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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 919 · 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: 3(x − 1) = 2x + 6. What is x?
  2. 2.Solve: t/2 + t/5 = 21. What is t?
  3. 3.Solve: 3p + 9 = p + 27. What is p?
  4. 4.The sum of four consecutive whole numbers is 98. What is the largest of them?
  5. 5.Solve: 6p + 19 = 5p + 26. What is p?
  6. 6.Solve: 6(t − 5) = 5t + 4. What is t?
  7. 7.Solve: p/3 + p/4 = 14. What is p?
  8. 8.Solve: 6(x − 4) = 3x + 39. What is x?
  9. 9.Solve: n/6 + n/5 = 77. What is n?
  10. 10.The length of a rectangle is 13 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
  11. 11.Solve: 4(y − 5) = 3y + 9. What is y?
  12. 12.Solve: 6y + 17 = 3y + 47. What is y?
  13. 13.Solve: y/2 + y/4 = 18. What is y?
  14. 14.Solve: 5p + 7 = p + 35. What is p?
  15. 15.Solve: n/2 + n/5 = 42. What is n?
  16. 16.Solve: 3(n − 1) = n + 17. What is n?
  17. 17.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?
  18. 18.The length of a rectangle is 3 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
  19. 19.Solve: 3(n − 1) = 2n + 8. What is n?
  20. 20.Solve: 3(m − 4) = m + 4. What is m?
  21. 21.The sum of four consecutive whole numbers is 242. What is the smallest of them?
  22. 22.Solve: 5(n − 4) = 3n + 2. What is n?
  23. 23.Solve: 3(n − 2) = 2n + 10. What is n?
  24. 24.Solve: 5(p − 4) = 3p + 14. What is p?
  25. 25.Solve: 4y + 4 = y + 34. What is y?
  26. 26.The length of a rectangle is 8 cm more than its width. Its perimeter is 72 cm. What is its width (in cm)?
  27. 27.A father is 12 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?
  28. 28.Solve: 5m + 9 = 3m + 11. What is m?
  29. 29.Solve: 4(y − 4) = 2y + 14. What is y?
  30. 30.Solve: 9n + 14 = 6n + 29. What is n?
  31. 31.The length of a rectangle is 5 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
  32. 32.Solve: 5p + 7 = 4p + 9. What is p?
  33. 33.A father is 27 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?
  34. 34.The sum of three consecutive whole numbers is 24. What is the largest of them?
  35. 35.A father is 8 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  36. 36.Solve: 3(y − 1) = y + 25. What is y?
  37. 37.The length of a rectangle is 11 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  38. 38.The length of a rectangle is 1 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  39. 39.Solve: 6x + 12 = 2x + 52. What is x?
  40. 40.Solve: 3(n − 1) = n + 3. What is n?

Answer key

  1. 9
  2. 30
  3. 9
  4. 26
  5. 7
  6. 34
  7. 24
  8. 21
  9. 210
  10. 24
  11. 29
  12. 10
  13. 24
  14. 7
  15. 60
  16. 10
  17. 4
  18. 26
  19. 11
  20. 8
  21. 59
  22. 11
  23. 16
  24. 17
  25. 10
  26. 14
  27. 5
  28. 1
  29. 15
  30. 5
  31. 18
  32. 2
  33. 6
  34. 9
  35. 6
  36. 14
  37. 3
  38. 29
  39. 10
  40. 3

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