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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 664 · 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.A father is 4 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  2. 2.The sum of four consecutive whole numbers is 58. What is the smallest of them?
  3. 3.The length of a rectangle is 14 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
  4. 4.Solve: 5(p − 1) = 4p + 5. What is p?
  5. 5.Solve: 6(t − 2) = 5t + 11. What is t?
  6. 6.The length of a rectangle is 9 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  7. 7.The length of a rectangle is 6 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  8. 8.Solve: 6(m − 1) = 4m + 12. What is m?
  9. 9.A father is 28 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?
  10. 10.The length of a rectangle is 1 cm more than its width. Its perimeter is 10 cm. What is its width (in cm)?
  11. 11.Solve: p/2 + p/6 = 4. What is p?
  12. 12.The length of a rectangle is 15 cm more than its width. Its perimeter is 150 cm. What is its width (in cm)?
  13. 13.The sum of four consecutive whole numbers is 42. What is the smallest of them?
  14. 14.The length of a rectangle is 10 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
  15. 15.Solve: 4n + 4 = 3n + 14. What is n?
  16. 16.Solve: 7m + 8 = m + 32. What is m?
  17. 17.Solve: 3y + 7 = 2y + 9. What is y?
  18. 18.Solve: 5(p − 3) = p + 29. What is p?
  19. 19.Solve: 6(y − 5) = y + 55. What is y?
  20. 20.The sum of four consecutive whole numbers is 162. What is the smallest of them?
  21. 21.The sum of two consecutive whole numbers is 11. What is the smallest of them?
  22. 22.Solve: m/2 + m/6 = 8. What is m?
  23. 23.Solve: 5x + 6 = 4x + 21. What is x?
  24. 24.Solve: 5(p − 4) = 4p + 13. What is p?
  25. 25.Solve: n/6 + n/3 = 6. What is n?
  26. 26.Solve: 3x + 6 = x + 14. What is x?
  27. 27.Solve: 4p + 13 = 3p + 18. What is p?
  28. 28.Solve: 4m + 15 = 3m + 24. What is m?
  29. 29.Solve: 6(m − 3) = 2m + 42. What is m?
  30. 30.The length of a rectangle is 2 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
  31. 31.The sum of four consecutive whole numbers is 202. What is the smallest of them?
  32. 32.The sum of four consecutive whole numbers is 150. What is the largest of them?
  33. 33.Solve: 4(p − 1) = p + 26. What is p?
  34. 34.Solve: 8x + 4 = 2x + 70. What is x?
  35. 35.A father is 33 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?
  36. 36.A father is 30 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  37. 37.Solve: 3x + 14 = 2x + 28. What is x?
  38. 38.Solve: 7x + 12 = 2x + 42. What is x?
  39. 39.The sum of two consecutive whole numbers is 61. What is the smallest of them?
  40. 40.A father is 34 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. 2
  2. 13
  3. 25
  4. 10
  5. 23
  6. 11
  7. 4
  8. 9
  9. 11
  10. 2
  11. 6
  12. 30
  13. 9
  14. 4
  15. 10
  16. 4
  17. 2
  18. 11
  19. 17
  20. 39
  21. 5
  22. 12
  23. 15
  24. 33
  25. 12
  26. 4
  27. 5
  28. 9
  29. 15
  30. 22
  31. 49
  32. 39
  33. 10
  34. 11
  35. 8
  36. 3
  37. 14
  38. 6
  39. 30
  40. 12

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