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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 842 · 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: 6(m − 5) = 4m + 20. What is m?
  2. 2.The length of a rectangle is 11 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  3. 3.Solve: y/2 + y/3 = 15. What is y?
  4. 4.Solve: x/4 + x/2 = 15. What is x?
  5. 5.Solve: 4x + 13 = 3x + 24. What is x?
  6. 6.Solve: y/6 + y/3 = 6. What is y?
  7. 7.Solve: 4t + 20 = 3t + 32. What is t?
  8. 8.Solve: 3x + 17 = x + 47. What is x?
  9. 9.A father is 14 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  10. 10.A father is 24 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?
  11. 11.A father is 18 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?
  12. 12.The length of a rectangle is 3 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  13. 13.Solve: 9x + 13 = 2x + 55. What is x?
  14. 14.Solve: 5(p − 1) = 4p + 3. What is p?
  15. 15.The sum of two consecutive whole numbers is 107. What is the largest of them?
  16. 16.Solve: 4t + 6 = 2t + 22. What is t?
  17. 17.Solve: 3m + 11 = 2m + 22. What is m?
  18. 18.Solve: 7m + 4 = m + 40. What is m?
  19. 19.The length of a rectangle is 10 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  20. 20.Solve: 8x + 15 = 3x + 80. What is x?
  21. 21.Solve: 7p + 1 = 3p + 25. What is p?
  22. 22.Solve: 5(n − 2) = 3n + 20. What is n?
  23. 23.Solve: 5m + 13 = 3m + 35. What is m?
  24. 24.A father is 15 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  25. 25.Solve: 4(x − 4) = x + 14. What is x?
  26. 26.The length of a rectangle is 13 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  27. 27.The length of a rectangle is 1 cm more than its width. Its perimeter is 14 cm. What is its width (in cm)?
  28. 28.Solve: 3y + 3 = 2y + 9. What is y?
  29. 29.A father is 42 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  30. 30.Solve: 3x + 3 = x + 29. What is x?
  31. 31.The sum of three consecutive whole numbers is 81. What is the largest of them?
  32. 32.Solve: 6n + 12 = n + 52. What is n?
  33. 33.Solve: 4(y − 5) = y + 19. What is y?
  34. 34.The sum of four consecutive whole numbers is 110. What is the smallest of them?
  35. 35.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?
  36. 36.A father is 7 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  37. 37.Solve: 6(y − 5) = y + 5. What is y?
  38. 38.Solve: 7y + 15 = y + 105. What is y?
  39. 39.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?
  40. 40.Solve: 8t + 14 = 6t + 26. What is t?

Answer key

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

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