Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 561 · 40 sums

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.

1. 1.A father is 14 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
2. 2.The length of a rectangle is 6 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
3. 3.A father is 16 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
4. 4.Solve: 6(m − 1) = 5m + 13. What is m?
5. 5.Solve: 5(x − 2) = 2x + 17. What is x?
6. 6.Solve: 3(n − 2) = n + 24. What is n?
7. 7.A father is 36 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?
8. 8.The length of a rectangle is 8 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
9. 9.The length of a rectangle is 14 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
10. 10.Solve: 7x + 20 = 5x + 50. What is x?
11. 11.The length of a rectangle is 12 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
12. 12.The sum of four consecutive whole numbers is 30. What is the smallest of them?
13. 13.Solve: 9p + 20 = 3p + 74. What is p?
14. 14.The sum of two consecutive whole numbers is 45. What is the smallest of them?
15. 15.The length of a rectangle is 12 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
16. 16.Solve: 9n + 11 = 3n + 89. What is n?
17. 17.Solve: 6m + 1 = 2m + 53. What is m?
18. 18.Solve: 4y + 4 = 2y + 14. What is y?
19. 19.A father is 32 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?
20. 20.A father is 9 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
21. 21.A father is 28 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?
22. 22.Solve: 7x + 2 = 6x + 3. What is x?
23. 23.Solve: 8t + 18 = 3t + 23. What is t?
24. 24.Solve: 3(n − 1) = n + 7. What is n?
25. 25.Solve: 3(y − 2) = y + 4. What is y?
26. 26.Solve: 3(x − 1) = x + 17. What is x?
27. 27.The sum of four consecutive whole numbers is 162. What is the smallest of them?
28. 28.The sum of four consecutive whole numbers is 198. What is the smallest of them?
29. 29.A father is 8 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
30. 30.Solve: n/4 + n/5 = 9. What is n?
31. 31.Solve: 6(x − 2) = x + 3. What is x?
32. 32.Solve: p/4 + p/2 = 6. What is p?
33. 33.The length of a rectangle is 7 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
34. 34.Solve: 8t + 1 = 2t + 55. What is t?
35. 35.Solve: 9n + 7 = 6n + 40. What is n?
36. 36.A father is 36 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
37. 37.The sum of two consecutive whole numbers is 79. What is the smallest of them?
38. 38.Solve: 4(m − 3) = 3m + 3. What is m?
39. 39.The length of a rectangle is 2 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
40. 40.A father is 45 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?

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