Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 224 · 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 2 years, the father will be four times as old as his son. How old is the son now?
2. 2.A father is 48 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?
3. 3.The length of a rectangle is 4 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
4. 4.A father is 15 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
5. 5.The length of a rectangle is 14 cm more than its width. Its perimeter is 148 cm. What is its width (in cm)?
6. 6.Solve: 3(m − 4) = 2m + 5. What is m?
7. 7.Solve: t/2 + t/4 = 21. What is t?
8. 8.The sum of two consecutive whole numbers is 39. What is the largest of them?
9. 9.Solve: 8p + 6 = 7p + 20. What is p?
10. 10.A father is 36 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?
11. 11.A father is 28 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?
12. 12.Solve: 4(y − 2) = 2y + 10. What is y?
13. 13.The length of a rectangle is 10 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
14. 14.Solve: 5(p − 2) = p + 30. What is p?
15. 15.Solve: 4y + 19 = 3y + 25. What is y?
16. 16.The sum of three consecutive whole numbers is 24. What is the smallest of them?
17. 17.Solve: n/5 + n/6 = 44. What is n?
18. 18.The sum of four consecutive whole numbers is 106. What is the largest of them?
19. 19.A father is 12 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?
20. 20.Solve: 3p + 6 = p + 30. What is p?
21. 21.A father is 12 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
22. 22.Solve: 4(x − 2) = 3x + 10. What is x?
23. 23.A father is 15 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
24. 24.Solve: 3(y − 2) = 2y + 3. What is y?
25. 25.Solve: 6y + 3 = 5y + 17. What is y?
26. 26.Solve: m/6 + m/4 = 15. What is m?
27. 27.The sum of four consecutive whole numbers is 74. What is the largest of them?
28. 28.Solve: x/6 + x/5 = 66. What is x?
29. 29.Solve: p/6 + p/2 = 16. What is p?
30. 30.The length of a rectangle is 2 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
31. 31.The length of a rectangle is 6 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
32. 32.Solve: 5(y − 1) = y + 27. What is y?
33. 33.Solve: 5(x − 2) = x + 14. What is x?
34. 34.The length of a rectangle is 10 cm more than its width. Its perimeter is 88 cm. What is its width (in cm)?
35. 35.Solve: 6(m − 1) = m + 54. What is m?
36. 36.Solve: 4(x − 3) = x + 24. What is x?
37. 37.A father is 30 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?
38. 38.Solve: 4n + 8 = n + 14. What is n?
39. 39.Solve: 4y + 7 = 2y + 13. What is y?
40. 40.Solve: 3(y − 2) = y + 2. What is y?

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