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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 497 · 40 sums
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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/3 + x/5 = 56. What is x?
  2. 2.Solve: p/5 + p/4 = 18. What is p?
  3. 3.The length of a rectangle is 11 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  4. 4.The length of a rectangle is 5 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  5. 5.Solve: 6(n − 2) = 2n + 8. What is n?
  6. 6.Solve: 3n + 19 = 2n + 20. What is n?
  7. 7.The length of a rectangle is 2 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  8. 8.A father is 5 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  9. 9.Solve: 3(x − 4) = 2x + 7. What is x?
  10. 10.Solve: 5(p − 5) = p + 15. What is p?
  11. 11.A father is 30 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
  12. 12.Solve: 7t + 5 = 6t + 19. What is t?
  13. 13.Solve: 9x + 3 = x + 99. What is x?
  14. 14.Solve: 6(p − 1) = p + 4. What is p?
  15. 15.The sum of two consecutive whole numbers is 41. What is the smallest of them?
  16. 16.Solve: 7p + 5 = p + 95. What is p?
  17. 17.A father is 34 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?
  18. 18.Solve: 5n + 9 = 4n + 14. What is n?
  19. 19.The sum of four consecutive whole numbers is 226. What is the smallest of them?
  20. 20.Solve: 5y + 15 = 2y + 18. What is y?
  21. 21.Solve: 5n + 18 = n + 66. What is n?
  22. 22.Solve: 9p + 12 = 6p + 36. What is p?
  23. 23.A father is 30 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
  24. 24.Solve: m/5 + m/6 = 77. What is m?
  25. 25.The length of a rectangle is 8 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  26. 26.Solve: 6x + 8 = 2x + 20. What is x?
  27. 27.Solve: p/5 + p/3 = 8. What is p?
  28. 28.Solve: 5p + 19 = 3p + 27. What is p?
  29. 29.Solve: 3(x − 3) = x + 1. What is x?
  30. 30.The sum of four consecutive whole numbers is 86. What is the smallest of them?
  31. 31.The length of a rectangle is 12 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
  32. 32.Solve: 3(x − 5) = 2x + 6. What is x?
  33. 33.The sum of two consecutive whole numbers is 35. What is the smallest of them?
  34. 34.Solve: 4(t − 1) = t + 2. What is t?
  35. 35.Solve: 9x + 10 = 7x + 16. What is x?
  36. 36.Solve: 3(y − 1) = y + 5. What is y?
  37. 37.Solve: m/6 + m/3 = 15. What is m?
  38. 38.Solve: 5(m − 1) = 4m + 13. What is m?
  39. 39.Solve: 9x + 16 = 5x + 76. What is x?
  40. 40.A father is 32 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?

Answer key

  1. 105
  2. 40
  3. 24
  4. 21
  5. 5
  6. 1
  7. 23
  8. 3
  9. 19
  10. 10
  11. 4
  12. 14
  13. 12
  14. 2
  15. 20
  16. 15
  17. 10
  18. 5
  19. 55
  20. 1
  21. 12
  22. 8
  23. 9
  24. 210
  25. 17
  26. 3
  27. 15
  28. 4
  29. 5
  30. 20
  31. 2
  32. 21
  33. 17
  34. 2
  35. 3
  36. 4
  37. 30
  38. 18
  39. 15
  40. 11

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