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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 498 · 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 10 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  2. 2.A father is 20 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?
  3. 3.The length of a rectangle is 11 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  4. 4.Solve: 5(x − 4) = x + 52. What is x?
  5. 5.Solve: p/5 + p/2 = 21. What is p?
  6. 6.The sum of two consecutive whole numbers is 39. What is the smallest of them?
  7. 7.Solve: 3t + 13 = t + 27. What is t?
  8. 8.Solve: 9x + 6 = x + 110. What is x?
  9. 9.A father is 32 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?
  10. 10.Solve: 4t + 2 = t + 47. What is t?
  11. 11.Solve: 6(t − 1) = t + 19. What is t?
  12. 12.Solve: 3(t − 1) = t + 5. What is t?
  13. 13.Solve: t/5 + t/6 = 88. What is t?
  14. 14.The sum of four consecutive whole numbers is 214. What is the smallest of them?
  15. 15.Solve: 7p + 6 = 4p + 18. What is p?
  16. 16.The length of a rectangle is 5 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  17. 17.The sum of three consecutive whole numbers is 36. What is the largest of them?
  18. 18.Solve: 3m + 1 = m + 5. What is m?
  19. 19.Solve: y/4 + y/2 = 9. What is y?
  20. 20.The sum of two consecutive whole numbers is 43. What is the smallest of them?
  21. 21.Solve: y/4 + y/3 = 49. What is y?
  22. 22.Solve: 7p + 3 = 3p + 47. What is p?
  23. 23.A father is 18 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?
  24. 24.Solve: 6t + 9 = t + 49. What is t?
  25. 25.The length of a rectangle is 9 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  26. 26.The length of a rectangle is 11 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  27. 27.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?
  28. 28.The length of a rectangle is 5 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  29. 29.Solve: m/2 + m/3 = 20. What is m?
  30. 30.The length of a rectangle is 4 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  31. 31.Solve: p/5 + p/2 = 49. What is p?
  32. 32.Solve: x/6 + x/4 = 40. What is x?
  33. 33.Solve: 9n + 8 = 4n + 83. What is n?
  34. 34.Solve: 4(p − 2) = p + 28. What is p?
  35. 35.A father is 14 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  36. 36.The length of a rectangle is 11 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  37. 37.Solve: 3p + 4 = 2p + 19. What is p?
  38. 38.Solve: m/2 + m/6 = 28. What is m?
  39. 39.Solve: 3n + 13 = 2n + 21. What is n?
  40. 40.The sum of four consecutive whole numbers is 178. What is the smallest of them?

Answer key

  1. 23
  2. 8
  3. 10
  4. 18
  5. 30
  6. 19
  7. 7
  8. 13
  9. 10
  10. 15
  11. 5
  12. 4
  13. 240
  14. 52
  15. 4
  16. 29
  17. 13
  18. 2
  19. 12
  20. 21
  21. 84
  22. 11
  23. 5
  24. 8
  25. 11
  26. 25
  27. 3
  28. 12
  29. 24
  30. 7
  31. 70
  32. 96
  33. 15
  34. 12
  35. 11
  36. 14
  37. 15
  38. 42
  39. 8
  40. 43

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