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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 931 · 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 9 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  2. 2.The sum of two consecutive whole numbers is 41. What is the smallest of them?
  3. 3.Solve: 6(m − 2) = 2m + 16. What is m?
  4. 4.Solve: 8t + 16 = 4t + 36. What is t?
  5. 5.The sum of two consecutive whole numbers is 107. What is the largest of them?
  6. 6.The sum of three consecutive whole numbers is 141. What is the smallest of them?
  7. 7.A father is 4 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  8. 8.A father is 22 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?
  9. 9.Solve: y/6 + y/2 = 32. What is y?
  10. 10.Solve: 4(p − 3) = p + 18. What is p?
  11. 11.The sum of three consecutive whole numbers is 153. What is the smallest of them?
  12. 12.Solve: m/3 + m/5 = 56. What is m?
  13. 13.The sum of three consecutive whole numbers is 93. What is the largest of them?
  14. 14.The sum of two consecutive whole numbers is 57. What is the smallest of them?
  15. 15.Solve: 7x + 1 = 5x + 29. What is x?
  16. 16.The sum of two consecutive whole numbers is 119. What is the smallest of them?
  17. 17.Solve: m/2 + m/5 = 21. What is m?
  18. 18.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?
  19. 19.Solve: t/2 + t/5 = 21. What is t?
  20. 20.Solve: 3(y − 4) = y + 18. What is y?
  21. 21.Solve: m/3 + m/6 = 18. What is m?
  22. 22.The length of a rectangle is 12 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  23. 23.A father is 30 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?
  24. 24.Solve: 9x + 2 = 7x + 26. What is x?
  25. 25.Solve: 6(n − 2) = 3n + 6. What is n?
  26. 26.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?
  27. 27.The sum of three consecutive whole numbers is 39. What is the smallest of them?
  28. 28.A father is 8 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  29. 29.A father is 22 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  30. 30.A father is 48 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?
  31. 31.Solve: n/2 + n/4 = 6. What is n?
  32. 32.Solve: 4(x − 1) = 2x + 14. What is x?
  33. 33.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?
  34. 34.Solve: 4(x − 3) = x + 21. What is x?
  35. 35.A father is 60 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?
  36. 36.Solve: 3(y − 3) = 2y + 8. What is y?
  37. 37.The length of a rectangle is 1 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  38. 38.Solve: 5(n − 3) = 4n + 6. What is n?
  39. 39.Solve: 8n + 14 = 5n + 38. What is n?
  40. 40.A father is 10 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?

Answer key

  1. 13
  2. 20
  3. 7
  4. 5
  5. 54
  6. 46
  7. 2
  8. 4
  9. 48
  10. 10
  11. 50
  12. 105
  13. 32
  14. 28
  15. 14
  16. 59
  17. 30
  18. 4
  19. 30
  20. 15
  21. 36
  22. 22
  23. 8
  24. 12
  25. 6
  26. 7
  27. 12
  28. 4
  29. 8
  30. 9
  31. 8
  32. 9
  33. 6
  34. 11
  35. 12
  36. 17
  37. 15
  38. 21
  39. 8
  40. 4

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