Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 67 · 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 24 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?
2. 2.Solve: 3(t − 1) = 2t + 4. What is t?
3. 3.The sum of two consecutive whole numbers is 15. What is the smallest of them?
4. 4.The length of a rectangle is 15 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
5. 5.Solve: 6(m − 1) = 4m + 2. What is m?
6. 6.Solve: 4p + 4 = p + 25. What is p?
7. 7.Solve: p/6 + p/5 = 44. What is p?
8. 8.The length of a rectangle is 8 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
9. 9.The length of a rectangle is 13 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
10. 10.The sum of four consecutive whole numbers is 170. What is the largest of them?
11. 11.The length of a rectangle is 7 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
12. 12.A father is 36 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?
13. 13.Solve: p/3 + p/4 = 56. What is p?
14. 14.Solve: 4(m − 2) = m + 19. What is m?
15. 15.Solve: 3(y − 1) = 2y + 6. What is y?
16. 16.The sum of three consecutive whole numbers is 18. What is the smallest of them?
17. 17.Solve: 4(n − 3) = 2n + 10. What is n?
18. 18.Solve: 6m + 6 = 5m + 17. What is m?
19. 19.Solve: 4(x − 5) = 3x + 10. What is x?
20. 20.Solve: x/4 + x/5 = 45. What is x?
21. 21.Solve: 3p + 20 = p + 38. What is p?
22. 22.A father is 10 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?
23. 23.Solve: t/5 + t/2 = 28. What is t?
24. 24.A father is 22 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?
25. 25.Solve: 3x + 15 = x + 41. What is x?
26. 26.The sum of four consecutive whole numbers is 202. What is the largest of them?
27. 27.Solve: 4(x − 5) = 2x + 4. What is x?
28. 28.The sum of three consecutive whole numbers is 129. What is the smallest of them?
29. 29.A father is 13 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
30. 30.The sum of four consecutive whole numbers is 90. What is the smallest of them?
31. 31.Solve: n/5 + n/6 = 66. What is n?
32. 32.Solve: 4(y − 4) = y + 14. What is y?
33. 33.A father is 48 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?
34. 34.The sum of two consecutive whole numbers is 29. What is the smallest of them?
35. 35.The length of a rectangle is 12 cm more than its width. Its perimeter is 144 cm. What is its width (in cm)?
36. 36.The length of a rectangle is 2 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
37. 37.The length of a rectangle is 8 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
38. 38.Solve: 3p + 14 = p + 40. What is p?
39. 39.The sum of two consecutive whole numbers is 121. What is the largest of them?
40. 40.Solve: 7x + 3 = 2x + 63. What is x?

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