Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 430 · 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.A father is 16 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
3. 3.Solve: 9x + 1 = 8x + 2. What is x?
4. 4.The sum of two consecutive whole numbers is 117. What is the largest of them?
5. 5.Solve: 5(m − 1) = m + 3. What is m?
6. 6.The sum of four consecutive whole numbers is 46. What is the largest of them?
7. 7.The length of a rectangle is 3 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
8. 8.The length of a rectangle is 4 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
9. 9.A father is 45 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?
10. 10.Solve: 8t + 17 = 3t + 82. What is t?
11. 11.Solve: 3(t − 1) = t + 3. What is t?
12. 12.Solve: 3y + 4 = 2y + 17. What is y?
13. 13.Solve: 4(n − 4) = 2n + 18. What is n?
14. 14.The sum of two consecutive whole numbers is 41. What is the largest of them?
15. 15.Solve: 3(p − 1) = p + 21. What is p?
16. 16.Solve: 6p + 20 = p + 45. What is p?
17. 17.A father is 18 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?
18. 18.The length of a rectangle is 10 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
19. 19.The length of a rectangle is 7 cm more than its width. Its perimeter is 66 cm. What is its width (in cm)?
20. 20.Solve: 5y + 11 = 4y + 16. What is y?
21. 21.A father is 48 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
22. 22.A father is 36 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?
23. 23.A father is 16 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?
24. 24.A father is 26 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?
25. 25.A father is 26 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?
26. 26.Solve: n/2 + n/3 = 15. What is n?
27. 27.Solve: y/6 + y/5 = 11. What is y?
28. 28.Solve: 3x + 20 = 2x + 23. What is x?
29. 29.A father is 11 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
30. 30.Solve: 6(t − 2) = 3t + 15. What is t?
31. 31.Solve: t/5 + t/6 = 77. What is t?
32. 32.The sum of four consecutive whole numbers is 230. What is the smallest of them?
33. 33.The length of a rectangle is 7 cm more than its width. Its perimeter is 54 cm. What is its width (in cm)?
34. 34.The sum of three consecutive whole numbers is 180. What is the smallest of them?
35. 35.A father is 22 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?
36. 36.A father is 15 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?
37. 37.Solve: x/2 + x/4 = 9. What is x?
38. 38.A father is 24 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?
39. 39.Solve: 5(x − 4) = 3x + 6. What is x?
40. 40.Solve: 6(n − 2) = 2n + 16. What is n?

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