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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 781 · 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 4 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  2. 2.Solve: n/2 + n/3 = 15. What is n?
  3. 3.Solve: x/2 + x/4 = 6. What is x?
  4. 4.A father is 17 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  5. 5.Solve: 6(x − 4) = x + 46. What is x?
  6. 6.A father is 10 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  7. 7.Solve: 3(y − 4) = y + 6. What is y?
  8. 8.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?
  9. 9.The sum of four consecutive whole numbers is 118. What is the largest of them?
  10. 10.The length of a rectangle is 15 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  11. 11.The length of a rectangle is 7 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  12. 12.The length of a rectangle is 11 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  13. 13.Solve: 3(p − 3) = p + 19. What is p?
  14. 14.Solve: m/2 + m/6 = 20. What is m?
  15. 15.Solve: 7x + 5 = 4x + 35. What is x?
  16. 16.The length of a rectangle is 4 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
  17. 17.Solve: p/2 + p/3 = 25. What is p?
  18. 18.Solve: 5(x − 2) = 3x + 20. What is x?
  19. 19.Solve: 6(y − 5) = 4y + 18. What is y?
  20. 20.Solve: 8n + 14 = 3n + 89. What is n?
  21. 21.The length of a rectangle is 4 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  22. 22.A father is 24 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 sum of two consecutive whole numbers is 29. What is the smallest of them?
  24. 24.Solve: p/4 + p/3 = 56. What is p?
  25. 25.The sum of two consecutive whole numbers is 19. What is the largest of them?
  26. 26.The sum of four consecutive whole numbers is 214. What is the smallest of them?
  27. 27.The sum of two consecutive whole numbers is 71. What is the smallest of them?
  28. 28.Solve: 3x + 9 = x + 25. What is x?
  29. 29.Solve: 3(p − 1) = p + 11. What is p?
  30. 30.A father is 7 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  31. 31.Solve: 6p + 6 = 3p + 36. What is p?
  32. 32.Solve: p/4 + p/6 = 10. What is p?
  33. 33.Solve: 3(t − 3) = 2t + 7. What is t?
  34. 34.Solve: p/2 + p/4 = 21. What is p?
  35. 35.The sum of three consecutive whole numbers is 120. What is the largest of them?
  36. 36.Solve: 8m + 7 = 3m + 17. What is m?
  37. 37.Solve: x/6 + x/5 = 11. What is x?
  38. 38.Solve: p/6 + p/5 = 11. What is p?
  39. 39.Solve: 3(p − 5) = p + 1. What is p?
  40. 40.The length of a rectangle is 9 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?

Answer key

  1. 21
  2. 18
  3. 8
  4. 11
  5. 14
  6. 9
  7. 9
  8. 10
  9. 31
  10. 6
  11. 18
  12. 2
  13. 14
  14. 30
  15. 10
  16. 4
  17. 30
  18. 15
  19. 24
  20. 15
  21. 11
  22. 10
  23. 14
  24. 96
  25. 10
  26. 52
  27. 35
  28. 8
  29. 7
  30. 6
  31. 10
  32. 24
  33. 16
  34. 28
  35. 41
  36. 2
  37. 30
  38. 30
  39. 8
  40. 16

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