Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 905 · 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 9 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
2. 2.Solve: 6m + 9 = 5m + 13. What is m?
3. 3.Solve: 3(n − 1) = n + 15. What is n?
4. 4.A father is 6 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?
5. 5.The length of a rectangle is 10 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
6. 6.Solve: 4(n − 3) = 2n + 26. What is n?
7. 7.Solve: 6(y − 5) = y + 40. What is y?
8. 8.The sum of three consecutive whole numbers is 144. What is the largest of them?
9. 9.The sum of three consecutive whole numbers is 60. What is the smallest of them?
10. 10.Solve: 9y + 3 = y + 35. What is y?
11. 11.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?
12. 12.The length of a rectangle is 13 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
13. 13.The length of a rectangle is 10 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
14. 14.The sum of three consecutive whole numbers is 129. What is the largest of them?
15. 15.Solve: 7x + 18 = x + 36. What is x?
16. 16.The length of a rectangle is 15 cm more than its width. Its perimeter is 78 cm. What is its width (in cm)?
17. 17.Solve: t/4 + t/3 = 35. What is t?
18. 18.Solve: 4(m − 3) = m + 27. What is m?
19. 19.The sum of three consecutive whole numbers is 93. What is the smallest of them?
20. 20.A father is 22 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
21. 21.Solve: 7t + 16 = t + 106. What is t?
22. 22.Solve: y/5 + y/6 = 88. What is y?
23. 23.The sum of two consecutive whole numbers is 69. What is the smallest of them?
24. 24.A father is 15 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?
25. 25.Solve: y/6 + y/3 = 9. What is y?
26. 26.The length of a rectangle is 1 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
27. 27.Solve: 9p + 18 = 8p + 26. What is p?
28. 28.Solve: 5(p − 3) = 3p + 17. What is p?
29. 29.The length of a rectangle is 11 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
30. 30.A father is 27 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?
31. 31.A father is 26 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?
32. 32.A father is 22 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?
33. 33.Solve: 6n + 4 = 5n + 13. What is n?
34. 34.Solve: 3(p − 3) = 2p + 2. What is p?
35. 35.A father is 39 years older than his son. In 2 years, the father will be four times as old as his son. How old is the son now?
36. 36.Solve: t/3 + t/4 = 7. What is t?
37. 37.A father is 27 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?
38. 38.Solve: 3(m − 3) = 2m + 10. What is m?
39. 39.Solve: y/3 + y/5 = 40. What is y?
40. 40.Solve: n/6 + n/4 = 10. What is n?

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