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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 461 · 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: 4(n − 3) = 3n + 7. What is n?
  2. 2.A father is 16 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?
  3. 3.A father is 39 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
  4. 4.Solve: 5(y − 4) = y + 32. What is y?
  5. 5.The length of a rectangle is 15 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
  6. 6.The sum of three consecutive whole numbers is 72. What is the smallest of them?
  7. 7.Solve: m/3 + m/4 = 56. What is m?
  8. 8.The length of a rectangle is 13 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  9. 9.A father is 15 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  10. 10.Solve: 3y + 17 = y + 43. What is y?
  11. 11.Solve: 4(t − 4) = t + 20. What is t?
  12. 12.A father is 9 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  13. 13.Solve: n/5 + n/2 = 42. What is n?
  14. 14.A father is 21 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?
  15. 15.The sum of four consecutive whole numbers is 102. What is the smallest of them?
  16. 16.Solve: x/5 + x/3 = 56. What is x?
  17. 17.The length of a rectangle is 5 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  18. 18.A father is 33 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?
  19. 19.The sum of four consecutive whole numbers is 42. What is the largest of them?
  20. 20.A father is 19 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  21. 21.The sum of two consecutive whole numbers is 27. What is the largest of them?
  22. 22.The sum of four consecutive whole numbers is 78. What is the smallest of them?
  23. 23.A father is 14 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  24. 24.Solve: p/3 + p/6 = 21. What is p?
  25. 25.Solve: 5(m − 5) = 4m + 12. What is m?
  26. 26.The length of a rectangle is 10 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  27. 27.The length of a rectangle is 2 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  28. 28.The length of a rectangle is 2 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  29. 29.Solve: 6(x − 1) = 3x + 24. What is x?
  30. 30.Solve: 5(p − 1) = 2p + 28. What is p?
  31. 31.The sum of two consecutive whole numbers is 13. What is the smallest of them?
  32. 32.Solve: 3(p − 2) = p + 26. What is p?
  33. 33.The sum of two consecutive whole numbers is 19. What is the largest of them?
  34. 34.A father is 12 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  35. 35.The length of a rectangle is 5 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  36. 36.Solve: 4(x − 3) = 3x + 1. What is x?
  37. 37.A father is 18 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  38. 38.The sum of two consecutive whole numbers is 17. What is the smallest of them?
  39. 39.A father is 12 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  40. 40.The sum of three consecutive whole numbers is 165. What is the largest of them?

Answer key

  1. 19
  2. 5
  3. 5
  4. 13
  5. 25
  6. 23
  7. 96
  8. 6
  9. 8
  10. 13
  11. 12
  12. 7
  13. 60
  14. 4
  15. 24
  16. 105
  17. 9
  18. 10
  19. 12
  20. 11
  21. 14
  22. 18
  23. 12
  24. 42
  25. 37
  26. 17
  27. 22
  28. 21
  29. 10
  30. 11
  31. 6
  32. 16
  33. 10
  34. 11
  35. 6
  36. 13
  37. 7
  38. 8
  39. 5
  40. 56

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