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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 752 · 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: 3(p − 2) = p + 14. What is p?
  2. 2.The sum of two consecutive whole numbers is 101. What is the smallest of them?
  3. 3.Solve: p/4 + p/3 = 28. What is p?
  4. 4.Solve: 4(t − 5) = 2t + 2. What is t?
  5. 5.Solve: 3(x − 2) = x + 6. What is x?
  6. 6.Solve: 5(y − 3) = y + 21. What is y?
  7. 7.Solve: 6(n − 1) = 4n + 2. What is n?
  8. 8.Solve: 4(x − 4) = x + 2. What is x?
  9. 9.Solve: x/4 + x/2 = 12. What is x?
  10. 10.A father is 6 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  11. 11.Solve: 6(p − 1) = 3p + 21. What is p?
  12. 12.The length of a rectangle is 9 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  13. 13.The length of a rectangle is 5 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  14. 14.Solve: 6x + 15 = 5x + 21. What is x?
  15. 15.The sum of two consecutive whole numbers is 53. What is the largest of them?
  16. 16.Solve: 3(m − 5) = 2m + 1. What is m?
  17. 17.A father is 33 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  18. 18.A father is 5 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  19. 19.Solve: 4(t − 2) = 3t + 8. What is t?
  20. 20.Solve: t/6 + t/2 = 8. What is t?
  21. 21.The sum of two consecutive whole numbers is 29. What is the smallest of them?
  22. 22.The length of a rectangle is 9 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  23. 23.Solve: 9t + 5 = 2t + 47. What is t?
  24. 24.The length of a rectangle is 14 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  25. 25.Solve: 3t + 5 = t + 29. What is t?
  26. 26.The sum of three consecutive whole numbers is 93. What is the smallest of them?
  27. 27.A father is 42 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
  28. 28.Solve: 4n + 1 = n + 37. What is n?
  29. 29.Solve: 5x + 15 = 2x + 27. What is x?
  30. 30.A father is 7 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  31. 31.Solve: t/5 + t/2 = 14. What is t?
  32. 32.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  33. 33.A father is 8 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  34. 34.A father is 12 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  35. 35.A father is 10 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?
  36. 36.Solve: 5m + 15 = m + 23. What is m?
  37. 37.Solve: 5(y − 4) = 2y + 1. What is y?
  38. 38.The sum of three consecutive whole numbers is 33. What is the largest of them?
  39. 39.Solve: x/2 + x/6 = 28. What is x?
  40. 40.Solve: n/4 + n/2 = 18. What is n?

Answer key

  1. 10
  2. 50
  3. 48
  4. 11
  5. 6
  6. 9
  7. 4
  8. 6
  9. 16
  10. 3
  11. 9
  12. 3
  13. 9
  14. 6
  15. 27
  16. 16
  17. 7
  18. 4
  19. 16
  20. 12
  21. 14
  22. 5
  23. 6
  24. 17
  25. 12
  26. 30
  27. 10
  28. 12
  29. 4
  30. 4
  31. 20
  32. 2
  33. 4
  34. 4
  35. 4
  36. 2
  37. 7
  38. 12
  39. 42
  40. 24

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