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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 419 · 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 12 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
  2. 2.The length of a rectangle is 9 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
  3. 3.Solve: 4(t − 2) = t + 7. What is t?
  4. 4.A father is 33 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?
  5. 5.Solve: 5(n − 5) = 2n + 38. What is n?
  6. 6.The length of a rectangle is 10 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
  7. 7.Solve: 9p + 1 = 3p + 37. What is p?
  8. 8.The sum of four consecutive whole numbers is 114. What is the largest of them?
  9. 9.The length of a rectangle is 2 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  10. 10.Solve: n/4 + n/5 = 63. What is n?
  11. 11.Solve: m/2 + m/4 = 9. What is m?
  12. 12.The length of a rectangle is 4 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
  13. 13.The length of a rectangle is 3 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
  14. 14.Solve: x/5 + x/4 = 54. What is x?
  15. 15.Solve: 5(t − 2) = 4t + 1. What is t?
  16. 16.Solve: n/6 + n/5 = 11. What is n?
  17. 17.Solve: 3(x − 3) = 2x + 2. What is x?
  18. 18.Solve: 4t + 17 = 3t + 30. What is t?
  19. 19.Solve: 5(t − 3) = 3t + 23. What is t?
  20. 20.A father is 36 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
  21. 21.The sum of two consecutive whole numbers is 23. What is the largest of them?
  22. 22.Solve: 9x + 4 = 5x + 36. What is x?
  23. 23.The sum of three consecutive whole numbers is 159. What is the largest of them?
  24. 24.Solve: 6(p − 1) = 3p + 36. What is p?
  25. 25.Solve: 5(x − 5) = x + 23. What is x?
  26. 26.A father is 7 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
  27. 27.Solve: 6(n − 5) = 5n + 1. What is n?
  28. 28.Solve: p/2 + p/6 = 12. What is p?
  29. 29.Solve: 5n + 1 = n + 13. What is n?
  30. 30.Solve: 4(m − 1) = m + 14. What is m?
  31. 31.Solve: 4(x − 3) = x + 18. What is x?
  32. 32.Solve: y/6 + y/3 = 15. What is y?
  33. 33.The length of a rectangle is 13 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  34. 34.Solve: p/3 + p/6 = 6. What is p?
  35. 35.Solve: 5(t − 5) = 4t + 4. What is t?
  36. 36.The sum of three consecutive whole numbers is 162. What is the smallest of them?
  37. 37.The length of a rectangle is 1 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
  38. 38.A father is 39 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  39. 39.Solve: 6(y − 1) = 5y + 3. What is y?
  40. 40.Solve: 5(t − 1) = 2t + 34. What is t?

Answer key

  1. 19
  2. 4
  3. 5
  4. 9
  5. 21
  6. 7
  7. 6
  8. 30
  9. 28
  10. 140
  11. 12
  12. 24
  13. 30
  14. 120
  15. 11
  16. 30
  17. 11
  18. 13
  19. 19
  20. 10
  21. 12
  22. 8
  23. 54
  24. 14
  25. 12
  26. 5
  27. 31
  28. 18
  29. 3
  30. 6
  31. 10
  32. 30
  33. 4
  34. 12
  35. 29
  36. 53
  37. 15
  38. 12
  39. 9
  40. 13

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