Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 48 · 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.Solve: 4n + 1 = 2n + 21. What is n?
2. 2.Solve: 5y + 18 = y + 62. What is y?
3. 3.Solve: 3(y − 5) = y + 23. What is y?
4. 4.Solve: 8y + 17 = 2y + 53. What is y?
5. 5.The sum of two consecutive whole numbers is 19. What is the largest of them?
6. 6.The sum of four consecutive whole numbers is 198. What is the largest of them?
7. 7.The length of a rectangle is 7 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
8. 8.The sum of two consecutive whole numbers is 93. What is the smallest of them?
9. 9.Solve: 5(p − 4) = 2p + 19. What is p?
10. 10.The length of a rectangle is 4 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
11. 11.Solve: x/6 + x/5 = 66. What is x?
12. 12.A father is 45 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
13. 13.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?
14. 14.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
15. 15.A father is 20 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
16. 16.Solve: p/2 + p/6 = 12. What is p?
17. 17.The length of a rectangle is 14 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
18. 18.Solve: n/4 + n/2 = 18. What is n?
19. 19.The sum of three consecutive whole numbers is 117. What is the largest of them?
20. 20.A father is 30 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?
21. 21.The length of a rectangle is 3 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
22. 22.The sum of three consecutive whole numbers is 165. What is the smallest of them?
23. 23.The sum of three consecutive whole numbers is 120. What is the smallest of them?
24. 24.Solve: 3p + 1 = 2p + 7. What is p?
25. 25.The length of a rectangle is 8 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
26. 26.Solve: 3p + 18 = p + 38. What is p?
27. 27.The length of a rectangle is 7 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
28. 28.A father is 8 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
29. 29.Solve: 5x + 9 = 2x + 21. What is x?
30. 30.Solve: 5(n − 2) = 3n + 8. What is n?
31. 31.Solve: 3(t − 5) = t + 21. What is t?
32. 32.The length of a rectangle is 3 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
33. 33.Solve: 4(n − 1) = 2n + 16. What is n?
34. 34.The sum of two consecutive whole numbers is 17. What is the smallest of them?
35. 35.The length of a rectangle is 11 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
36. 36.Solve: n/2 + n/6 = 8. What is n?
37. 37.Solve: 6(t − 2) = 3t + 30. What is t?
38. 38.Solve: 3(n − 4) = n + 6. What is n?
39. 39.The length of a rectangle is 7 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
40. 40.Solve: 3x + 12 = 2x + 16. What is x?

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