Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 63 · 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 15 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
2. 2.Solve: n/3 + n/4 = 56. What is n?
3. 3.Solve: 3(t − 5) = t + 7. What is t?
4. 4.The sum of four consecutive whole numbers is 50. What is the smallest of them?
5. 5.The sum of two consecutive whole numbers is 15. What is the smallest of them?
6. 6.Solve: 6(y − 3) = 5y + 13. What is y?
7. 7.A father is 8 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
8. 8.Solve: m/4 + m/3 = 56. What is m?
9. 9.Solve: 4(x − 4) = 2x + 10. What is x?
10. 10.Solve: 6(m − 5) = 4m + 4. What is m?
11. 11.A father is 16 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?
12. 12.Solve: y/5 + y/3 = 24. What is y?
13. 13.Solve: y/3 + y/4 = 7. What is y?
14. 14.A father is 30 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?
15. 15.Solve: 7y + 3 = 2y + 63. What is y?
16. 16.A father is 5 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
17. 17.The length of a rectangle is 5 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
18. 18.Solve: 5y + 3 = 4y + 7. What is y?
19. 19.Solve: 6(m − 5) = m + 35. What is m?
20. 20.Solve: 4x + 3 = 2x + 11. What is x?
21. 21.A father is 36 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?
22. 22.Solve: 9x + 12 = 5x + 20. What is x?
23. 23.The length of a rectangle is 3 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
24. 24.Solve: 3(m − 4) = 2m + 6. What is m?
25. 25.The sum of four consecutive whole numbers is 42. What is the smallest of them?
26. 26.Solve: 6(t − 2) = 2t + 52. What is t?
27. 27.Solve: t/6 + t/5 = 11. What is t?
28. 28.The length of a rectangle is 2 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
29. 29.The length of a rectangle is 15 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
30. 30.The length of a rectangle is 9 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
31. 31.Solve: x/3 + x/5 = 64. What is x?
32. 32.The sum of four consecutive whole numbers is 202. What is the largest of them?
33. 33.Solve: 4(y − 1) = 2y + 8. What is y?
34. 34.The sum of three consecutive whole numbers is 18. What is the smallest of them?
35. 35.A father is 8 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
36. 36.Solve: 5(n − 3) = n + 33. What is n?
37. 37.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?
38. 38.Solve: x/4 + x/2 = 6. What is x?
39. 39.Solve: 5x + 18 = 2x + 54. What is x?
40. 40.A father is 10 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?

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