Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 568 · 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 24 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?
2. 2.Solve: 4(y − 4) = y + 20. What is y?
3. 3.The length of a rectangle is 2 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
4. 4.Solve: 6(p − 1) = 2p + 10. What is p?
5. 5.Solve: n/6 + n/2 = 12. What is n?
6. 6.Solve: 6(m − 4) = 2m + 48. What is m?
7. 7.The sum of two consecutive whole numbers is 21. What is the largest of them?
8. 8.Solve: 6t + 10 = 2t + 22. What is t?
9. 9.A father is 45 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?
10. 10.A father is 20 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
11. 11.Solve: m/3 + m/4 = 56. What is m?
12. 12.A father is 11 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
13. 13.A father is 24 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
14. 14.The sum of three consecutive whole numbers is 141. What is the largest of them?
15. 15.A father is 14 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
16. 16.Solve: 3(y − 3) = 2y + 9. What is y?
17. 17.The length of a rectangle is 10 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
18. 18.Solve: 9m + 10 = 5m + 62. What is m?
19. 19.The sum of four consecutive whole numbers is 226. What is the largest of them?
20. 20.Solve: 3(x − 3) = 2x + 2. What is x?
21. 21.The sum of three consecutive whole numbers is 180. What is the smallest of them?
22. 22.Solve: 5(n − 4) = 2n + 7. What is n?
23. 23.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?
24. 24.Solve: n/3 + n/2 = 35. What is n?
25. 25.Solve: 4(m − 1) = m + 17. What is m?
26. 26.Solve: 7x + 18 = 3x + 74. What is x?
27. 27.Solve: 5y + 8 = 4y + 11. What is y?
28. 28.A father is 15 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.A father is 7 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
30. 30.A father is 33 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?
31. 31.Solve: 3m + 16 = 2m + 26. What is m?
32. 32.The length of a rectangle is 4 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
33. 33.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
34. 34.A father is 30 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?
35. 35.The sum of two consecutive whole numbers is 119. What is the smallest of them?
36. 36.Solve: y/5 + y/6 = 55. What is y?
37. 37.The sum of three consecutive whole numbers is 84. What is the largest of them?
38. 38.The length of a rectangle is 12 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
39. 39.The sum of two consecutive whole numbers is 105. What is the largest of them?
40. 40.Solve: 4(t − 3) = 2t + 8. What is t?

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