Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 693 · 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: 5n + 4 = 2n + 7. What is n?
2. 2.A father is 16 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?
3. 3.Solve: 6m + 20 = m + 60. What is m?
4. 4.Solve: 5x + 3 = 3x + 9. What is x?
5. 5.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?
6. 6.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?
7. 7.Solve: 7y + 7 = 5y + 33. What is y?
8. 8.The length of a rectangle is 14 cm more than its width. Its perimeter is 140 cm. What is its width (in cm)?
9. 9.A father is 33 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?
10. 10.Solve: 3(p − 5) = p + 17. What is p?
11. 11.The length of a rectangle is 3 cm more than its width. Its perimeter is 106 cm. What is its width (in cm)?
12. 12.Solve: y/6 + y/3 = 3. What is y?
13. 13.A father is 9 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?
14. 14.The length of a rectangle is 14 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
15. 15.Solve: 5(x − 5) = 4x + 8. What is x?
16. 16.Solve: 5x + 18 = 3x + 28. What is x?
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.The length of a rectangle is 7 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
19. 19.Solve: 9m + 2 = 4m + 17. What is m?
20. 20.Solve: x/4 + x/2 = 3. What is x?
21. 21.The sum of four consecutive whole numbers is 82. What is the largest of them?
22. 22.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?
23. 23.Solve: 4(x − 5) = 2x + 2. What is x?
24. 24.Solve: 5(n − 3) = 4n + 3. What is n?
25. 25.Solve: 6(p − 3) = 5p + 6. What is p?
26. 26.Solve: 3y + 1 = 2y + 4. What is y?
27. 27.A father is 39 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?
28. 28.Solve: 3(y − 5) = y + 17. What is y?
29. 29.The length of a rectangle is 3 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
30. 30.The length of a rectangle is 9 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
31. 31.The length of a rectangle is 4 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
32. 32.Solve: 4(n − 1) = 3n + 10. What is n?
33. 33.The sum of four consecutive whole numbers is 238. What is the smallest of them?
34. 34.A father is 24 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?
35. 35.The length of a rectangle is 8 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
36. 36.Solve: y/6 + y/4 = 25. What is y?
37. 37.A father is 28 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?
38. 38.Solve: 6(y − 4) = y + 56. What is y?
39. 39.The length of a rectangle is 3 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
40. 40.The length of a rectangle is 15 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?

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