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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 642 · 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 218. What is the largest of them?
  2. 2.The length of a rectangle is 6 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  3. 3.The sum of four consecutive whole numbers is 94. What is the smallest of them?
  4. 4.Solve: 6t + 19 = 5t + 26. What is t?
  5. 5.The length of a rectangle is 12 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  6. 6.The length of a rectangle is 3 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  7. 7.Solve: 8t + 12 = 5t + 42. What is t?
  8. 8.Solve: 4p + 7 = 2p + 11. What is p?
  9. 9.The length of a rectangle is 11 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
  10. 10.Solve: 5y + 2 = y + 38. What is y?
  11. 11.Solve: 4(t − 3) = 2t + 24. What is t?
  12. 12.Solve: 3(m − 3) = m + 15. What is m?
  13. 13.Solve: 9y + 4 = 8y + 9. What is y?
  14. 14.Solve: 3y + 2 = y + 16. What is y?
  15. 15.A father is 9 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  16. 16.A father is 45 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?
  17. 17.A father is 30 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?
  18. 18.Solve: n/5 + n/4 = 36. What is n?
  19. 19.The length of a rectangle is 1 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  20. 20.Solve: 4(m − 1) = 2m + 10. What is m?
  21. 21.Solve: y/6 + y/4 = 5. What is y?
  22. 22.The sum of three consecutive whole numbers is 30. What is the smallest of them?
  23. 23.Solve: t/3 + t/2 = 30. What is t?
  24. 24.A father is 26 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  25. 25.The sum of two consecutive whole numbers is 91. What is the smallest of them?
  26. 26.Solve: p/2 + p/4 = 15. What is p?
  27. 27.Solve: 4x + 11 = x + 14. What is x?
  28. 28.Solve: y/6 + y/2 = 28. What is y?
  29. 29.Solve: 5p + 14 = 2p + 29. What is p?
  30. 30.Solve: 6(m − 2) = 3m + 9. What is m?
  31. 31.A father is 12 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?
  32. 32.Solve: 4(p − 5) = 2p + 18. What is p?
  33. 33.Solve: x/3 + x/4 = 21. What is x?
  34. 34.The sum of two consecutive whole numbers is 39. What is the largest of them?
  35. 35.The sum of four consecutive whole numbers is 90. What is the smallest of them?
  36. 36.The length of a rectangle is 2 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  37. 37.Solve: n/5 + n/3 = 8. What is n?
  38. 38.The sum of two consecutive whole numbers is 113. What is the smallest of them?
  39. 39.Solve: 5(m − 4) = 3m + 22. What is m?
  40. 40.Solve: 3(n − 1) = n + 19. What is n?

Answer key

  1. 56
  2. 18
  3. 22
  4. 7
  5. 17
  6. 9
  7. 10
  8. 2
  9. 20
  10. 9
  11. 18
  12. 12
  13. 5
  14. 7
  15. 5
  16. 10
  17. 7
  18. 80
  19. 23
  20. 7
  21. 12
  22. 9
  23. 36
  24. 6
  25. 45
  26. 20
  27. 1
  28. 42
  29. 5
  30. 7
  31. 2
  32. 19
  33. 36
  34. 20
  35. 21
  36. 14
  37. 15
  38. 56
  39. 21
  40. 11

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