Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 550 · 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: 5(p − 1) = 2p + 16. What is p?
2. 2.The length of a rectangle is 4 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
3. 3.A father is 11 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
4. 4.Solve: 3x + 7 = x + 19. What is x?
5. 5.A father is 28 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?
6. 6.A father is 42 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?
7. 7.Solve: 6m + 16 = 3m + 28. What is m?
8. 8.Solve: 7n + 13 = 4n + 49. What is n?
9. 9.The sum of four consecutive whole numbers is 38. What is the largest of them?
10. 10.Solve: 7t + 14 = 2t + 54. What is t?
11. 11.Solve: 7p + 8 = p + 38. What is p?
12. 12.Solve: 5(n − 5) = 4n + 8. What is n?
13. 13.Solve: 8n + 1 = 2n + 91. What is n?
14. 14.Solve: 9t + 6 = t + 22. What is t?
15. 15.The sum of four consecutive whole numbers is 94. What is the largest of them?
16. 16.The length of a rectangle is 13 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
17. 17.Solve: 6(p − 1) = 5p + 9. What is p?
18. 18.The length of a rectangle is 8 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
19. 19.The length of a rectangle is 14 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
20. 20.The length of a rectangle is 5 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
21. 21.Solve: 4(y − 3) = 2y + 16. What is y?
22. 22.Solve: n/3 + n/6 = 6. What is n?
23. 23.Solve: 7t + 6 = 2t + 71. What is t?
24. 24.The sum of four consecutive whole numbers is 182. What is the smallest of them?
25. 25.A father is 13 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
26. 26.A father is 10 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
27. 27.The sum of three consecutive whole numbers is 108. What is the largest of them?
28. 28.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?
29. 29.The sum of two consecutive whole numbers is 83. What is the smallest of them?
30. 30.A father is 19 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
31. 31.Solve: t/2 + t/5 = 7. What is t?
32. 32.Solve: n/6 + n/5 = 55. What is n?
33. 33.Solve: 4y + 15 = 3y + 24. What is y?
34. 34.The sum of two consecutive whole numbers is 51. What is the smallest of them?
35. 35.Solve: 3t + 13 = t + 17. What is t?
36. 36.The sum of four consecutive whole numbers is 206. What is the largest of them?
37. 37.Solve: 6(y − 2) = y + 63. What is y?
38. 38.The length of a rectangle is 10 cm more than its width. Its perimeter is 140 cm. What is its width (in cm)?
39. 39.A father is 21 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?
40. 40.The sum of three consecutive whole numbers is 18. What is the smallest of them?

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