Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 831 · 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.The sum of four consecutive whole numbers is 206. What is the largest of them?
2. 2.The sum of two consecutive whole numbers is 45. What is the largest of them?
3. 3.Solve: 8x + 18 = 7x + 22. What is x?
4. 4.Solve: 4(n − 2) = 3n + 4. What is n?
5. 5.A father is 20 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
6. 6.Solve: y/2 + y/3 = 20. What is y?
7. 7.The length of a rectangle is 2 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
8. 8.A father is 13 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
9. 9.Solve: 5(n − 1) = 4n + 1. What is n?
10. 10.A father is 12 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
11. 11.A father is 8 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
12. 12.A father is 15 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?
13. 13.A father is 33 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 sum of two consecutive whole numbers is 29. What is the smallest of them?
15. 15.The sum of four consecutive whole numbers is 134. What is the largest of them?
16. 16.Solve: t/2 + t/6 = 20. What is t?
17. 17.Solve: 4(p − 5) = p + 13. What is p?
18. 18.The length of a rectangle is 10 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
19. 19.Solve: 6(m − 2) = 3m + 21. What is m?
20. 20.The length of a rectangle is 1 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
21. 21.A father is 22 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?
22. 22.Solve: 6(m − 4) = 3m + 39. What is m?
23. 23.The length of a rectangle is 7 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
24. 24.Solve: 3(p − 3) = 2p + 2. What is p?
25. 25.Solve: p/6 + p/2 = 32. What is p?
26. 26.Solve: 5y + 18 = 3y + 48. What is y?
27. 27.The length of a rectangle is 11 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
28. 28.A father is 27 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?
29. 29.A father is 30 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?
30. 30.The sum of four consecutive whole numbers is 50. What is the smallest of them?
31. 31.A father is 20 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?
32. 32.The sum of two consecutive whole numbers is 43. What is the largest of them?
33. 33.Solve: x/6 + x/5 = 22. What is x?
34. 34.Solve: 6(n − 4) = n + 26. What is n?
35. 35.Solve: 6m + 3 = 3m + 21. What is m?
36. 36.Solve: 6(m − 1) = m + 29. What is m?
37. 37.Solve: 7x + 6 = x + 60. What is x?
38. 38.Solve: 8p + 2 = 6p + 6. What is p?
39. 39.A father is 5 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
40. 40.The sum of three consecutive whole numbers is 177. What is the smallest of them?

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