Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 782 · 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 32 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?
2. 2.Solve: t/4 + t/2 = 24. What is t?
3. 3.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?
4. 4.Solve: 3(n − 2) = n + 6. What is n?
5. 5.Solve: 5t + 2 = t + 46. What is t?
6. 6.The sum of three consecutive whole numbers is 21. What is the smallest of them?
7. 7.Solve: 5(p − 4) = 4p + 4. What is p?
8. 8.A father is 16 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?
9. 9.The length of a rectangle is 14 cm more than its width. Its perimeter is 64 cm. What is its width (in cm)?
10. 10.The sum of four consecutive whole numbers is 166. What is the largest of them?
11. 11.Solve: 5x + 10 = 4x + 14. What is x?
12. 12.The sum of two consecutive whole numbers is 103. What is the largest of them?
13. 13.Solve: 7n + 12 = 6n + 19. What is n?
14. 14.Solve: 4p + 3 = 3p + 7. What is p?
15. 15.The length of a rectangle is 11 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
16. 16.Solve: 8x + 19 = x + 33. What is x?
17. 17.Solve: 6(t − 2) = 2t + 12. What is t?
18. 18.Solve: 3(p − 3) = p + 1. What is p?
19. 19.The sum of three consecutive whole numbers is 24. What is the smallest of them?
20. 20.Solve: 5p + 1 = p + 5. What is p?
21. 21.The length of a rectangle is 11 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
22. 22.A father is 33 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
23. 23.Solve: 4(n − 5) = 2n + 26. What is n?
24. 24.Solve: 4(p − 5) = 3p + 8. What is p?
25. 25.Solve: 4n + 5 = n + 11. What is n?
26. 26.The sum of four consecutive whole numbers is 178. What is the smallest of them?
27. 27.The sum of three consecutive whole numbers is 150. What is the largest of them?
28. 28.A father is 18 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?
29. 29.Solve: n/2 + n/5 = 49. What is n?
30. 30.Solve: 4(p − 2) = 2p + 6. What is p?
31. 31.A father is 39 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?
32. 32.Solve: 6m + 6 = 5m + 7. What is m?
33. 33.The length of a rectangle is 1 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
34. 34.A father is 18 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?
35. 35.A father is 15 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
36. 36.Solve: 4(t − 1) = t + 2. What is t?
37. 37.A father is 9 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
38. 38.The sum of three consecutive whole numbers is 78. What is the smallest of them?
39. 39.A father is 26 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?
40. 40.A father is 18 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?

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