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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 454 · 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: 5(x − 1) = 3x + 5. What is x?
  2. 2.Solve: 4(m − 5) = 2m + 26. What is m?
  3. 3.A father is 17 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  4. 4.Solve: n/4 + n/2 = 15. What is n?
  5. 5.The sum of four consecutive whole numbers is 110. What is the largest of them?
  6. 6.Solve: p/5 + p/4 = 54. What is p?
  7. 7.Solve: 6t + 17 = 3t + 23. What is t?
  8. 8.Solve: 4(t − 4) = 2t + 10. What is t?
  9. 9.Solve: 4x + 17 = 3x + 25. What is x?
  10. 10.A father is 54 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?
  11. 11.Solve: 3(x − 4) = 2x + 8. What is x?
  12. 12.Solve: 6n + 7 = 3n + 22. What is n?
  13. 13.Solve: 9t + 19 = 6t + 31. What is t?
  14. 14.A father is 18 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  15. 15.The sum of two consecutive whole numbers is 119. What is the largest of them?
  16. 16.The length of a rectangle is 7 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
  17. 17.Solve: 4(y − 4) = 3y + 3. What is y?
  18. 18.Solve: 4(t − 5) = 3t + 2. What is t?
  19. 19.Solve: 3t + 7 = 2t + 8. What is t?
  20. 20.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?
  21. 21.The length of a rectangle is 4 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  22. 22.The sum of three consecutive whole numbers is 165. What is the smallest of them?
  23. 23.Solve: 6(m − 3) = 2m + 14. What is m?
  24. 24.The length of a rectangle is 10 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  25. 25.Solve: 7y + 9 = 6y + 11. What is y?
  26. 26.Solve: x/5 + x/2 = 7. What is x?
  27. 27.The sum of four consecutive whole numbers is 86. What is the smallest of them?
  28. 28.The sum of two consecutive whole numbers is 37. What is the smallest of them?
  29. 29.Solve: 4(y − 5) = 2y + 4. What is y?
  30. 30.Solve: t/5 + t/2 = 14. What is t?
  31. 31.The length of a rectangle is 15 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  32. 32.Solve: 3y + 12 = y + 22. What is y?
  33. 33.The length of a rectangle is 6 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  34. 34.The sum of four consecutive whole numbers is 218. What is the smallest of them?
  35. 35.A father is 9 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  36. 36.The length of a rectangle is 15 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  37. 37.Solve: 3(m − 3) = 2m + 12. What is m?
  38. 38.The length of a rectangle is 11 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
  39. 39.Solve: 7p + 8 = 2p + 43. What is p?
  40. 40.Solve: 3p + 9 = p + 15. What is p?

Answer key

  1. 5
  2. 23
  3. 11
  4. 20
  5. 29
  6. 120
  7. 2
  8. 13
  9. 8
  10. 11
  11. 20
  12. 5
  13. 4
  14. 10
  15. 60
  16. 2
  17. 19
  18. 22
  19. 1
  20. 8
  21. 29
  22. 54
  23. 8
  24. 9
  25. 2
  26. 10
  27. 20
  28. 18
  29. 12
  30. 20
  31. 24
  32. 5
  33. 6
  34. 53
  35. 2
  36. 15
  37. 21
  38. 27
  39. 7
  40. 3

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