Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 222 · 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 16 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?
2. 2.The sum of four consecutive whole numbers is 134. What is the largest of them?
3. 3.Solve: 3(m − 3) = 2m + 10. What is m?
4. 4.The sum of two consecutive whole numbers is 29. What is the smallest of them?
5. 5.A father is 30 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?
6. 6.A father is 34 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
7. 7.The sum of four consecutive whole numbers is 74. What is the largest of them?
8. 8.The sum of four consecutive whole numbers is 50. What is the smallest of them?
9. 9.The length of a rectangle is 7 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
10. 10.Solve: x/2 + x/3 = 40. What is x?
11. 11.Solve: 3(n − 2) = 2n + 5. What is n?
12. 12.A father is 21 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?
13. 13.Solve: 9y + 10 = 8y + 23. What is y?
14. 14.Solve: 6(p − 5) = p + 50. What is p?
15. 15.A father is 30 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
16. 16.A father is 42 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?
17. 17.Solve: 3(y − 5) = y + 17. What is y?
18. 18.Solve: 9x + 3 = 4x + 38. What is x?
19. 19.A father is 21 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?
20. 20.Solve: 5(y − 1) = 3y + 3. What is y?
21. 21.A father is 24 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
22. 22.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?
23. 23.Solve: p/6 + p/4 = 20. What is p?
24. 24.The sum of three consecutive whole numbers is 48. What is the largest of them?
25. 25.Solve: 5(p − 1) = 4p + 4. What is p?
26. 26.The length of a rectangle is 2 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
27. 27.Solve: y/3 + y/2 = 25. What is y?
28. 28.Solve: 3(y − 4) = y + 18. What is y?
29. 29.The length of a rectangle is 2 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
30. 30.Solve: m/3 + m/5 = 48. What is m?
31. 31.The sum of three consecutive whole numbers is 63. What is the smallest of them?
32. 32.Solve: 8x + 11 = 2x + 41. What is x?
33. 33.Solve: t/4 + t/5 = 54. What is t?
34. 34.A father is 8 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
35. 35.The sum of four consecutive whole numbers is 150. What is the smallest of them?
36. 36.Solve: 8x + 13 = x + 69. What is x?
37. 37.Solve: y/6 + y/3 = 9. What is y?
38. 38.The length of a rectangle is 4 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
39. 39.The sum of four consecutive whole numbers is 214. What is the smallest of them?
40. 40.Solve: 5x + 13 = 2x + 19. What is x?

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