x/4 = 9. What is x?
  26. 26.A father is 36 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?
  27. 27.Solve: p/2 + p/4 = 12. What is p?
  28. 28.Solve: 3(m − 5) = 2m + 3. What is m?
  29. 29.Solve: p/3 + p/6 = 3. What is p?
  30. 30.Solve: 5(n − 4) = 3n + 24. What is n?
  31. 31.Solve: 3(n − 2) = 2n + 12. What is n?
  32. 32.The sum of three consecutive whole numbers is 18. What is the smallest of them?
  33. 33.A father is 13 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  34. 34.A father is 20 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?
  35. 35.Solve: 6(x − 4) = 4x + 24. What is x?
  36. 36.A father is 21 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?
  37. 37.The sum of three consecutive whole numbers is 51. What is the largest of them?
  38. 38.Solve: 7x + 19 = 2x + 49. What is x?
  39. 39.The length of a rectangle is 9 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  40. 40.Solve: 5m + 3 = 2m + 9. What is m?

Answer key

  1. 5
  2. 21
  3. 13
  4. 90
  5. 8
  6. 10
  7. 30
  8. 3
  9. 1
  10. 21
  11. 13
  12. 8
  13. 50
  14. 33
  15. 6
  16. 51
  17. 3
  18. 3
  19. 4
  20. 14
  21. 11
  22. 28
  23. 8
  24. 6
  25. 20
  26. 10
  27. 16
  28. 18
  29. 6
  30. 22
  31. 18
  32. 5
  33. 10
  34. 4
  35. 24
  36. 4
  37. 18
  38. 6
  39. 15
  40. 2

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