Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 663 · 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 54 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
2. 2.Solve: 4(t − 3) = t + 18. What is t?
3. 3.Solve: t/6 + t/3 = 12. What is t?
4. 4.A father is 8 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
5. 5.Solve: 8t + 17 = 7t + 19. What is t?
6. 6.The sum of two consecutive whole numbers is 29. What is the largest of them?
7. 7.Solve: x/3 + x/2 = 40. What is x?
8. 8.Solve: 4y + 13 = 2y + 17. What is y?
9. 9.Solve: 4(x − 1) = 2x + 20. What is x?
10. 10.The length of a rectangle is 3 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
11. 11.The length of a rectangle is 8 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
12. 12.Solve: p/3 + p/6 = 18. What is p?
13. 13.The sum of two consecutive whole numbers is 107. What is the largest of them?
14. 14.The length of a rectangle is 7 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
15. 15.Solve: 6m + 10 = 3m + 40. What is m?
16. 16.The length of a rectangle is 9 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
17. 17.A father is 28 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?
18. 18.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?
19. 19.The length of a rectangle is 12 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
20. 20.The length of a rectangle is 1 cm more than its width. Its perimeter is 94 cm. What is its width (in cm)?
21. 21.Solve: 4m + 3 = 3m + 13. What is m?
22. 22.The length of a rectangle is 7 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
23. 23.The length of a rectangle is 14 cm more than its width. Its perimeter is 136 cm. What is its width (in cm)?
24. 24.Solve: 9n + 20 = n + 36. What is n?
25. 25.A father is 30 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?
26. 26.A father is 28 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?
27. 27.Solve: x/2 + x/4 = 24. What is x?
28. 28.Solve: p/6 + p/3 = 9. What is p?
29. 29.The sum of two consecutive whole numbers is 89. What is the largest of them?
30. 30.A father is 42 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?
31. 31.The sum of four consecutive whole numbers is 34. What is the largest of them?
32. 32.Solve: 8m + 15 = m + 29. What is m?
33. 33.Solve: 3p + 12 = 2p + 18. What is p?
34. 34.The sum of two consecutive whole numbers is 33. What is the largest of them?
35. 35.Solve: 3(m − 3) = 2m + 9. What is m?
36. 36.Solve: p/6 + p/2 = 12. What is p?
37. 37.Solve: 3x + 7 = x + 21. What is x?
38. 38.Solve: x/2 + x/5 = 21. What is x?
39. 39.A father is 48 years older than his son. In 8 years, the father will be four times as old as his son. How old is the son now?
40. 40.The sum of three consecutive whole numbers is 102. What is the smallest of them?

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