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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 681 · 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 11 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  2. 2.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?
  3. 3.The length of a rectangle is 7 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  4. 4.A father is 30 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  5. 5.The sum of two consecutive whole numbers is 95. What is the smallest of them?
  6. 6.A father is 13 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  7. 7.A father is 18 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  8. 8.Solve: 3x + 4 = x + 6. What is x?
  9. 9.Solve: x/5 + x/3 = 24. What is x?
  10. 10.Solve: 3x + 4 = x + 24. What is x?
  11. 11.Solve: t/2 + t/3 = 20. What is t?
  12. 12.Solve: x/4 + x/2 = 21. What is x?
  13. 13.Solve: 4(m − 2) = m + 25. What is m?
  14. 14.A father is 45 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  15. 15.Solve: 4(x − 1) = x + 35. What is x?
  16. 16.Solve: t/4 + t/3 = 56. What is t?
  17. 17.The length of a rectangle is 10 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  18. 18.The length of a rectangle is 11 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  19. 19.Solve: 4(n − 4) = 3n + 9. What is n?
  20. 20.Solve: 3m + 11 = m + 13. What is m?
  21. 21.The length of a rectangle is 3 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  22. 22.The sum of three consecutive whole numbers is 153. What is the largest of them?
  23. 23.The length of a rectangle is 13 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  24. 24.The length of a rectangle is 1 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  25. 25.The sum of four consecutive whole numbers is 214. What is the smallest of them?
  26. 26.Solve: 6y + 3 = y + 43. What is y?
  27. 27.Solve: 3(n − 5) = n + 3. What is n?
  28. 28.Solve: y/2 + y/4 = 3. What is y?
  29. 29.Solve: 4(x − 2) = x + 19. What is x?
  30. 30.Solve: 6n + 13 = 4n + 19. What is n?
  31. 31.The length of a rectangle is 12 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  32. 32.A father is 12 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  33. 33.The length of a rectangle is 6 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  34. 34.The sum of two consecutive whole numbers is 33. What is the largest of them?
  35. 35.The sum of three consecutive whole numbers is 27. What is the largest of them?
  36. 36.A father is 11 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  37. 37.The sum of three consecutive whole numbers is 141. What is the smallest of them?
  38. 38.Solve: x/5 + x/4 = 63. What is x?
  39. 39.Solve: m/4 + m/2 = 15. What is m?
  40. 40.The length of a rectangle is 12 cm more than its width. Its perimeter is 72 cm. What is its width (in cm)?

Answer key

  1. 20
  2. 6
  3. 9
  4. 2
  5. 47
  6. 7
  7. 3
  8. 1
  9. 45
  10. 10
  11. 24
  12. 28
  13. 11
  14. 12
  15. 13
  16. 96
  17. 26
  18. 29
  19. 25
  20. 1
  21. 6
  22. 52
  23. 10
  24. 17
  25. 52
  26. 8
  27. 9
  28. 4
  29. 9
  30. 3
  31. 16
  32. 8
  33. 16
  34. 17
  35. 10
  36. 4
  37. 46
  38. 140
  39. 20
  40. 12

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