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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 790 · 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.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
  2. 2.Solve: 3p + 5 = 2p + 18. What is p?
  3. 3.The length of a rectangle is 15 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
  4. 4.Solve: 8x + 5 = x + 103. What is x?
  5. 5.Solve: x/5 + x/4 = 27. What is x?
  6. 6.The sum of three consecutive whole numbers is 159. What is the smallest of them?
  7. 7.A father is 30 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?
  8. 8.Solve: 3(p − 1) = 2p + 9. What is p?
  9. 9.Solve: 9x + 1 = 3x + 79. What is x?
  10. 10.Solve: 5(y − 1) = 2y + 31. What is y?
  11. 11.Solve: 4(p − 2) = p + 25. What is p?
  12. 12.Solve: 5(p − 3) = 3p + 25. What is p?
  13. 13.Solve: x/6 + x/2 = 4. What is x?
  14. 14.Solve: 9p + 6 = 5p + 38. What is p?
  15. 15.Solve: 5(n − 5) = 4n + 9. What is n?
  16. 16.Solve: m/3 + m/2 = 35. What is m?
  17. 17.Solve: n/2 + n/6 = 20. What is n?
  18. 18.Solve: y/4 + y/2 = 18. What is y?
  19. 19.Solve: m/5 + m/4 = 27. What is m?
  20. 20.The sum of three consecutive whole numbers is 87. What is the largest of them?
  21. 21.Solve: y/6 + y/4 = 15. What is y?
  22. 22.Solve: 5(m − 3) = 2m + 27. What is m?
  23. 23.A father is 9 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  24. 24.The length of a rectangle is 14 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  25. 25.The length of a rectangle is 2 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  26. 26.Solve: 5(y − 5) = 3y + 17. What is y?
  27. 27.The length of a rectangle is 14 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  28. 28.Solve: t/2 + t/4 = 6. What is t?
  29. 29.A father is 7 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  30. 30.Solve: 9y + 5 = y + 37. What is y?
  31. 31.The sum of two consecutive whole numbers is 21. What is the largest of them?
  32. 32.Solve: t/6 + t/2 = 12. What is t?
  33. 33.Solve: 9n + 6 = 2n + 48. What is n?
  34. 34.A father is 12 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
  35. 35.Solve: 7x + 15 = 3x + 27. What is x?
  36. 36.Solve: 4x + 11 = 2x + 17. What is x?
  37. 37.The sum of two consecutive whole numbers is 89. What is the smallest of them?
  38. 38.The sum of four consecutive whole numbers is 42. What is the largest of them?
  39. 39.Solve: x/2 + x/3 = 40. What is x?
  40. 40.The length of a rectangle is 8 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?

Answer key

  1. 2
  2. 13
  3. 7
  4. 14
  5. 60
  6. 52
  7. 8
  8. 12
  9. 13
  10. 12
  11. 11
  12. 20
  13. 6
  14. 8
  15. 34
  16. 42
  17. 30
  18. 24
  19. 60
  20. 30
  21. 36
  22. 14
  23. 5
  24. 15
  25. 27
  26. 21
  27. 6
  28. 8
  29. 6
  30. 4
  31. 11
  32. 18
  33. 6
  34. 3
  35. 3
  36. 3
  37. 44
  38. 12
  39. 48
  40. 6

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