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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 595 · 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 11 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  2. 2.The sum of two consecutive whole numbers is 15. What is the smallest of them?
  3. 3.Solve: n/2 + n/4 = 9. What is n?
  4. 4.The sum of four consecutive whole numbers is 242. What is the smallest of them?
  5. 5.A father is 42 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  6. 6.The sum of two consecutive whole numbers is 13. What is the smallest of them?
  7. 7.A father is 36 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  8. 8.Solve: 6(p − 4) = 2p + 32. What is p?
  9. 9.Solve: 9m + 1 = 4m + 16. What is m?
  10. 10.Solve: 3(m − 5) = m + 11. What is m?
  11. 11.Solve: 4(p − 3) = p + 30. What is p?
  12. 12.A father is 8 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  13. 13.The length of a rectangle is 12 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  14. 14.A father is 24 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?
  15. 15.The length of a rectangle is 9 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  16. 16.The length of a rectangle is 2 cm more than its width. Its perimeter is 16 cm. What is its width (in cm)?
  17. 17.The length of a rectangle is 14 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  18. 18.Solve: 5x + 6 = 2x + 36. What is x?
  19. 19.Solve: 3(p − 2) = 2p + 4. What is p?
  20. 20.The length of a rectangle is 14 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  21. 21.Solve: 4t + 6 = 2t + 32. What is t?
  22. 22.Solve: 5(y − 5) = 4y + 5. What is y?
  23. 23.Solve: t/3 + t/6 = 24. What is t?
  24. 24.The sum of two consecutive whole numbers is 75. What is the largest of them?
  25. 25.The sum of two consecutive whole numbers is 87. What is the smallest of them?
  26. 26.Solve: p/3 + p/2 = 5. What is p?
  27. 27.Solve: n/4 + n/3 = 35. What is n?
  28. 28.Solve: 6n + 8 = 2n + 28. What is n?
  29. 29.A father is 14 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  30. 30.Solve: y/4 + y/6 = 25. What is y?
  31. 31.Solve: 5(y − 1) = 4y + 5. What is y?
  32. 32.Solve: 3(x − 3) = 2x + 10. What is x?
  33. 33.The length of a rectangle is 13 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  34. 34.Solve: 9y + 10 = 2y + 31. What is y?
  35. 35.Solve: y/5 + y/2 = 56. What is y?
  36. 36.Solve: y/6 + y/5 = 88. What is y?
  37. 37.Solve: p/4 + p/2 = 9. What is p?
  38. 38.Solve: 4(n − 1) = n + 23. What is n?
  39. 39.Solve: 4(t − 1) = t + 2. What is t?
  40. 40.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?

Answer key

  1. 8
  2. 7
  3. 12
  4. 59
  5. 9
  6. 6
  7. 11
  8. 14
  9. 3
  10. 13
  11. 14
  12. 5
  13. 9
  14. 6
  15. 3
  16. 3
  17. 4
  18. 10
  19. 10
  20. 6
  21. 13
  22. 30
  23. 48
  24. 38
  25. 43
  26. 6
  27. 60
  28. 5
  29. 8
  30. 60
  31. 10
  32. 19
  33. 6
  34. 3
  35. 80
  36. 240
  37. 12
  38. 9
  39. 2
  40. 6

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