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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 549 · 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.Solve: m/5 + m/6 = 77. What is m?
  2. 2.Solve: 6(m − 4) = 2m + 12. What is m?
  3. 3.Solve: 3x + 18 = 2x + 26. What is x?
  4. 4.A father is 7 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  5. 5.A father is 36 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?
  6. 6.The sum of two consecutive whole numbers is 117. What is the smallest of them?
  7. 7.The sum of four consecutive whole numbers is 198. What is the smallest of them?
  8. 8.The sum of three consecutive whole numbers is 105. What is the smallest of them?
  9. 9.The length of a rectangle is 2 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  10. 10.Solve: 7n + 5 = 5n + 21. What is n?
  11. 11.Solve: 4(y − 2) = 2y + 10. What is y?
  12. 12.The length of a rectangle is 7 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
  13. 13.Solve: p/6 + p/4 = 5. What is p?
  14. 14.The length of a rectangle is 13 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  15. 15.The length of a rectangle is 12 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  16. 16.Solve: 5m + 1 = m + 21. What is m?
  17. 17.The sum of three consecutive whole numbers is 108. What is the smallest of them?
  18. 18.The sum of three consecutive whole numbers is 132. What is the largest of them?
  19. 19.Solve: p/3 + p/6 = 21. What is p?
  20. 20.The sum of two consecutive whole numbers is 45. What is the smallest of them?
  21. 21.The length of a rectangle is 6 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  22. 22.Solve: 3m + 17 = m + 47. What is m?
  23. 23.A father is 36 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?
  24. 24.Solve: 9p + 18 = p + 58. What is p?
  25. 25.Solve: n/5 + n/6 = 22. What is n?
  26. 26.A father is 33 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  27. 27.Solve: t/6 + t/4 = 35. What is t?
  28. 28.Solve: 4(n − 1) = 2n + 26. What is n?
  29. 29.Solve: 6(x − 1) = 5x + 11. What is x?
  30. 30.Solve: x/3 + x/2 = 25. What is x?
  31. 31.Solve: 5x + 8 = x + 16. What is x?
  32. 32.Solve: 9y + 3 = 6y + 18. What is y?
  33. 33.The length of a rectangle is 4 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
  34. 34.Solve: y/6 + y/3 = 18. What is y?
  35. 35.A father is 10 years older than his son. In 8 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 126 cm. What is its width (in cm)?
  37. 37.The length of a rectangle is 15 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  38. 38.A father is 42 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?
  39. 39.Solve: t/2 + t/3 = 10. What is t?
  40. 40.A father is 8 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?

Answer key

  1. 210
  2. 9
  3. 8
  4. 4
  5. 10
  6. 58
  7. 48
  8. 34
  9. 8
  10. 8
  11. 9
  12. 30
  13. 12
  14. 7
  15. 22
  16. 5
  17. 35
  18. 45
  19. 42
  20. 22
  21. 14
  22. 15
  23. 12
  24. 5
  25. 60
  26. 4
  27. 84
  28. 15
  29. 17
  30. 30
  31. 2
  32. 5
  33. 30
  34. 36
  35. 2
  36. 26
  37. 27
  38. 10
  39. 12
  40. 7

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