Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 182 · 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.Solve: n/6 + n/4 = 40. What is n?
2. 2.A father is 33 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?
3. 3.The length of a rectangle is 2 cm more than its width. Its perimeter is 48 cm. What is its width (in cm)?
4. 4.The length of a rectangle is 3 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
5. 5.A father is 12 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
6. 6.The length of a rectangle is 1 cm more than its width. Its perimeter is 58 cm. What is its width (in cm)?
7. 7.Solve: 4t + 7 = t + 43. What is t?
8. 8.Solve: 9m + 14 = 4m + 84. What is m?
9. 9.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?
10. 10.A father is 18 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
11. 11.Solve: 4x + 18 = x + 24. What is x?
12. 12.The length of a rectangle is 9 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
13. 13.A father is 18 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?
14. 14.Solve: 9x + 6 = x + 54. What is x?
15. 15.The sum of three consecutive whole numbers is 99. What is the largest of them?
16. 16.A father is 30 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?
17. 17.Solve: 6p + 6 = 3p + 27. What is p?
18. 18.A father is 39 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?
19. 19.The length of a rectangle is 14 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
20. 20.Solve: 3m + 7 = m + 11. What is m?
21. 21.A father is 11 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
22. 22.Solve: 7x + 5 = 5x + 7. What is x?
23. 23.Solve: t/6 + t/4 = 10. What is t?
24. 24.The length of a rectangle is 11 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
25. 25.The sum of four consecutive whole numbers is 186. What is the largest of them?
26. 26.The sum of three consecutive whole numbers is 120. What is the largest of them?
27. 27.The sum of four consecutive whole numbers is 182. What is the smallest of them?
28. 28.Solve: 3(t − 2) = 2t + 4. What is t?
29. 29.Solve: n/5 + n/6 = 77. What is n?
30. 30.Solve: 5(x − 3) = x + 1. What is x?
31. 31.Solve: 5n + 4 = 4n + 7. What is n?
32. 32.Solve: 5(n − 3) = n + 33. What is n?
33. 33.The sum of three consecutive whole numbers is 126. What is the smallest of them?
34. 34.Solve: 5(y − 1) = 3y + 11. What is y?
35. 35.Solve: 3x + 14 = x + 40. What is x?
36. 36.Solve: 6n + 13 = 5n + 18. What is n?
37. 37.The length of a rectangle is 14 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
38. 38.The sum of three consecutive whole numbers is 129. What is the largest of them?
39. 39.Solve: 3(p − 3) = 2p + 8. What is p?
40. 40.Solve: y/6 + y/3 = 3. What is y?

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