Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 232 · 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 11 years older than his son. In 6 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 5 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
3. 3.Solve: 4(x − 4) = x + 20. What is x?
4. 4.Solve: 6(n − 3) = 5n + 2. What is n?
5. 5.Solve: 9t + 11 = 8t + 13. What is t?
6. 6.Solve: 6(x − 4) = 5x + 3. What is x?
7. 7.The sum of two consecutive whole numbers is 23. What is the smallest of them?
8. 8.Solve: 3(m − 2) = 2m + 5. What is m?
9. 9.Solve: 5(x − 1) = 4x + 10. What is x?
10. 10.A father is 17 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
11. 11.The length of a rectangle is 9 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
12. 12.A father is 11 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
13. 13.A father is 18 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
14. 14.The length of a rectangle is 11 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
15. 15.The length of a rectangle is 4 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
16. 16.The sum of three consecutive whole numbers is 177. What is the largest of them?
17. 17.Solve: 3y + 15 = y + 19. What is y?
18. 18.Solve: n/4 + n/6 = 15. What is n?
19. 19.The sum of four consecutive whole numbers is 58. What is the smallest of them?
20. 20.Solve: 9m + 11 = 6m + 38. What is m?
21. 21.Solve: 8x + 12 = 4x + 44. What is x?
22. 22.The sum of two consecutive whole numbers is 55. What is the smallest of them?
23. 23.A father is 18 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
24. 24.Solve: 6y + 10 = 3y + 37. What is y?
25. 25.Solve: n/4 + n/5 = 63. What is n?
26. 26.Solve: x/2 + x/3 = 5. What is x?
27. 27.A father is 42 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?
28. 28.The sum of two consecutive whole numbers is 103. What is the smallest of them?
29. 29.Solve: 5(t − 1) = 3t + 3. What is t?
30. 30.The sum of two consecutive whole numbers is 105. What is the smallest of them?
31. 31.The length of a rectangle is 5 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
32. 32.The length of a rectangle is 9 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
33. 33.A father is 10 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
34. 34.Solve: 6(n − 3) = n + 27. What is n?
35. 35.Solve: 6(x − 4) = 5x + 9. What is x?
36. 36.Solve: n/3 + n/2 = 15. What is n?
37. 37.A father is 21 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?
38. 38.Solve: 3(p − 3) = 2p + 12. What is p?
39. 39.The length of a rectangle is 6 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
40. 40.Solve: 9n + 12 = 7n + 36. What is n?

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