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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 207 · 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 10 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  2. 2.A father is 39 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?
  3. 3.Solve: 6(x − 2) = x + 38. What is x?
  4. 4.Solve: 5t + 19 = 4t + 31. What is t?
  5. 5.Solve: 3n + 3 = n + 5. What is n?
  6. 6.Solve: 3(p − 3) = p + 9. What is p?
  7. 7.Solve: 5x + 9 = 3x + 37. What is x?
  8. 8.The sum of two consecutive whole numbers is 103. What is the smallest of them?
  9. 9.A father is 39 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?
  10. 10.A father is 3 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  11. 11.Solve: 6(x − 1) = x + 24. What is x?
  12. 12.The sum of three consecutive whole numbers is 84. What is the smallest of them?
  13. 13.Solve: 5(y − 4) = y + 28. What is y?
  14. 14.Solve: 6(x − 2) = 4x + 18. What is x?
  15. 15.A father is 14 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  16. 16.Solve: 3(p − 5) = 2p + 6. What is p?
  17. 17.A father is 10 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  18. 18.Solve: 4y + 17 = 3y + 25. What is y?
  19. 19.The sum of three consecutive whole numbers is 102. What is the largest of them?
  20. 20.Solve: 6(p − 2) = 3p + 27. What is p?
  21. 21.The length of a rectangle is 4 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  22. 22.The length of a rectangle is 15 cm more than its width. Its perimeter is 142 cm. What is its width (in cm)?
  23. 23.Solve: 6y + 15 = 5y + 26. What is y?
  24. 24.Solve: 6m + 7 = 4m + 27. What is m?
  25. 25.A father is 24 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?
  26. 26.The length of a rectangle is 5 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  27. 27.Solve: 7m + 8 = m + 98. What is m?
  28. 28.The sum of three consecutive whole numbers is 111. What is the smallest of them?
  29. 29.Solve: 6(m − 2) = 3m + 30. What is m?
  30. 30.The sum of four consecutive whole numbers is 218. What is the smallest of them?
  31. 31.Solve: 9m + 11 = 7m + 31. What is m?
  32. 32.A father is 24 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?
  33. 33.Solve: 8m + 3 = 3m + 23. What is m?
  34. 34.Solve: 3(t − 4) = t + 14. What is t?
  35. 35.Solve: x/2 + x/5 = 7. What is x?
  36. 36.A father is 36 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?
  37. 37.Solve: n/6 + n/3 = 9. What is n?
  38. 38.The sum of two consecutive whole numbers is 25. What is the smallest of them?
  39. 39.Solve: 7x + 9 = 2x + 64. What is x?
  40. 40.Solve: x/2 + x/3 = 10. What is x?

Answer key

  1. 18
  2. 10
  3. 10
  4. 12
  5. 1
  6. 9
  7. 14
  8. 51
  9. 8
  10. 2
  11. 6
  12. 27
  13. 12
  14. 15
  15. 12
  16. 21
  17. 3
  18. 8
  19. 35
  20. 13
  21. 21
  22. 28
  23. 11
  24. 10
  25. 11
  26. 15
  27. 15
  28. 36
  29. 14
  30. 53
  31. 10
  32. 3
  33. 4
  34. 13
  35. 10
  36. 9
  37. 18
  38. 12
  39. 11
  40. 12

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