Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 422 · 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 8 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
2. 2.Solve: x/6 + x/3 = 3. What is x?
3. 3.Solve: 9n + 6 = 3n + 96. What is n?
4. 4.The sum of two consecutive whole numbers is 77. What is the smallest of them?
5. 5.The sum of four consecutive whole numbers is 58. What is the smallest of them?
6. 6.Solve: m/4 + m/5 = 45. What is m?
7. 7.Solve: p/3 + p/2 = 10. What is p?
8. 8.Solve: p/6 + p/3 = 15. What is p?
9. 9.The sum of three consecutive whole numbers is 177. What is the largest of them?
10. 10.The length of a rectangle is 8 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
11. 11.The sum of two consecutive whole numbers is 107. What is the smallest of them?
12. 12.Solve: 3(m − 1) = m + 11. What is m?
13. 13.The sum of four consecutive whole numbers is 86. What is the largest of them?
14. 14.Solve: 5(m − 5) = 3m + 11. What is m?
15. 15.A father is 48 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?
16. 16.Solve: t/5 + t/2 = 14. What is t?
17. 17.Solve: 5(y − 2) = 3y + 18. What is y?
18. 18.The length of a rectangle is 14 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
19. 19.The length of a rectangle is 4 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
20. 20.Solve: 6(n − 5) = 5n + 5. What is n?
21. 21.The length of a rectangle is 7 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
22. 22.The sum of three consecutive whole numbers is 42. What is the largest of them?
23. 23.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?
24. 24.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?
25. 25.Solve: 4(p − 3) = 2p + 8. What is p?
26. 26.A father is 21 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?
27. 27.Solve: 9p + 4 = 4p + 74. What is p?
28. 28.The length of a rectangle is 9 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
29. 29.Solve: p/5 + p/3 = 16. What is p?
30. 30.The sum of three consecutive whole numbers is 138. What is the smallest of them?
31. 31.Solve: 6n + 4 = 2n + 16. What is n?
32. 32.The length of a rectangle is 4 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
33. 33.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?
34. 34.Solve: 4y + 19 = 2y + 27. What is y?
35. 35.Solve: y/5 + y/4 = 72. What is y?
36. 36.Solve: 6(t − 4) = 4t + 6. What is t?
37. 37.Solve: t/4 + t/6 = 20. What is t?
38. 38.Solve: 8n + 12 = 2n + 24. What is n?
39. 39.A father is 16 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
40. 40.The length of a rectangle is 1 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?

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