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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 223 · 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.The length of a rectangle is 2 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  2. 2.Solve: 3(n − 3) = 2n + 5. What is n?
  3. 3.The length of a rectangle is 15 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
  4. 4.The length of a rectangle is 1 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  5. 5.The sum of three consecutive whole numbers is 123. What is the smallest of them?
  6. 6.Solve: 6(x − 3) = 2x + 22. What is x?
  7. 7.Solve: 5(y − 2) = 4y + 1. What is y?
  8. 8.The sum of two consecutive whole numbers is 79. What is the largest of them?
  9. 9.Solve: t/2 + t/3 = 15. What is t?
  10. 10.Solve: m/6 + m/5 = 88. What is m?
  11. 11.The sum of two consecutive whole numbers is 103. What is the smallest of them?
  12. 12.Solve: t/2 + t/6 = 20. What is t?
  13. 13.The length of a rectangle is 7 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  14. 14.Solve: 5(x − 1) = 4x + 2. What is x?
  15. 15.Solve: 7t + 15 = 2t + 25. What is t?
  16. 16.The length of a rectangle is 14 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  17. 17.Solve: 5p + 4 = 2p + 49. What is p?
  18. 18.Solve: p/2 + p/4 = 6. What is p?
  19. 19.The length of a rectangle is 6 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  20. 20.Solve: 5p + 11 = 3p + 23. What is p?
  21. 21.Solve: 3x + 18 = x + 20. What is x?
  22. 22.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?
  23. 23.A father is 32 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  24. 24.Solve: 4(p − 1) = p + 38. What is p?
  25. 25.Solve: 6y + 13 = 3y + 43. What is y?
  26. 26.Solve: 3(n − 4) = 2n + 1. What is n?
  27. 27.Solve: 4(y − 4) = 2y + 6. What is y?
  28. 28.The length of a rectangle is 13 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
  29. 29.The length of a rectangle is 6 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
  30. 30.A father is 36 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?
  31. 31.Solve: 5p + 13 = 2p + 28. What is p?
  32. 32.The length of a rectangle is 9 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  33. 33.Solve: p/3 + p/5 = 56. What is p?
  34. 34.The sum of four consecutive whole numbers is 94. What is the largest of them?
  35. 35.Solve: m/3 + m/6 = 9. What is m?
  36. 36.Solve: 6t + 15 = 3t + 27. What is t?
  37. 37.The sum of three consecutive whole numbers is 171. What is the largest of them?
  38. 38.Solve: n/5 + n/2 = 49. What is n?
  39. 39.Solve: 9y + 5 = 8y + 15. What is y?
  40. 40.Solve: 3(p − 5) = p + 25. What is p?

Answer key

  1. 24
  2. 14
  3. 19
  4. 18
  5. 40
  6. 10
  7. 11
  8. 40
  9. 18
  10. 240
  11. 51
  12. 30
  13. 4
  14. 7
  15. 2
  16. 5
  17. 15
  18. 8
  19. 18
  20. 6
  21. 1
  22. 8
  23. 9
  24. 14
  25. 10
  26. 13
  27. 11
  28. 7
  29. 2
  30. 9
  31. 5
  32. 19
  33. 105
  34. 25
  35. 18
  36. 4
  37. 58
  38. 70
  39. 10
  40. 20

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