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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 312 · 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: x/2 + x/6 = 16. What is x?
  2. 2.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?
  3. 3.Solve: x/5 + x/3 = 16. What is x?
  4. 4.The length of a rectangle is 12 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  5. 5.The length of a rectangle is 3 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  6. 6.Solve: 6(m − 3) = 2m + 22. What is m?
  7. 7.Solve: 5(t − 1) = 2t + 37. What is t?
  8. 8.Solve: m/4 + m/6 = 20. What is m?
  9. 9.Solve: 6m + 5 = 4m + 21. What is m?
  10. 10.Solve: x/6 + x/4 = 30. What is x?
  11. 11.Solve: 7p + 7 = 4p + 25. What is p?
  12. 12.Solve: n/4 + n/3 = 56. What is n?
  13. 13.Solve: 3(p − 2) = 2p + 2. What is p?
  14. 14.Solve: 3m + 10 = m + 16. What is m?
  15. 15.Solve: 9t + 9 = 2t + 93. What is t?
  16. 16.The sum of three consecutive whole numbers is 156. What is the largest of them?
  17. 17.The sum of three consecutive whole numbers is 153. What is the smallest of them?
  18. 18.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?
  19. 19.Solve: 4(n − 3) = n + 15. What is n?
  20. 20.The length of a rectangle is 8 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  21. 21.The length of a rectangle is 9 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
  22. 22.Solve: 5(y − 4) = 4y + 5. What is y?
  23. 23.Solve: 8p + 12 = p + 75. What is p?
  24. 24.Solve: 7m + 15 = m + 33. What is m?
  25. 25.A father is 13 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  26. 26.Solve: y/2 + y/5 = 7. What is y?
  27. 27.Solve: 4(y − 1) = y + 17. What is y?
  28. 28.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?
  29. 29.Solve: 3m + 16 = 2m + 26. What is m?
  30. 30.Solve: 4t + 14 = t + 20. What is t?
  31. 31.The sum of four consecutive whole numbers is 74. What is the smallest of them?
  32. 32.The sum of four consecutive whole numbers is 46. What is the largest of them?
  33. 33.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?
  34. 34.Solve: 5(x − 5) = 4x + 13. What is x?
  35. 35.Solve: 6x + 3 = 3x + 27. What is x?
  36. 36.A father is 13 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  37. 37.Solve: 4(y − 3) = 3y + 7. What is y?
  38. 38.Solve: 4(x − 4) = x + 11. What is x?
  39. 39.The sum of two consecutive whole numbers is 23. What is the largest of them?
  40. 40.Solve: 3(n − 3) = 2n + 1. What is n?

Answer key

  1. 24
  2. 3
  3. 30
  4. 14
  5. 17
  6. 10
  7. 14
  8. 48
  9. 8
  10. 72
  11. 6
  12. 96
  13. 8
  14. 3
  15. 12
  16. 53
  17. 50
  18. 7
  19. 9
  20. 19
  21. 15
  22. 25
  23. 9
  24. 3
  25. 6
  26. 10
  27. 7
  28. 5
  29. 10
  30. 2
  31. 17
  32. 13
  33. 10
  34. 38
  35. 8
  36. 9
  37. 19
  38. 9
  39. 12
  40. 10

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