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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 501 · 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 15 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
  2. 2.A father is 13 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  3. 3.The length of a rectangle is 2 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
  4. 4.The sum of four consecutive whole numbers is 114. What is the smallest of them?
  5. 5.Solve: 5m + 13 = m + 21. What is m?
  6. 6.Solve: 3(y − 1) = y + 5. What is y?
  7. 7.The length of a rectangle is 1 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
  8. 8.Solve: 8x + 19 = 2x + 97. What is x?
  9. 9.Solve: y/4 + y/2 = 3. What is y?
  10. 10.Solve: 9t + 11 = 4t + 61. What is t?
  11. 11.Solve: y/3 + y/2 = 25. What is y?
  12. 12.Solve: 6(x − 4) = 2x + 4. What is x?
  13. 13.A father is 42 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  14. 14.Solve: 5(n − 1) = 3n + 23. What is n?
  15. 15.The length of a rectangle is 12 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  16. 16.Solve: 5(t − 5) = 4t + 12. What is t?
  17. 17.Solve: 4y + 1 = y + 7. What is y?
  18. 18.The sum of two consecutive whole numbers is 25. What is the smallest of them?
  19. 19.A father is 16 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
  20. 20.Solve: x/4 + x/2 = 3. What is x?
  21. 21.The length of a rectangle is 6 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
  22. 22.Solve: 6p + 14 = p + 69. What is p?
  23. 23.Solve: p/3 + p/2 = 20. What is p?
  24. 24.The sum of two consecutive whole numbers is 109. What is the smallest of them?
  25. 25.Solve: x/2 + x/6 = 20. What is x?
  26. 26.Solve: 6(m − 3) = 2m + 34. What is m?
  27. 27.A father is 26 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?
  28. 28.Solve: x/6 + x/2 = 20. What is x?
  29. 29.A father is 12 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  30. 30.The length of a rectangle is 5 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  31. 31.Solve: 9p + 8 = 5p + 68. What is p?
  32. 32.Solve: 3(m − 1) = 2m + 3. What is m?
  33. 33.The length of a rectangle is 10 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  34. 34.The length of a rectangle is 11 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
  35. 35.Solve: p/4 + p/2 = 12. What is p?
  36. 36.Solve: 4p + 12 = p + 36. What is p?
  37. 37.Solve: t/2 + t/3 = 25. What is t?
  38. 38.Solve: 8m + 18 = 2m + 36. What is m?
  39. 39.Solve: 6n + 7 = 5n + 16. What is n?
  40. 40.The sum of four consecutive whole numbers is 134. What is the largest of them?

Answer key

  1. 15
  2. 9
  3. 19
  4. 27
  5. 2
  6. 4
  7. 9
  8. 13
  9. 4
  10. 10
  11. 30
  12. 7
  13. 9
  14. 14
  15. 8
  16. 37
  17. 2
  18. 12
  19. 8
  20. 4
  21. 29
  22. 11
  23. 24
  24. 54
  25. 30
  26. 13
  27. 11
  28. 30
  29. 10
  30. 6
  31. 15
  32. 6
  33. 7
  34. 28
  35. 16
  36. 8
  37. 30
  38. 3
  39. 9
  40. 35

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