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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 902 · 40 sums
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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: 4p + 5 = p + 14. What is p?
  2. 2.Solve: 8y + 13 = 7y + 17. What is y?
  3. 3.Solve: m/5 + m/2 = 49. What is m?
  4. 4.The sum of four consecutive whole numbers is 138. What is the largest of them?
  5. 5.The length of a rectangle is 9 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  6. 6.A father is 15 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  7. 7.The sum of three consecutive whole numbers is 150. What is the smallest of them?
  8. 8.Solve: 4x + 17 = 2x + 29. What is x?
  9. 9.Solve: y/2 + y/3 = 5. What is y?
  10. 10.Solve: 3(x − 1) = 2x + 7. What is x?
  11. 11.Solve: 4y + 14 = 3y + 27. What is y?
  12. 12.The length of a rectangle is 3 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  13. 13.The sum of three consecutive whole numbers is 18. What is the largest of them?
  14. 14.The sum of two consecutive whole numbers is 65. What is the largest of them?
  15. 15.Solve: 3x + 2 = x + 14. What is x?
  16. 16.Solve: y/4 + y/6 = 30. What is y?
  17. 17.A father is 11 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  18. 18.Solve: 5(m − 2) = 3m + 18. What is m?
  19. 19.The sum of two consecutive whole numbers is 21. What is the smallest of them?
  20. 20.The sum of four consecutive whole numbers is 146. What is the smallest of them?
  21. 21.A father is 12 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  22. 22.The length of a rectangle is 4 cm more than its width. Its perimeter is 16 cm. What is its width (in cm)?
  23. 23.The length of a rectangle is 6 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  24. 24.Solve: m/2 + m/3 = 35. What is m?
  25. 25.The length of a rectangle is 7 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  26. 26.The sum of two consecutive whole numbers is 81. What is the smallest of them?
  27. 27.A father is 24 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?
  28. 28.Solve: t/5 + t/6 = 22. What is t?
  29. 29.Solve: 6(y − 2) = 5y + 10. What is y?
  30. 30.Solve: 6(t − 1) = 5t + 7. What is t?
  31. 31.The length of a rectangle is 12 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  32. 32.Solve: n/6 + n/3 = 18. What is n?
  33. 33.Solve: y/2 + y/3 = 15. What is y?
  34. 34.Solve: m/6 + m/5 = 33. What is m?
  35. 35.Solve: x/5 + x/3 = 24. What is x?
  36. 36.Solve: 3(m − 5) = m + 5. What is m?
  37. 37.Solve: 6y + 1 = y + 76. What is y?
  38. 38.The length of a rectangle is 9 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
  39. 39.The length of a rectangle is 6 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  40. 40.Solve: 4p + 10 = 3p + 23. What is p?

Answer key

  1. 3
  2. 4
  3. 70
  4. 36
  5. 5
  6. 12
  7. 49
  8. 6
  9. 6
  10. 10
  11. 13
  12. 10
  13. 7
  14. 33
  15. 6
  16. 72
  17. 7
  18. 14
  19. 10
  20. 35
  21. 7
  22. 2
  23. 20
  24. 42
  25. 20
  26. 40
  27. 7
  28. 60
  29. 22
  30. 13
  31. 7
  32. 36
  33. 18
  34. 90
  35. 45
  36. 10
  37. 15
  38. 29
  39. 26
  40. 13

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