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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 353 · 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: 6(n − 4) = 4n + 22. What is n?
  2. 2.Solve: m/3 + m/5 = 16. What is m?
  3. 3.The length of a rectangle is 10 cm more than its width. Its perimeter is 136 cm. What is its width (in cm)?
  4. 4.The length of a rectangle is 11 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
  5. 5.Solve: 3n + 14 = n + 24. What is n?
  6. 6.Solve: n/3 + n/2 = 5. What is n?
  7. 7.Solve: 5(p − 1) = 2p + 1. What is p?
  8. 8.Solve: 5(x − 1) = x + 7. What is x?
  9. 9.Solve: 6(t − 2) = t + 28. What is t?
  10. 10.The length of a rectangle is 1 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  11. 11.Solve: t/4 + t/5 = 36. What is t?
  12. 12.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?
  13. 13.A father is 10 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  14. 14.The length of a rectangle is 7 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  15. 15.The sum of four consecutive whole numbers is 150. What is the smallest of them?
  16. 16.Solve: 3(p − 3) = p + 7. What is p?
  17. 17.Solve: y/3 + y/5 = 32. What is y?
  18. 18.Solve: x/4 + x/5 = 45. What is x?
  19. 19.Solve: 4x + 12 = x + 33. What is x?
  20. 20.The length of a rectangle is 14 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  21. 21.Solve: 3(n − 3) = n + 1. What is n?
  22. 22.Solve: m/3 + m/2 = 30. What is m?
  23. 23.A father is 14 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?
  24. 24.The length of a rectangle is 15 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  25. 25.The sum of two consecutive whole numbers is 109. What is the largest of them?
  26. 26.Solve: 6t + 6 = 5t + 15. What is t?
  27. 27.Solve: y/3 + y/5 = 40. What is y?
  28. 28.Solve: n/3 + n/4 = 49. What is n?
  29. 29.Solve: 3(x − 2) = x + 20. What is x?
  30. 30.The length of a rectangle is 9 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
  31. 31.Solve: 5t + 20 = 2t + 50. What is t?
  32. 32.The length of a rectangle is 7 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  33. 33.The sum of two consecutive whole numbers is 119. What is the largest of them?
  34. 34.Solve: y/6 + y/2 = 8. What is y?
  35. 35.The length of a rectangle is 8 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  36. 36.The sum of four consecutive whole numbers is 114. What is the largest of them?
  37. 37.The sum of two consecutive whole numbers is 99. What is the largest of them?
  38. 38.The sum of three consecutive whole numbers is 105. What is the largest of them?
  39. 39.Solve: 4(n − 3) = 3n + 3. What is n?
  40. 40.Solve: 3p + 13 = 2p + 24. What is p?

Answer key

  1. 23
  2. 30
  3. 29
  4. 29
  5. 5
  6. 6
  7. 2
  8. 3
  9. 8
  10. 10
  11. 80
  12. 11
  13. 2
  14. 18
  15. 36
  16. 8
  17. 60
  18. 100
  19. 7
  20. 2
  21. 5
  22. 36
  23. 6
  24. 9
  25. 55
  26. 9
  27. 75
  28. 84
  29. 13
  30. 29
  31. 10
  32. 4
  33. 60
  34. 12
  35. 22
  36. 30
  37. 50
  38. 36
  39. 15
  40. 11

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