Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 659 · 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: y/5 + y/2 = 14. What is y?
2. 2.Solve: 6n + 13 = 2n + 65. What is n?
3. 3.A father is 20 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?
4. 4.The sum of four consecutive whole numbers is 238. What is the smallest of them?
5. 5.The length of a rectangle is 7 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
6. 6.Solve: 8n + 17 = 5n + 23. What is n?
7. 7.Solve: 3(t − 1) = 2t + 13. What is t?
8. 8.Solve: 9x + 19 = 3x + 109. What is x?
9. 9.Solve: t/3 + t/5 = 48. What is t?
10. 10.Solve: p/2 + p/6 = 24. What is p?
11. 11.Solve: 5n + 15 = 4n + 23. What is n?
12. 12.The length of a rectangle is 12 cm more than its width. Its perimeter is 136 cm. What is its width (in cm)?
13. 13.Solve: 6(n − 4) = 4n + 4. What is n?
14. 14.The sum of three consecutive whole numbers is 132. What is the largest of them?
15. 15.Solve: 8n + 7 = 4n + 31. What is n?
16. 16.A father is 9 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
17. 17.Solve: p/2 + p/4 = 6. What is p?
18. 18.The length of a rectangle is 14 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
19. 19.Solve: 6x + 11 = 5x + 16. What is x?
20. 20.Solve: 5(y − 2) = 2y + 5. What is y?
21. 21.Solve: n/5 + n/2 = 7. What is n?
22. 22.Solve: 5y + 1 = y + 45. What is y?
23. 23.The length of a rectangle is 1 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
24. 24.A father is 10 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
25. 25.Solve: t/6 + t/2 = 32. What is t?
26. 26.Solve: 6t + 14 = 4t + 16. What is t?
27. 27.Solve: 4(x − 1) = x + 29. What is x?
28. 28.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?
29. 29.The length of a rectangle is 13 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
30. 30.Solve: 4n + 5 = 3n + 19. What is n?
31. 31.A father is 18 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?
32. 32.The length of a rectangle is 4 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
33. 33.Solve: 9n + 18 = 2n + 25. What is n?
34. 34.The sum of three consecutive whole numbers is 180. What is the largest of them?
35. 35.A father is 57 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?
36. 36.A father is 15 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
37. 37.Solve: 6x + 7 = 2x + 15. What is x?
38. 38.A father is 12 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
39. 39.Solve: 6p + 1 = p + 31. What is p?
40. 40.A father is 27 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?

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