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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 515 · 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 3 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  2. 2.Solve: 4t + 3 = t + 18. What is t?
  3. 3.Solve: 4(p − 5) = 2p + 12. What is p?
  4. 4.Solve: 3t + 4 = t + 18. What is t?
  5. 5.The sum of four consecutive whole numbers is 54. What is the largest of them?
  6. 6.Solve: 6(p − 1) = 3p + 12. What is p?
  7. 7.The sum of three consecutive whole numbers is 51. What is the smallest of them?
  8. 8.The sum of two consecutive whole numbers is 65. What is the largest of them?
  9. 9.Solve: 5(x − 4) = 3x + 12. What is x?
  10. 10.Solve: 8t + 15 = 6t + 37. What is t?
  11. 11.The sum of four consecutive whole numbers is 194. What is the smallest of them?
  12. 12.Solve: 5(m − 1) = 2m + 19. What is m?
  13. 13.Solve: 5(n − 2) = 3n + 24. What is n?
  14. 14.Solve: t/6 + t/2 = 28. What is t?
  15. 15.The length of a rectangle is 3 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  16. 16.The length of a rectangle is 1 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  17. 17.The length of a rectangle is 4 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  18. 18.A father is 11 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  19. 19.A father is 10 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  20. 20.The sum of three consecutive whole numbers is 54. What is the smallest of them?
  21. 21.The length of a rectangle is 11 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  22. 22.Solve: m/3 + m/4 = 56. What is m?
  23. 23.Solve: p/5 + p/3 = 16. What is p?
  24. 24.Solve: y/5 + y/3 = 32. What is y?
  25. 25.Solve: 6p + 13 = 4p + 17. What is p?
  26. 26.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?
  27. 27.Solve: 6(n − 3) = 5n + 10. What is n?
  28. 28.Solve: m/3 + m/4 = 21. What is m?
  29. 29.Solve: 3(x − 1) = x + 15. What is x?
  30. 30.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?
  31. 31.Solve: 7p + 15 = 6p + 27. What is p?
  32. 32.Solve: t/4 + t/3 = 56. What is t?
  33. 33.Solve: 6y + 7 = y + 32. What is y?
  34. 34.A father is 8 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?
  35. 35.The length of a rectangle is 3 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  36. 36.A father is 39 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?
  37. 37.Solve: n/5 + n/4 = 27. What is n?
  38. 38.Solve: n/5 + n/6 = 22. What is n?
  39. 39.Solve: 5(t − 3) = t + 33. What is t?
  40. 40.A father is 24 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?

Answer key

  1. 9
  2. 5
  3. 16
  4. 7
  5. 15
  6. 6
  7. 16
  8. 33
  9. 16
  10. 11
  11. 47
  12. 8
  13. 17
  14. 42
  15. 21
  16. 10
  17. 7
  18. 7
  19. 3
  20. 17
  21. 21
  22. 96
  23. 30
  24. 60
  25. 2
  26. 2
  27. 28
  28. 36
  29. 9
  30. 2
  31. 12
  32. 96
  33. 5
  34. 3
  35. 6
  36. 9
  37. 60
  38. 60
  39. 12
  40. 7

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