Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 900 · 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 15 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
2. 2.The length of a rectangle is 10 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
3. 3.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?
4. 4.Solve: n/6 + n/5 = 33. What is n?
5. 5.The length of a rectangle is 12 cm more than its width. Its perimeter is 124 cm. What is its width (in cm)?
6. 6.Solve: 5(p − 4) = p + 44. What is p?
7. 7.The sum of two consecutive whole numbers is 105. What is the largest of them?
8. 8.Solve: 9m + 1 = 3m + 43. What is m?
9. 9.Solve: 6(t − 4) = 3t + 24. What is t?
10. 10.Solve: 6n + 2 = 3n + 8. What is n?
11. 11.Solve: n/5 + n/4 = 72. What is n?
12. 12.The sum of two consecutive whole numbers is 77. What is the largest of them?
13. 13.Solve: 9y + 11 = 2y + 25. What is y?
14. 14.The sum of three consecutive whole numbers is 78. What is the largest of them?
15. 15.The length of a rectangle is 3 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
16. 16.Solve: 4m + 15 = m + 33. What is m?
17. 17.Solve: m/2 + m/4 = 21. What is m?
18. 18.A father is 45 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?
19. 19.A father is 22 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?
20. 20.A father is 18 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?
21. 21.Solve: 5(t − 4) = 2t + 1. What is t?
22. 22.Solve: 3(y − 1) = 2y + 4. What is y?
23. 23.Solve: 4(t − 5) = t + 22. What is t?
24. 24.A father is 9 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
25. 25.A father is 17 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
26. 26.Solve: 4(n − 1) = 2n + 14. What is n?
27. 27.Solve: 3(y − 2) = y + 10. What is y?
28. 28.The length of a rectangle is 4 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
29. 29.Solve: 5x + 7 = x + 51. What is x?
30. 30.A father is 18 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
31. 31.Solve: 4(y − 1) = 3y + 7. What is y?
32. 32.Solve: 3t + 19 = 2t + 34. What is t?
33. 33.A father is 4 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
34. 34.Solve: 6t + 6 = 5t + 8. What is t?
35. 35.Solve: 3(p − 1) = p + 15. What is p?
36. 36.Solve: 4p + 10 = 3p + 25. What is p?
37. 37.The sum of four consecutive whole numbers is 118. What is the largest of them?
38. 38.Solve: 9m + 16 = 8m + 24. What is m?
39. 39.A father is 26 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?
40. 40.A father is 7 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?

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