Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 201 · 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 3 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
2. 2.Solve: 3(x − 1) = x + 3. What is x?
3. 3.Solve: 3(m − 1) = m + 5. What is m?
4. 4.The length of a rectangle is 13 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
5. 5.A father is 36 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?
6. 6.Solve: 4y + 1 = 3y + 11. What is y?
7. 7.Solve: n/4 + n/6 = 10. What is n?
8. 8.Solve: 6(n − 1) = 3n + 36. What is n?
9. 9.The sum of four consecutive whole numbers is 170. What is the largest of them?
10. 10.Solve: 3(t − 1) = 2t + 11. What is t?
11. 11.The sum of four consecutive whole numbers is 142. What is the smallest of them?
12. 12.The sum of three consecutive whole numbers is 39. What is the smallest of them?
13. 13.Solve: y/3 + y/4 = 42. What is y?
14. 14.Solve: n/3 + n/2 = 30. What is n?
15. 15.Solve: 3(m − 2) = 2m + 5. What is m?
16. 16.Solve: n/3 + n/2 = 25. What is n?
17. 17.Solve: 8y + 13 = 6y + 43. What is y?
18. 18.Solve: x/5 + x/4 = 9. What is x?
19. 19.The sum of three consecutive whole numbers is 42. What is the smallest of them?
20. 20.The sum of four consecutive whole numbers is 242. What is the largest of them?
21. 21.A father is 33 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?
22. 22.The length of a rectangle is 3 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
23. 23.The sum of two consecutive whole numbers is 59. What is the smallest of them?
24. 24.The length of a rectangle is 2 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
25. 25.Solve: 9t + 1 = 2t + 15. What is t?
26. 26.Solve: 5(x − 2) = 3x + 12. What is x?
27. 27.Solve: x/3 + x/5 = 8. What is x?
28. 28.Solve: 5p + 1 = p + 33. What is p?
29. 29.A father is 12 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?
30. 30.Solve: 3(n − 3) = n + 5. What is n?
31. 31.The sum of two consecutive whole numbers is 87. What is the smallest of them?
32. 32.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?
33. 33.A father is 24 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?
34. 34.Solve: 5(t − 3) = 3t + 7. What is t?
35. 35.Solve: 4(x − 1) = 2x + 8. What is x?
36. 36.A father is 36 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?
37. 37.Solve: 4(p − 2) = 3p + 8. What is p?
38. 38.The length of a rectangle is 12 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
39. 39.Solve: 4m + 13 = 3m + 18. What is m?
40. 40.A father is 17 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?

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