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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 689 · 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 92 cm. What is its width (in cm)?
  2. 2.Solve: 3(y − 3) = 2y + 8. What is y?
  3. 3.Solve: 3(y − 3) = y + 1. What is y?
  4. 4.Solve: t/4 + t/2 = 24. What is t?
  5. 5.Solve: y/5 + y/6 = 22. What is y?
  6. 6.Solve: 3(t − 4) = t + 22. What is t?
  7. 7.The sum of three consecutive whole numbers is 174. What is the largest of them?
  8. 8.A father is 54 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?
  9. 9.Solve: x/5 + x/6 = 11. What is x?
  10. 10.The length of a rectangle is 5 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  11. 11.Solve: 5y + 3 = 3y + 5. What is y?
  12. 12.Solve: m/5 + m/4 = 18. What is m?
  13. 13.A father is 30 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?
  14. 14.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?
  15. 15.Solve: 5(t − 1) = 4t + 8. What is t?
  16. 16.Solve: 3x + 8 = 2x + 15. What is x?
  17. 17.Solve: y/2 + y/4 = 3. What is y?
  18. 18.Solve: 7y + 14 = 3y + 34. What is y?
  19. 19.The sum of four consecutive whole numbers is 118. What is the smallest of them?
  20. 20.Solve: x/5 + x/4 = 27. What is x?
  21. 21.Solve: 9y + 4 = 8y + 11. What is y?
  22. 22.A father is 16 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  23. 23.The length of a rectangle is 9 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  24. 24.Solve: y/6 + y/3 = 21. What is y?
  25. 25.A father is 24 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?
  26. 26.The sum of four consecutive whole numbers is 218. What is the smallest of them?
  27. 27.Solve: 5(t − 1) = t + 15. What is t?
  28. 28.A father is 11 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  29. 29.Solve: 8y + 19 = 5y + 25. What is y?
  30. 30.The length of a rectangle is 5 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  31. 31.Solve: 6(y − 2) = y + 58. What is y?
  32. 32.Solve: x/5 + x/3 = 48. What is x?
  33. 33.The length of a rectangle is 3 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  34. 34.Solve: 6(p − 1) = 2p + 18. What is p?
  35. 35.A father is 18 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?
  36. 36.The sum of two consecutive whole numbers is 113. What is the largest of them?
  37. 37.Solve: 4(p − 2) = p + 16. What is p?
  38. 38.Solve: 3(n − 3) = 2n + 2. What is n?
  39. 39.Solve: m/3 + m/2 = 10. What is m?
  40. 40.Solve: 6y + 12 = 4y + 20. What is y?

Answer key

  1. 20
  2. 17
  3. 5
  4. 32
  5. 60
  6. 17
  7. 59
  8. 12
  9. 30
  10. 23
  11. 1
  12. 40
  13. 7
  14. 8
  15. 13
  16. 7
  17. 4
  18. 5
  19. 28
  20. 60
  21. 7
  22. 6
  23. 21
  24. 42
  25. 6
  26. 53
  27. 5
  28. 10
  29. 2
  30. 15
  31. 14
  32. 90
  33. 13
  34. 6
  35. 2
  36. 57
  37. 8
  38. 11
  39. 12
  40. 4

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