Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 294 · 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.The length of a rectangle is 5 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
2. 2.Solve: y/2 + y/6 = 16. What is y?
3. 3.A father is 36 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?
4. 4.Solve: y/4 + y/2 = 24. What is y?
5. 5.Solve: 7x + 11 = 5x + 17. What is x?
6. 6.Solve: 6(x − 3) = 3x + 15. What is x?
7. 7.Solve: t/2 + t/4 = 12. What is t?
8. 8.Solve: 5(t − 5) = 3t + 19. What is t?
9. 9.The sum of two consecutive whole numbers is 89. What is the smallest of them?
10. 10.The sum of three consecutive whole numbers is 36. What is the smallest of them?
11. 11.The length of a rectangle is 14 cm more than its width. Its perimeter is 148 cm. What is its width (in cm)?
12. 12.A father is 20 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?
13. 13.The length of a rectangle is 6 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
14. 14.A father is 14 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?
15. 15.A father is 20 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?
16. 16.Solve: n/3 + n/5 = 16. What is n?
17. 17.The sum of two consecutive whole numbers is 109. What is the smallest of them?
18. 18.The sum of four consecutive whole numbers is 142. What is the largest of them?
19. 19.A father is 45 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?
20. 20.Solve: 4(t − 5) = 3t + 12. What is t?
21. 21.Solve: t/4 + t/3 = 42. What is t?
22. 22.Solve: 4(y − 2) = 2y + 20. What is y?
23. 23.Solve: t/3 + t/4 = 14. What is t?
24. 24.A father is 18 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?
25. 25.Solve: y/5 + y/2 = 21. What is y?
26. 26.Solve: 6(m − 5) = 2m + 6. What is m?
27. 27.Solve: 5(p − 5) = p + 3. What is p?
28. 28.The length of a rectangle is 8 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
29. 29.Solve: 3(x − 1) = x + 5. What is x?
30. 30.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?
31. 31.Solve: 6n + 8 = 5n + 19. What is n?
32. 32.Solve: 4t + 9 = 3t + 18. What is t?
33. 33.Solve: 4(p − 4) = 3p + 10. What is p?
34. 34.The length of a rectangle is 3 cm more than its width. Its perimeter is 34 cm. What is its width (in cm)?
35. 35.The length of a rectangle is 5 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
36. 36.Solve: 6(m − 5) = 4m + 24. What is m?
37. 37.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?
38. 38.Solve: 4(n − 3) = 3n + 13. What is n?
39. 39.Solve: 4(y − 3) = y + 36. What is y?
40. 40.The length of a rectangle is 1 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?

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