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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 596 · 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: 5(t − 5) = t + 23. What is t?
  2. 2.Solve: 3m + 9 = 2m + 14. What is m?
  3. 3.Solve: 9x + 13 = 5x + 49. What is x?
  4. 4.Solve: 3(m − 3) = 2m + 13. What is m?
  5. 5.The length of a rectangle is 10 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
  6. 6.Solve: 6(t − 5) = 4t + 24. What is t?
  7. 7.Solve: n/2 + n/4 = 15. What is n?
  8. 8.Solve: m/2 + m/6 = 24. What is m?
  9. 9.The length of a rectangle is 12 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  10. 10.Solve: 3m + 18 = m + 40. What is m?
  11. 11.Solve: 4(y − 2) = y + 28. What is y?
  12. 12.Solve: 6(t − 1) = 2t + 14. What is t?
  13. 13.Solve: 7m + 19 = 5m + 25. What is m?
  14. 14.A father is 13 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  15. 15.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?
  16. 16.A father is 16 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  17. 17.Solve: y/3 + y/4 = 28. What is y?
  18. 18.The length of a rectangle is 15 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
  19. 19.The sum of four consecutive whole numbers is 186. What is the largest of them?
  20. 20.Solve: 7m + 1 = 3m + 45. What is m?
  21. 21.Solve: n/4 + n/2 = 3. What is n?
  22. 22.Solve: 5(t − 2) = 3t + 6. What is t?
  23. 23.Solve: 4(p − 1) = p + 8. What is p?
  24. 24.Solve: t/2 + t/4 = 12. What is t?
  25. 25.Solve: 6(y − 1) = y + 54. What is y?
  26. 26.The length of a rectangle is 5 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
  27. 27.Solve: 3p + 17 = p + 43. What is p?
  28. 28.The sum of three consecutive whole numbers is 144. What is the smallest of them?
  29. 29.Solve: p/4 + p/5 = 45. What is p?
  30. 30.Solve: 3(x − 1) = 2x + 11. What is x?
  31. 31.The sum of two consecutive whole numbers is 101. What is the largest of them?
  32. 32.A father is 32 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
  33. 33.Solve: 9p + 8 = 5p + 20. What is p?
  34. 34.A father is 4 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
  35. 35.The sum of two consecutive whole numbers is 91. What is the smallest of them?
  36. 36.The length of a rectangle is 4 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  37. 37.Solve: 5m + 3 = m + 47. What is m?
  38. 38.Solve: 7t + 5 = 5t + 31. What is t?
  39. 39.Solve: m/2 + m/6 = 28. What is m?
  40. 40.Solve: m/3 + m/5 = 8. What is m?

Answer key

  1. 12
  2. 5
  3. 9
  4. 22
  5. 19
  6. 27
  7. 20
  8. 36
  9. 7
  10. 11
  11. 12
  12. 5
  13. 3
  14. 6
  15. 6
  16. 11
  17. 48
  18. 9
  19. 48
  20. 11
  21. 4
  22. 8
  23. 4
  24. 16
  25. 12
  26. 5
  27. 13
  28. 47
  29. 100
  30. 14
  31. 51
  32. 10
  33. 3
  34. 3
  35. 45
  36. 12
  37. 11
  38. 13
  39. 42
  40. 15

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