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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 49 · 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 6 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  2. 2.Solve: 5(y − 2) = y + 30. What is y?
  3. 3.Solve: x/5 + x/2 = 56. What is x?
  4. 4.Solve: 6(n − 3) = 2n + 18. What is n?
  5. 5.A father is 15 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?
  6. 6.Solve: 4(t − 3) = 3t + 9. What is t?
  7. 7.Solve: 4(y − 3) = 3y + 6. What is y?
  8. 8.Solve: p/4 + p/5 = 36. What is p?
  9. 9.Solve: 4m + 2 = 3m + 11. What is m?
  10. 10.The sum of two consecutive whole numbers is 111. What is the smallest of them?
  11. 11.The length of a rectangle is 5 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  12. 12.Solve: 3(m − 4) = m + 8. What is m?
  13. 13.A father is 18 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?
  14. 14.Solve: 3m + 11 = m + 35. What is m?
  15. 15.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?
  16. 16.The length of a rectangle is 4 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  17. 17.Solve: 4(p − 2) = 2p + 2. What is p?
  18. 18.Solve: 5y + 4 = 4y + 9. What is y?
  19. 19.A father is 30 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?
  20. 20.Solve: 3m + 12 = 2m + 23. What is m?
  21. 21.Solve: n/5 + n/6 = 55. What is n?
  22. 22.The sum of three consecutive whole numbers is 78. What is the largest of them?
  23. 23.The length of a rectangle is 10 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  24. 24.Solve: x/4 + x/5 = 9. What is x?
  25. 25.Solve: m/3 + m/4 = 35. What is m?
  26. 26.The sum of three consecutive whole numbers is 96. What is the largest of them?
  27. 27.Solve: m/6 + m/2 = 28. What is m?
  28. 28.The length of a rectangle is 10 cm more than its width. Its perimeter is 140 cm. What is its width (in cm)?
  29. 29.Solve: y/2 + y/5 = 56. What is y?
  30. 30.A father is 39 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?
  31. 31.A father is 9 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  32. 32.Solve: y/3 + y/2 = 30. What is y?
  33. 33.Solve: p/6 + p/3 = 21. What is p?
  34. 34.A father is 48 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  35. 35.A father is 4 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  36. 36.The sum of two consecutive whole numbers is 23. What is the smallest of them?
  37. 37.Solve: 3(x − 1) = x + 1. What is x?
  38. 38.Solve: 8n + 5 = 5n + 11. What is n?
  39. 39.Solve: 5(n − 2) = n + 18. What is n?
  40. 40.Solve: 6x + 8 = 2x + 24. What is x?

Answer key

  1. 19
  2. 10
  3. 80
  4. 9
  5. 3
  6. 21
  7. 18
  8. 80
  9. 9
  10. 55
  11. 5
  12. 10
  13. 2
  14. 12
  15. 4
  16. 27
  17. 5
  18. 5
  19. 8
  20. 11
  21. 150
  22. 27
  23. 10
  24. 20
  25. 60
  26. 33
  27. 42
  28. 30
  29. 80
  30. 7
  31. 3
  32. 36
  33. 42
  34. 9
  35. 2
  36. 11
  37. 2
  38. 2
  39. 7
  40. 4

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