Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 923 · 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 7 cm more than its width. Its perimeter is 110 cm. What is its width (in cm)?
2. 2.Solve: 5(x − 5) = 3x + 7. What is x?
3. 3.Solve: 3(p − 4) = 2p + 11. What is p?
4. 4.The sum of three consecutive whole numbers is 153. What is the smallest of them?
5. 5.Solve: n/4 + n/2 = 6. What is n?
6. 6.Solve: t/4 + t/2 = 9. What is t?
7. 7.Solve: 4(p − 2) = p + 16. What is p?
8. 8.A father is 18 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
9. 9.Solve: 3(t − 3) = 2t + 1. What is t?
10. 10.Solve: p/4 + p/2 = 21. What is p?
11. 11.The sum of two consecutive whole numbers is 79. What is the smallest of them?
12. 12.The sum of three consecutive whole numbers is 156. What is the largest of them?
13. 13.Solve: 5(p − 2) = 3p + 26. What is p?
14. 14.Solve: m/3 + m/4 = 49. What is m?
15. 15.The length of a rectangle is 1 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
16. 16.A father is 45 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?
17. 17.A father is 21 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?
18. 18.The sum of three consecutive whole numbers is 36. What is the largest of them?
19. 19.The sum of three consecutive whole numbers is 75. What is the smallest of them?
20. 20.The length of a rectangle is 10 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
21. 21.Solve: 5(t − 2) = 2t + 29. What is t?
22. 22.Solve: 7t + 10 = 5t + 22. What is t?
23. 23.Solve: 3(t − 3) = 2t + 6. What is t?
24. 24.A father is 34 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: 5(t − 1) = 3t + 19. What is t?
26. 26.Solve: y/3 + y/6 = 21. What is y?
27. 27.A father is 15 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
28. 28.Solve: 8n + 19 = 3n + 39. What is n?
29. 29.Solve: m/5 + m/6 = 22. What is m?
30. 30.The length of a rectangle is 7 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
31. 31.A father is 8 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
32. 32.The length of a rectangle is 7 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
33. 33.A father is 14 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?
34. 34.The length of a rectangle is 12 cm more than its width. Its perimeter is 120 cm. What is its width (in cm)?
35. 35.The length of a rectangle is 2 cm more than its width. Its perimeter is 72 cm. What is its width (in cm)?
36. 36.Solve: p/2 + p/3 = 35. What is p?
37. 37.A father is 30 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
38. 38.Solve: 5t + 3 = 2t + 21. What is t?
39. 39.The sum of four consecutive whole numbers is 122. What is the smallest of them?
40. 40.Solve: 4(t − 1) = t + 35. What is t?

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