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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 59 · 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: 9t + 17 = 6t + 20. What is t?
  2. 2.Solve: 8n + 17 = 7n + 32. What is n?
  3. 3.Solve: y/4 + y/3 = 14. What is y?
  4. 4.Solve: 4(y − 1) = y + 26. What is y?
  5. 5.Solve: p/2 + p/5 = 21. What is p?
  6. 6.The length of a rectangle is 6 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  7. 7.Solve: 3(m − 3) = m + 5. What is m?
  8. 8.Solve: 8p + 17 = p + 38. What is p?
  9. 9.A father is 8 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  10. 10.Solve: 6(n − 2) = n + 3. What is n?
  11. 11.A father is 14 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  12. 12.A father is 3 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  13. 13.Solve: 5(t − 2) = 3t + 14. What is t?
  14. 14.Solve: 4m + 3 = 3m + 15. What is m?
  15. 15.Solve: 5(n − 1) = 4n + 2. What is n?
  16. 16.The length of a rectangle is 8 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  17. 17.Solve: 3x + 18 = 2x + 31. What is x?
  18. 18.Solve: y/3 + y/6 = 12. What is y?
  19. 19.Solve: m/5 + m/6 = 77. What is m?
  20. 20.The length of a rectangle is 1 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  21. 21.Solve: p/6 + p/2 = 32. What is p?
  22. 22.Solve: 6(x − 3) = 5x + 2. What is x?
  23. 23.Solve: 8p + 9 = 6p + 23. What is p?
  24. 24.Solve: 6y + 13 = 5y + 15. What is y?
  25. 25.A father is 14 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  26. 26.The sum of four consecutive whole numbers is 162. What is the largest of them?
  27. 27.Solve: 3(p − 1) = p + 7. What is p?
  28. 28.The sum of three consecutive whole numbers is 36. What is the largest of them?
  29. 29.Solve: 5m + 8 = 4m + 11. What is m?
  30. 30.Solve: 3(n − 2) = n + 16. What is n?
  31. 31.The sum of three consecutive whole numbers is 66. What is the largest of them?
  32. 32.The sum of two consecutive whole numbers is 93. What is the smallest of them?
  33. 33.The length of a rectangle is 10 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  34. 34.Solve: 3y + 10 = 2y + 17. What is y?
  35. 35.Solve: 6(y − 2) = 3y + 9. What is y?
  36. 36.Solve: x/5 + x/6 = 88. What is x?
  37. 37.The length of a rectangle is 5 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  38. 38.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?
  39. 39.Solve: 6t + 5 = t + 65. What is t?
  40. 40.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?

Answer key

  1. 1
  2. 15
  3. 24
  4. 10
  5. 30
  6. 9
  7. 7
  8. 3
  9. 5
  10. 3
  11. 6
  12. 2
  13. 12
  14. 12
  15. 7
  16. 6
  17. 13
  18. 24
  19. 210
  20. 12
  21. 48
  22. 20
  23. 7
  24. 2
  25. 8
  26. 42
  27. 5
  28. 13
  29. 3
  30. 11
  31. 23
  32. 46
  33. 4
  34. 7
  35. 7
  36. 240
  37. 29
  38. 7
  39. 12
  40. 7

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