Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 118 · 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.Solve: n/5 + n/6 = 33. What is n?
2. 2.A father is 20 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?
3. 3.Solve: 5x + 6 = x + 38. What is x?
4. 4.Solve: 9n + 6 = 4n + 76. What is n?
5. 5.Solve: x/5 + x/3 = 56. What is x?
6. 6.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?
7. 7.Solve: 4(p − 1) = 3p + 7. What is p?
8. 8.The length of a rectangle is 3 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
9. 9.A father is 9 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
10. 10.Solve: 6(t − 1) = 5t + 10. What is t?
11. 11.A father is 36 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?
12. 12.The length of a rectangle is 7 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
13. 13.A father is 7 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
14. 14.Solve: 4(x − 2) = 2x + 14. What is x?
15. 15.The length of a rectangle is 1 cm more than its width. Its perimeter is 10 cm. What is its width (in cm)?
16. 16.Solve: p/6 + p/3 = 24. What is p?
17. 17.Solve: n/6 + n/2 = 20. What is n?
18. 18.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
19. 19.Solve: 6(y − 1) = 2y + 22. What is y?
20. 20.The length of a rectangle is 4 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
21. 21.The sum of three consecutive whole numbers is 180. What is the smallest of them?
22. 22.Solve: 8y + 13 = 3y + 43. What is y?
23. 23.The sum of three consecutive whole numbers is 141. What is the smallest of them?
24. 24.Solve: 3(y − 4) = 2y + 13. What is y?
25. 25.Solve: 6y + 9 = 2y + 37. What is y?
26. 26.A father is 18 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?
27. 27.The sum of two consecutive whole numbers is 115. What is the largest of them?
28. 28.The sum of three consecutive whole numbers is 18. What is the largest of them?
29. 29.Solve: 3n + 5 = n + 7. What is n?
30. 30.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?
31. 31.The sum of three consecutive whole numbers is 177. What is the smallest of them?
32. 32.A father is 6 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
33. 33.A father is 30 years older than his son. In 3 years, the father will be three times as old as his son. How old is the son now?
34. 34.Solve: 5(y − 4) = 3y + 16. What is y?
35. 35.The length of a rectangle is 9 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
36. 36.A father is 19 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.The sum of three consecutive whole numbers is 72. What is the largest of them?
38. 38.Solve: 4(m − 4) = 2m + 18. What is m?
39. 39.Solve: 4(t − 4) = 3t + 6. What is t?
40. 40.The length of a rectangle is 11 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?

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