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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 9 · 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 sum of four consecutive whole numbers is 86. What is the largest of them?
  2. 2.Solve: 4(t − 1) = t + 26. What is t?
  3. 3.A father is 12 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  4. 4.Solve: 8x + 12 = 6x + 38. What is x?
  5. 5.Solve: 7x + 13 = x + 103. What is x?
  6. 6.Solve: 4m + 2 = m + 14. What is m?
  7. 7.Solve: 7t + 15 = t + 93. What is t?
  8. 8.Solve: 8t + 2 = 7t + 7. What is t?
  9. 9.Solve: 7x + 4 = 4x + 10. What is x?
  10. 10.The sum of two consecutive whole numbers is 111. What is the largest of them?
  11. 11.The length of a rectangle is 5 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  12. 12.Solve: 7m + 11 = 6m + 12. What is m?
  13. 13.A father is 42 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?
  14. 14.The length of a rectangle is 4 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
  15. 15.A father is 26 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?
  16. 16.Solve: 3n + 4 = n + 12. What is n?
  17. 17.Solve: 3n + 9 = 2n + 11. What is n?
  18. 18.The sum of four consecutive whole numbers is 150. What is the smallest of them?
  19. 19.The length of a rectangle is 7 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  20. 20.Solve: 3(n − 2) = n + 8. What is n?
  21. 21.The length of a rectangle is 6 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  22. 22.The sum of two consecutive whole numbers is 91. What is the smallest of them?
  23. 23.The sum of four consecutive whole numbers is 50. What is the largest of them?
  24. 24.Solve: 3m + 7 = m + 35. What is m?
  25. 25.Solve: 4(t − 5) = 3t + 8. What is t?
  26. 26.The sum of four consecutive whole numbers is 194. What is the smallest of them?
  27. 27.The length of a rectangle is 7 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  28. 28.The length of a rectangle is 8 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
  29. 29.The length of a rectangle is 5 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
  30. 30.Solve: 4(x − 4) = x + 5. What is x?
  31. 31.The length of a rectangle is 9 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  32. 32.Solve: n/2 + n/3 = 30. What is n?
  33. 33.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?
  34. 34.Solve: p/6 + p/5 = 66. What is p?
  35. 35.Solve: 4(t − 1) = 2t + 26. What is t?
  36. 36.Solve: x/5 + x/3 = 40. What is x?
  37. 37.The sum of two consecutive whole numbers is 97. What is the largest of them?
  38. 38.Solve: 6(m − 5) = 4m + 16. What is m?
  39. 39.Solve: m/2 + m/6 = 16. What is m?
  40. 40.Solve: 7y + 16 = 2y + 31. What is y?

Answer key

  1. 23
  2. 10
  3. 9
  4. 13
  5. 15
  6. 4
  7. 13
  8. 5
  9. 2
  10. 56
  11. 28
  12. 1
  13. 12
  14. 9
  15. 10
  16. 4
  17. 2
  18. 36
  19. 8
  20. 7
  21. 7
  22. 45
  23. 14
  24. 14
  25. 28
  26. 47
  27. 7
  28. 13
  29. 3
  30. 7
  31. 4
  32. 36
  33. 3
  34. 180
  35. 15
  36. 75
  37. 49
  38. 23
  39. 24
  40. 3

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