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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 66 · 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 1 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
  2. 2.Solve: 6n + 9 = n + 29. What is n?
  3. 3.The length of a rectangle is 3 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  4. 4.The length of a rectangle is 5 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  5. 5.The length of a rectangle is 6 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
  6. 6.Solve: m/4 + m/5 = 18. What is m?
  7. 7.Solve: x/2 + x/4 = 6. What is x?
  8. 8.Solve: p/3 + p/5 = 40. What is p?
  9. 9.The sum of two consecutive whole numbers is 17. What is the largest of them?
  10. 10.Solve: y/3 + y/5 = 40. What is y?
  11. 11.Solve: y/2 + y/3 = 30. What is y?
  12. 12.A father is 22 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?
  13. 13.The sum of two consecutive whole numbers is 73. What is the largest of them?
  14. 14.The length of a rectangle is 6 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  15. 15.The length of a rectangle is 5 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
  16. 16.The sum of four consecutive whole numbers is 110. What is the smallest of them?
  17. 17.The length of a rectangle is 2 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  18. 18.Solve: 4m + 13 = 2m + 29. What is m?
  19. 19.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?
  20. 20.The length of a rectangle is 1 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
  21. 21.Solve: 6x + 11 = 5x + 13. What is x?
  22. 22.The length of a rectangle is 1 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
  23. 23.Solve: 5(n − 5) = n + 47. What is n?
  24. 24.A father is 18 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?
  25. 25.A father is 16 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
  26. 26.Solve: n/4 + n/2 = 21. What is n?
  27. 27.Solve: 6(y − 3) = 3y + 6. What is y?
  28. 28.The sum of four consecutive whole numbers is 42. What is the smallest of them?
  29. 29.The sum of four consecutive whole numbers is 166. What is the smallest of them?
  30. 30.A father is 27 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
  31. 31.The sum of four consecutive whole numbers is 234. What is the largest of them?
  32. 32.The sum of three consecutive whole numbers is 183. What is the largest of them?
  33. 33.Solve: m/4 + m/6 = 5. What is m?
  34. 34.Solve: 3(n − 3) = 2n + 4. What is n?
  35. 35.A father is 17 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  36. 36.Solve: x/3 + x/5 = 8. What is x?
  37. 37.Solve: 5(x − 3) = x + 37. What is x?
  38. 38.Solve: 6(m − 2) = m + 23. What is m?
  39. 39.The length of a rectangle is 6 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
  40. 40.A father is 27 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?

Answer key

  1. 23
  2. 4
  3. 16
  4. 10
  5. 7
  6. 40
  7. 8
  8. 75
  9. 9
  10. 75
  11. 36
  12. 10
  13. 37
  14. 28
  15. 4
  16. 26
  17. 18
  18. 8
  19. 5
  20. 28
  21. 2
  22. 24
  23. 18
  24. 6
  25. 6
  26. 28
  27. 8
  28. 9
  29. 40
  30. 7
  31. 60
  32. 62
  33. 12
  34. 13
  35. 10
  36. 15
  37. 13
  38. 7
  39. 19
  40. 3

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