Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 467 · 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 8 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
2. 2.The length of a rectangle is 11 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
3. 3.A father is 12 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?
4. 4.Solve: 4t + 6 = t + 9. What is t?
5. 5.The sum of four consecutive whole numbers is 218. What is the smallest of them?
6. 6.Solve: 5x + 8 = 3x + 20. What is x?
7. 7.The sum of three consecutive whole numbers is 54. What is the largest of them?
8. 8.The sum of two consecutive whole numbers is 31. What is the largest of them?
9. 9.Solve: 4m + 2 = 2m + 32. What is m?
10. 10.Solve: 5t + 20 = 2t + 53. What is t?
11. 11.Solve: y/3 + y/6 = 12. What is y?
12. 12.Solve: 6(m − 2) = 2m + 36. What is m?
13. 13.Solve: 7t + 20 = 4t + 50. What is t?
14. 14.The length of a rectangle is 2 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
15. 15.Solve: 6(p − 2) = 4p + 24. What is p?
16. 16.A father is 13 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
17. 17.A father is 13 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
18. 18.The sum of four consecutive whole numbers is 74. What is the largest of them?
19. 19.Solve: 3(p − 2) = 2p + 2. What is p?
20. 20.Solve: 4(t − 2) = 3t + 2. What is t?
21. 21.The length of a rectangle is 6 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
22. 22.Solve: t/3 + t/2 = 5. What is t?
23. 23.The sum of three consecutive whole numbers is 48. What is the smallest of them?
24. 24.Solve: 7y + 7 = 4y + 22. What is y?
25. 25.Solve: 3(t − 4) = t + 14. What is t?
26. 26.A father is 14 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?
27. 27.A father is 24 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
28. 28.Solve: 4(y − 3) = y + 6. What is y?
29. 29.Solve: 9y + 3 = 8y + 13. What is y?
30. 30.A father is 8 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?
31. 31.Solve: p/5 + p/6 = 44. What is p?
32. 32.The length of a rectangle is 1 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
33. 33.Solve: 4(t − 5) = t + 28. What is t?
34. 34.The sum of four consecutive whole numbers is 230. What is the largest of them?
35. 35.Solve: 7m + 3 = m + 15. What is m?
36. 36.A father is 9 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
37. 37.Solve: 6(t − 4) = 3t + 9. What is t?
38. 38.The sum of four consecutive whole numbers is 210. What is the smallest of them?
39. 39.Solve: 5t + 12 = 2t + 18. What is t?
40. 40.Solve: 3(p − 5) = p + 11. What is p?

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