Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 807 · 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: 5(y − 1) = 2y + 22. What is y?
2. 2.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
3. 3.Solve: 6(x − 3) = x + 2. What is x?
4. 4.Solve: 5(n − 3) = n + 49. What is n?
5. 5.A father is 60 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?
6. 6.Solve: 3(m − 1) = m + 17. What is m?
7. 7.Solve: 3t + 5 = 2t + 13. What is t?
8. 8.A father is 18 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?
9. 9.The length of a rectangle is 13 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
10. 10.Solve: 9y + 10 = 4y + 35. What is y?
11. 11.Solve: t/2 + t/3 = 5. What is t?
12. 12.The length of a rectangle is 12 cm more than its width. Its perimeter is 144 cm. What is its width (in cm)?
13. 13.A father is 42 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?
14. 14.The sum of four consecutive whole numbers is 150. What is the smallest of them?
15. 15.The length of a rectangle is 4 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
16. 16.Solve: 5(n − 1) = 3n + 11. What is n?
17. 17.A father is 16 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?
18. 18.A father is 14 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?
19. 19.The sum of four consecutive whole numbers is 42. What is the smallest of them?
20. 20.The length of a rectangle is 5 cm more than its width. Its perimeter is 126 cm. What is its width (in cm)?
21. 21.Solve: 5(x − 1) = 4x + 2. What is x?
22. 22.Solve: 4(n − 1) = 2n + 8. What is n?
23. 23.A father is 11 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
24. 24.Solve: 6(m − 3) = 2m + 10. What is m?
25. 25.A father is 11 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
26. 26.Solve: m/4 + m/6 = 25. What is m?
27. 27.Solve: 3x + 20 = 2x + 24. What is x?
28. 28.Solve: 4(p − 1) = 3p + 1. What is p?
29. 29.The sum of two consecutive whole numbers is 111. What is the smallest of them?
30. 30.Solve: 3(m − 4) = m + 8. What is m?
31. 31.The length of a rectangle is 2 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
32. 32.A father is 16 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
33. 33.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?
34. 34.The length of a rectangle is 9 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
35. 35.Solve: y/3 + y/2 = 25. What is y?
36. 36.The length of a rectangle is 6 cm more than its width. Its perimeter is 80 cm. What is its width (in cm)?
37. 37.Solve: 4(n − 3) = n + 12. What is n?
38. 38.Solve: 4(x − 4) = x + 8. What is x?
39. 39.A father is 18 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?
40. 40.A father is 20 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?

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