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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 445 · 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 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?
  2. 2.The sum of two consecutive whole numbers is 111. What is the largest of them?
  3. 3.Solve: 5(n − 1) = 3n + 1. What is n?
  4. 4.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?
  5. 5.A father is 24 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?
  6. 6.A father is 30 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?
  7. 7.Solve: 4(n − 2) = n + 37. What is n?
  8. 8.Solve: m/3 + m/2 = 15. What is m?
  9. 9.The sum of two consecutive whole numbers is 121. What is the largest of them?
  10. 10.Solve: 7p + 6 = 6p + 7. What is p?
  11. 11.The sum of three consecutive whole numbers is 27. What is the largest of them?
  12. 12.Solve: 4n + 17 = n + 23. What is n?
  13. 13.The sum of four consecutive whole numbers is 26. What is the smallest of them?
  14. 14.Solve: 4(n − 5) = n + 22. What is n?
  15. 15.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?
  16. 16.The length of a rectangle is 15 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  17. 17.The sum of three consecutive whole numbers is 21. What is the smallest of them?
  18. 18.The length of a rectangle is 5 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  19. 19.Solve: 5t + 14 = 3t + 22. What is t?
  20. 20.Solve: 5(x − 4) = x + 28. What is x?
  21. 21.Solve: y/4 + y/6 = 5. What is y?
  22. 22.The length of a rectangle is 13 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  23. 23.The length of a rectangle is 5 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  24. 24.Solve: x/2 + x/3 = 40. What is x?
  25. 25.The length of a rectangle is 8 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  26. 26.Solve: 3(y − 3) = y + 11. What is y?
  27. 27.Solve: 4(x − 2) = x + 28. What is x?
  28. 28.Solve: x/2 + x/5 = 28. What is x?
  29. 29.Solve: 5y + 4 = 4y + 6. What is y?
  30. 30.Solve: 6(p − 4) = 3p + 21. What is p?
  31. 31.Solve: 3(m − 4) = m + 24. What is m?
  32. 32.Solve: 9n + 1 = n + 17. What is n?
  33. 33.Solve: 7m + 12 = 3m + 28. What is m?
  34. 34.Solve: 7y + 7 = 2y + 42. What is y?
  35. 35.Solve: 4(x − 2) = x + 13. What is x?
  36. 36.Solve: 5y + 8 = 2y + 50. What is y?
  37. 37.Solve: 8n + 4 = 5n + 46. What is n?
  38. 38.Solve: 7n + 18 = 2n + 23. What is n?
  39. 39.Solve: 3(m − 3) = 2m + 7. What is m?
  40. 40.A father is 28 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?

Answer key

  1. 9
  2. 56
  3. 3
  4. 2
  5. 7
  6. 6
  7. 15
  8. 18
  9. 61
  10. 1
  11. 10
  12. 2
  13. 5
  14. 14
  15. 12
  16. 12
  17. 6
  18. 26
  19. 4
  20. 12
  21. 12
  22. 23
  23. 24
  24. 48
  25. 18
  26. 10
  27. 12
  28. 40
  29. 2
  30. 15
  31. 18
  32. 2
  33. 4
  34. 7
  35. 7
  36. 14
  37. 14
  38. 1
  39. 16
  40. 7

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