Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 590 · 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: 3(n − 2) = 2n + 4. What is n?
2. 2.A father is 18 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?
3. 3.Solve: 3(t − 2) = 2t + 12. What is t?
4. 4.A father is 30 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
5. 5.Solve: 4(p − 5) = p + 25. What is p?
6. 6.A father is 13 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
7. 7.The length of a rectangle is 10 cm more than its width. Its perimeter is 52 cm. What is its width (in cm)?
8. 8.Solve: n/5 + n/6 = 77. What is n?
9. 9.Solve: y/3 + y/4 = 56. What is y?
10. 10.Solve: 6(m − 3) = 3m + 18. What is m?
11. 11.The length of a rectangle is 9 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
12. 12.Solve: 8x + 11 = 4x + 55. What is x?
13. 13.The length of a rectangle is 3 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
14. 14.The sum of three consecutive whole numbers is 87. What is the smallest of them?
15. 15.Solve: 4y + 17 = 3y + 26. What is y?
16. 16.The sum of two consecutive whole numbers is 15. What is the smallest of them?
17. 17.Solve: t/2 + t/6 = 8. What is t?
18. 18.Solve: y/3 + y/4 = 42. What is y?
19. 19.A father is 12 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
20. 20.A father is 24 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?
21. 21.Solve: 4(m − 4) = 2m + 22. What is m?
22. 22.The sum of two consecutive whole numbers is 53. What is the largest of them?
23. 23.A father is 12 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
24. 24.Solve: 5(m − 5) = 3m + 19. What is m?
25. 25.A father is 39 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?
26. 26.The length of a rectangle is 8 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
27. 27.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?
28. 28.The length of a rectangle is 8 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
29. 29.The length of a rectangle is 7 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
30. 30.The sum of four consecutive whole numbers is 110. What is the smallest of them?
31. 31.The length of a rectangle is 1 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
32. 32.Solve: y/4 + y/5 = 45. What is y?
33. 33.Solve: 3x + 5 = x + 15. What is x?
34. 34.The sum of two consecutive whole numbers is 59. What is the smallest of them?
35. 35.Solve: 4(y − 2) = 3y + 9. What is y?
36. 36.The length of a rectangle is 4 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
37. 37.Solve: m/3 + m/6 = 21. What is m?
38. 38.Solve: 4n + 10 = 2n + 14. What is n?
39. 39.A father is 15 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
40. 40.Solve: 3(y − 5) = y + 3. What is y?

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