Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 875 · 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 27 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?
2. 2.A father is 14 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
3. 3.A father is 12 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?
4. 4.Solve: 3(x − 1) = 2x + 5. What is x?
5. 5.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?
6. 6.A father is 7 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
7. 7.The length of a rectangle is 4 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
8. 8.A father is 8 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
9. 9.The sum of four consecutive whole numbers is 82. What is the smallest of them?
10. 10.Solve: p/6 + p/2 = 12. What is p?
11. 11.The length of a rectangle is 3 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
12. 12.Solve: m/2 + m/5 = 35. What is m?
13. 13.The length of a rectangle is 1 cm more than its width. Its perimeter is 82 cm. What is its width (in cm)?
14. 14.Solve: 4(y − 3) = 2y + 18. What is y?
15. 15.Solve: 6(n − 4) = 5n + 2. What is n?
16. 16.A father is 36 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?
17. 17.Solve: 6(t − 3) = 5t + 8. What is t?
18. 18.The length of a rectangle is 7 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
19. 19.The sum of three consecutive whole numbers is 102. What is the largest of them?
20. 20.Solve: 6x + 9 = x + 64. What is x?
21. 21.Solve: 7y + 2 = y + 44. What is y?
22. 22.Solve: 4(y − 2) = y + 37. What is y?
23. 23.The length of a rectangle is 6 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
24. 24.A father is 18 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?
25. 25.The sum of three consecutive whole numbers is 24. What is the largest of them?
26. 26.Solve: 9p + 1 = p + 33. What is p?
27. 27.Solve: 3t + 15 = t + 29. What is t?
28. 28.Solve: 8x + 2 = 3x + 67. What is x?
29. 29.Solve: 3(y − 1) = 2y + 9. What is y?
30. 30.Solve: 8n + 18 = 5n + 63. What is n?
31. 31.Solve: 3n + 8 = 2n + 13. What is n?
32. 32.The length of a rectangle is 13 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
33. 33.Solve: 4(p − 4) = 2p + 12. What is p?
34. 34.Solve: 3t + 11 = t + 15. What is t?
35. 35.Solve: t/5 + t/2 = 7. What is t?
36. 36.The length of a rectangle is 10 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
37. 37.The sum of two consecutive whole numbers is 89. What is the largest of them?
38. 38.Solve: p/2 + p/6 = 8. What is p?
39. 39.The length of a rectangle is 13 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
40. 40.A father is 54 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?

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