Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 239 · 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 27 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?
2. 2.Solve: p/3 + p/6 = 21. What is p?
3. 3.Solve: 7n + 1 = 4n + 40. What is n?
4. 4.Solve: 9p + 5 = 2p + 61. What is p?
5. 5.The sum of two consecutive whole numbers is 95. What is the largest of them?
6. 6.A father is 9 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
7. 7.Solve: 7n + 3 = n + 27. What is n?
8. 8.Solve: 5(y − 5) = 2y + 35. What is y?
9. 9.The length of a rectangle is 8 cm more than its width. Its perimeter is 36 cm. What is its width (in cm)?
10. 10.Solve: t/6 + t/4 = 20. What is t?
11. 11.Solve: 5(m − 1) = 4m + 6. What is m?
12. 12.The length of a rectangle is 8 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
13. 13.A father is 30 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
14. 14.Solve: 6(y − 2) = y + 18. What is y?
15. 15.A father is 54 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?
16. 16.The sum of two consecutive whole numbers is 23. What is the largest of them?
17. 17.Solve: 4(n − 4) = n + 8. What is n?
18. 18.Solve: 6(x − 3) = 4x + 26. What is x?
19. 19.The length of a rectangle is 5 cm more than its width. Its perimeter is 130 cm. What is its width (in cm)?
20. 20.A father is 30 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
21. 21.The length of a rectangle is 8 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
22. 22.Solve: 3(n − 1) = n + 9. What is n?
23. 23.The length of a rectangle is 7 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
24. 24.The sum of two consecutive whole numbers is 33. What is the smallest of them?
25. 25.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?
26. 26.Solve: 5(p − 5) = p + 27. What is p?
27. 27.Solve: 3(y − 2) = 2y + 11. What is y?
28. 28.Solve: 3n + 15 = n + 21. What is n?
29. 29.Solve: x/2 + x/6 = 12. What is x?
30. 30.Solve: m/2 + m/3 = 15. What is m?
31. 31.The sum of three consecutive whole numbers is 18. What is the smallest of them?
32. 32.The length of a rectangle is 13 cm more than its width. Its perimeter is 98 cm. What is its width (in cm)?
33. 33.Solve: 5(p − 2) = 3p + 2. What is p?
34. 34.The sum of two consecutive whole numbers is 13. What is the smallest of them?
35. 35.Solve: 9x + 11 = 2x + 53. What is x?
36. 36.A father is 14 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
37. 37.The sum of four consecutive whole numbers is 46. What is the smallest of them?
38. 38.Solve: 6(p − 1) = p + 4. What is p?
39. 39.The length of a rectangle is 9 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
40. 40.Solve: x/6 + x/5 = 11. What is x?

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