Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 2 · 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.The length of a rectangle is 9 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
2. 2.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?
3. 3.A father is 39 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
4. 4.A father is 30 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?
5. 5.The sum of two consecutive whole numbers is 59. What is the smallest of them?
6. 6.Solve: 9m + 6 = 3m + 90. What is m?
7. 7.Solve: 3(t − 3) = 2t + 3. What is t?
8. 8.Solve: 9t + 2 = 3t + 38. What is t?
9. 9.The sum of four consecutive whole numbers is 158. What is the smallest of them?
10. 10.A father is 32 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?
11. 11.The length of a rectangle is 12 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
12. 12.Solve: 9t + 6 = 7t + 12. What is t?
13. 13.Solve: 4(x − 1) = 3x + 13. What is x?
14. 14.The sum of two consecutive whole numbers is 31. What is the smallest of them?
15. 15.Solve: 3n + 5 = n + 19. What is n?
16. 16.The sum of two consecutive whole numbers is 97. What is the smallest of them?
17. 17.The length of a rectangle is 13 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
18. 18.Solve: 3m + 18 = m + 36. What is m?
19. 19.A father is 14 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
20. 20.The length of a rectangle is 15 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
21. 21.Solve: x/6 + x/2 = 20. What is x?
22. 22.The length of a rectangle is 11 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
23. 23.The length of a rectangle is 4 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
24. 24.The sum of four consecutive whole numbers is 42. What is the smallest of them?
25. 25.Solve: 4(y − 1) = y + 29. What is y?
26. 26.The sum of four consecutive whole numbers is 234. What is the largest of them?
27. 27.Solve: p/6 + p/4 = 5. What is p?
28. 28.The length of a rectangle is 8 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
29. 29.Solve: x/3 + x/4 = 28. What is x?
30. 30.A father is 24 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?
31. 31.The length of a rectangle is 15 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
32. 32.A father is 20 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: 6(y − 3) = 5y + 12. What is y?
34. 34.Solve: p/3 + p/4 = 28. What is p?
35. 35.The length of a rectangle is 3 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
36. 36.Solve: 3t + 4 = 2t + 18. What is t?
37. 37.The sum of two consecutive whole numbers is 61. What is the smallest of them?
38. 38.A father is 30 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
39. 39.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?
40. 40.Solve: y/4 + y/5 = 72. What is y?

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