Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 432 · 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: 6(t − 5) = 3t + 33. What is t?
2. 2.A father is 21 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?
3. 3.The sum of three consecutive whole numbers is 168. What is the smallest of them?
4. 4.The length of a rectangle is 5 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
5. 5.The sum of two consecutive whole numbers is 73. What is the smallest of them?
6. 6.A father is 20 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?
7. 7.The sum of three consecutive whole numbers is 138. What is the smallest of them?
8. 8.The sum of three consecutive whole numbers is 174. What is the smallest of them?
9. 9.The length of a rectangle is 1 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
10. 10.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?
11. 11.Solve: p/3 + p/6 = 9. What is p?
12. 12.Solve: 3(x − 5) = x + 25. What is x?
13. 13.Solve: 5(y − 5) = 2y + 8. What is y?
14. 14.Solve: 4t + 8 = t + 26. What is t?
15. 15.A father is 28 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?
16. 16.Solve: 6(n − 4) = n + 56. What is n?
17. 17.Solve: m/4 + m/3 = 42. What is m?
18. 18.Solve: 3(n − 4) = n + 16. What is n?
19. 19.Solve: 3(t − 5) = 2t + 13. What is t?
20. 20.The sum of two consecutive whole numbers is 121. What is the smallest of them?
21. 21.The length of a rectangle is 8 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
22. 22.Solve: 6y + 4 = 4y + 6. What is y?
23. 23.Solve: x/3 + x/4 = 7. What is x?
24. 24.Solve: 5(n − 5) = 4n + 3. What is n?
25. 25.Solve: 6(y − 3) = 2y + 10. What is y?
26. 26.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?
27. 27.A father is 30 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?
28. 28.Solve: 5(n − 2) = 3n + 16. What is n?
29. 29.Solve: 6(y − 4) = y + 61. What is y?
30. 30.Solve: 7x + 3 = 3x + 27. What is x?
31. 31.Solve: 6(m − 2) = m + 18. What is m?
32. 32.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?
33. 33.Solve: 4(n − 3) = 3n + 11. What is n?
34. 34.Solve: 6(m − 4) = 3m + 33. What is m?
35. 35.A father is 9 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
36. 36.Solve: 4(p − 1) = p + 23. What is p?
37. 37.A father is 22 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?
38. 38.The length of a rectangle is 4 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
39. 39.The sum of three consecutive whole numbers is 180. What is the smallest of them?
40. 40.The length of a rectangle is 5 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?

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