Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 144 · 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 33 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?
2. 2.Solve: 5x + 17 = x + 49. What is x?
3. 3.The length of a rectangle is 5 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
4. 4.Solve: t/4 + t/6 = 15. What is t?
5. 5.Solve: 9m + 4 = 5m + 16. What is m?
6. 6.The sum of four consecutive whole numbers is 62. What is the smallest of them?
7. 7.The sum of four consecutive whole numbers is 54. What is the smallest of them?
8. 8.Solve: 3(y − 1) = 2y + 12. What is y?
9. 9.Solve: 6(p − 1) = 4p + 8. What is p?
10. 10.The sum of three consecutive whole numbers is 90. What is the largest of them?
11. 11.The sum of two consecutive whole numbers is 61. What is the smallest of them?
12. 12.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?
13. 13.Solve: 6(n − 1) = 4n + 12. What is n?
14. 14.The sum of two consecutive whole numbers is 15. What is the largest of them?
15. 15.The sum of two consecutive whole numbers is 31. What is the largest of them?
16. 16.The sum of four consecutive whole numbers is 30. What is the smallest of them?
17. 17.Solve: m/5 + m/4 = 9. What is m?
18. 18.The length of a rectangle is 9 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
19. 19.A father is 30 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?
20. 20.Solve: 4y + 9 = 3y + 10. What is y?
21. 21.Solve: 5(m − 1) = 3m + 15. What is m?
22. 22.A father is 14 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
23. 23.Solve: 7x + 8 = 3x + 20. What is x?
24. 24.The length of a rectangle is 4 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
25. 25.Solve: 4y + 20 = 2y + 32. What is y?
26. 26.Solve: 6(y − 2) = 5y + 6. What is y?
27. 27.Solve: 4(n − 3) = n + 36. What is n?
28. 28.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?
29. 29.A father is 51 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?
30. 30.Solve: 8y + 4 = 2y + 88. What is y?
31. 31.Solve: y/2 + y/3 = 15. What is y?
32. 32.Solve: 4(x − 5) = 2x + 24. What is x?
33. 33.A father is 27 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
34. 34.The sum of four consecutive whole numbers is 78. What is the smallest of them?
35. 35.The length of a rectangle is 8 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
36. 36.The length of a rectangle is 3 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
37. 37.Solve: 3(t − 1) = t + 13. What is t?
38. 38.Solve: 6m + 17 = 4m + 37. What is m?
39. 39.Solve: 4n + 16 = 3n + 19. What is n?
40. 40.Solve: m/4 + m/2 = 12. What is m?

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