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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 573 · 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.Solve: 5(x − 2) = x + 22. What is x?
  2. 2.The length of a rectangle is 1 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
  3. 3.The sum of four consecutive whole numbers is 82. What is the smallest of them?
  4. 4.Solve: x/4 + x/6 = 5. What is x?
  5. 5.The length of a rectangle is 2 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
  6. 6.Solve: m/6 + m/4 = 15. What is m?
  7. 7.The length of a rectangle is 1 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  8. 8.Solve: 3(t − 4) = 2t + 11. What is t?
  9. 9.Solve: 5(n − 3) = 4n + 10. What is n?
  10. 10.Solve: 3n + 13 = 2n + 21. What is n?
  11. 11.Solve: x/3 + x/2 = 20. What is x?
  12. 12.Solve: 3t + 4 = t + 30. What is t?
  13. 13.The length of a rectangle is 9 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
  14. 14.The length of a rectangle is 14 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  15. 15.Solve: 3(m − 4) = m + 20. What is m?
  16. 16.Solve: 3(t − 2) = 2t + 7. What is t?
  17. 17.The sum of two consecutive whole numbers is 29. What is the smallest of them?
  18. 18.A father is 20 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?
  19. 19.Solve: 6n + 18 = 3n + 51. What is n?
  20. 20.The length of a rectangle is 2 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
  21. 21.Solve: t/6 + t/5 = 66. What is t?
  22. 22.Solve: 3p + 5 = 2p + 12. What is p?
  23. 23.Solve: 9t + 6 = 7t + 8. What is t?
  24. 24.A father is 21 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?
  25. 25.Solve: 8y + 2 = 2y + 56. What is y?
  26. 26.Solve: 3(p − 3) = p + 21. What is p?
  27. 27.A father is 45 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?
  28. 28.The sum of two consecutive whole numbers is 75. What is the smallest of them?
  29. 29.Solve: 3(p − 3) = 2p + 8. What is p?
  30. 30.The sum of two consecutive whole numbers is 31. What is the largest of them?
  31. 31.Solve: 3x + 13 = 2x + 14. What is x?
  32. 32.The sum of two consecutive whole numbers is 79. What is the smallest of them?
  33. 33.Solve: 3x + 3 = 2x + 5. What is x?
  34. 34.Solve: 5(n − 2) = n + 38. What is n?
  35. 35.The sum of four consecutive whole numbers is 26. What is the largest of them?
  36. 36.The sum of two consecutive whole numbers is 101. What is the smallest of them?
  37. 37.A father is 40 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?
  38. 38.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?
  39. 39.Solve: n/2 + n/4 = 6. What is n?
  40. 40.A father is 10 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?

Answer key

  1. 8
  2. 4
  3. 19
  4. 12
  5. 12
  6. 36
  7. 17
  8. 23
  9. 25
  10. 8
  11. 24
  12. 13
  13. 6
  14. 24
  15. 16
  16. 13
  17. 14
  18. 5
  19. 11
  20. 30
  21. 180
  22. 7
  23. 1
  24. 4
  25. 9
  26. 15
  27. 8
  28. 37
  29. 17
  30. 16
  31. 1
  32. 39
  33. 2
  34. 12
  35. 8
  36. 50
  37. 12
  38. 2
  39. 8
  40. 4

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