Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 213 · 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 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?
2. 2.The sum of three consecutive whole numbers is 138. What is the smallest of them?
3. 3.Solve: 3n + 1 = n + 21. What is n?
4. 4.A father is 16 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
5. 5.Solve: 6m + 2 = 3m + 11. What is m?
6. 6.A father is 18 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: 6(x − 2) = 4x + 14. What is x?
8. 8.Solve: 3m + 6 = m + 34. What is m?
9. 9.The length of a rectangle is 4 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
10. 10.Solve: n/2 + n/5 = 56. What is n?
11. 11.The length of a rectangle is 10 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
12. 12.A father is 40 years older than his son. In 8 years, the father will be three times as old as his son. How old is the son now?
13. 13.The length of a rectangle is 8 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
14. 14.The sum of three consecutive whole numbers is 165. What is the largest of them?
15. 15.The sum of four consecutive whole numbers is 110. What is the smallest of them?
16. 16.Solve: 3n + 5 = n + 25. What is n?
17. 17.Solve: 3(t − 5) = 2t + 5. What is t?
18. 18.Solve: 6(n − 2) = 4n + 6. What is n?
19. 19.A father is 6 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
20. 20.A father is 12 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
21. 21.The sum of two consecutive whole numbers is 117. What is the smallest of them?
22. 22.Solve: 5x + 6 = x + 38. What is x?
23. 23.Solve: m/2 + m/4 = 3. What is m?
24. 24.The sum of two consecutive whole numbers is 83. What is the smallest of them?
25. 25.Solve: 3p + 10 = 2p + 24. What is p?
26. 26.A father is 42 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?
27. 27.Solve: 6(y − 3) = 2y + 18. What is y?
28. 28.Solve: 6x + 7 = 4x + 15. What is x?
29. 29.The sum of four consecutive whole numbers is 230. What is the largest of them?
30. 30.Solve: p/3 + p/6 = 24. What is p?
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: x/6 + x/5 = 66. What is x?
33. 33.Solve: 5y + 18 = 3y + 36. What is y?
34. 34.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?
35. 35.Solve: x/6 + x/2 = 32. What is x?
36. 36.The sum of two consecutive whole numbers is 57. What is the smallest of them?
37. 37.Solve: 6(t − 2) = 2t + 20. What is t?
38. 38.The sum of three consecutive whole numbers is 66. What is the largest of them?
39. 39.Solve: n/2 + n/3 = 15. What is n?
40. 40.The length of a rectangle is 2 cm more than its width. Its perimeter is 12 cm. What is its width (in cm)?

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