Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 90 · 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: 5(x − 2) = 4x + 3. What is x?
2. 2.Solve: 4(y − 3) = 2y + 14. What is y?
3. 3.Solve: 4(n − 1) = 3n + 13. What is n?
4. 4.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?
5. 5.Solve: 6(p − 2) = p + 28. What is p?
6. 6.The length of a rectangle is 1 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
7. 7.The sum of two consecutive whole numbers is 57. What is the smallest of them?
8. 8.Solve: 4(y − 1) = 3y + 4. What is y?
9. 9.Solve: 4y + 5 = 2y + 7. What is y?
10. 10.A father is 10 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
11. 11.A father is 14 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
12. 12.Solve: 9x + 13 = 2x + 76. What is x?
13. 13.The sum of two consecutive whole numbers is 105. What is the smallest of them?
14. 14.A father is 33 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?
15. 15.The length of a rectangle is 4 cm more than its width. Its perimeter is 92 cm. What is its width (in cm)?
16. 16.Solve: 8x + 13 = 6x + 19. What is x?
17. 17.The sum of three consecutive whole numbers is 63. What is the largest of them?
18. 18.Solve: 4t + 10 = t + 43. What is t?
19. 19.The length of a rectangle is 1 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
20. 20.Solve: x/3 + x/5 = 40. What is x?
21. 21.Solve: x/6 + x/2 = 24. What is x?
22. 22.Solve: 6x + 2 = 3x + 23. What is x?
23. 23.Solve: 8p + 8 = 4p + 12. What is p?
24. 24.The sum of four consecutive whole numbers is 214. What is the smallest of them?
25. 25.A father is 16 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?
26. 26.Solve: 6(m − 1) = 2m + 38. What is m?
27. 27.The sum of three consecutive whole numbers is 24. What is the smallest of them?
28. 28.The sum of four consecutive whole numbers is 242. What is the smallest of them?
29. 29.Solve: x/3 + x/6 = 21. What is x?
30. 30.The length of a rectangle is 10 cm more than its width. Its perimeter is 44 cm. What is its width (in cm)?
31. 31.Solve: 5t + 15 = 4t + 18. What is t?
32. 32.The sum of two consecutive whole numbers is 39. What is the smallest of them?
33. 33.The length of a rectangle is 2 cm more than its width. Its perimeter is 40 cm. What is its width (in cm)?
34. 34.A father is 13 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
35. 35.A father is 36 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
36. 36.Solve: t/6 + t/4 = 40. What is t?
37. 37.A father is 7 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
38. 38.Solve: 5y + 14 = y + 22. What is y?
39. 39.A father is 14 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
40. 40.Solve: m/2 + m/3 = 10. What is m?

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