Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 257 · 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 8 years, the father will be twice as old as his son. How old is the son now?
2. 2.Solve: 6(t − 2) = t + 43. What is t?
3. 3.Solve: y/4 + y/2 = 12. What is y?
4. 4.A father is 24 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?
5. 5.A father is 33 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?
6. 6.Solve: 6p + 11 = p + 26. What is p?
7. 7.Solve: y/3 + y/5 = 48. What is y?
8. 8.A father is 10 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
9. 9.A father is 30 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: 5p + 17 = 2p + 44. What is p?
11. 11.Solve: 6(p − 2) = 3p + 33. What is p?
12. 12.A father is 8 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?
13. 13.Solve: 3(m − 4) = 2m + 2. What is m?
14. 14.A father is 12 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
15. 15.Solve: t/3 + t/2 = 10. What is t?
16. 16.Solve: n/6 + n/3 = 15. What is n?
17. 17.Solve: 7n + 3 = 2n + 13. What is n?
18. 18.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?
19. 19.Solve: 3p + 18 = 2p + 20. What is p?
20. 20.The sum of four consecutive whole numbers is 54. What is the smallest of them?
21. 21.Solve: x/6 + x/4 = 30. What is x?
22. 22.The sum of two consecutive whole numbers is 37. What is the smallest of them?
23. 23.Solve: 3n + 17 = 2n + 31. What is n?
24. 24.Solve: 4(x − 3) = x + 39. What is x?
25. 25.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?
26. 26.The length of a rectangle is 2 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
27. 27.The length of a rectangle is 13 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
28. 28.A father is 33 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?
29. 29.Solve: 8m + 2 = 4m + 26. What is m?
30. 30.Solve: 4(m − 4) = 3m + 2. What is m?
31. 31.Solve: 5(y − 3) = 4y + 1. What is y?
32. 32.The sum of four consecutive whole numbers is 118. What is the largest of them?
33. 33.Solve: x/3 + x/5 = 24. What is x?
34. 34.Solve: 6(p − 4) = 3p + 3. What is p?
35. 35.Solve: 5(t − 2) = 2t + 5. What is t?
36. 36.The length of a rectangle is 11 cm more than its width. Its perimeter is 62 cm. What is its width (in cm)?
37. 37.The sum of four consecutive whole numbers is 166. What is the smallest of them?
38. 38.The length of a rectangle is 10 cm more than its width. Its perimeter is 136 cm. What is its width (in cm)?
39. 39.Solve: 3y + 3 = 2y + 17. What is y?
40. 40.The length of a rectangle is 14 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?

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