Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 27 · 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 70 cm. What is its width (in cm)?
2. 2.The length of a rectangle is 5 cm more than its width. Its perimeter is 102 cm. What is its width (in cm)?
3. 3.Solve: 4(p − 3) = 3p + 1. What is p?
4. 4.Solve: 3t + 9 = 2t + 23. What is t?
5. 5.Solve: y/4 + y/3 = 21. What is y?
6. 6.The sum of two consecutive whole numbers is 111. What is the largest of them?
7. 7.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
8. 8.The sum of three consecutive whole numbers is 126. What is the largest of them?
9. 9.Solve: 8x + 18 = 2x + 96. What is x?
10. 10.Solve: 6x + 15 = 2x + 27. What is x?
11. 11.Solve: m/4 + m/2 = 15. What is m?
12. 12.A father is 15 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
13. 13.Solve: 5(p − 4) = p + 24. What is p?
14. 14.Solve: p/2 + p/5 = 28. What is p?
15. 15.Solve: 4y + 20 = 3y + 30. What is y?
16. 16.Solve: 6(p − 4) = p + 36. What is p?
17. 17.Solve: 4x + 17 = 3x + 24. What is x?
18. 18.A father is 24 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?
19. 19.A father is 30 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: m/4 + m/5 = 27. What is m?
21. 21.The length of a rectangle is 15 cm more than its width. Its perimeter is 146 cm. What is its width (in cm)?
22. 22.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?
23. 23.Solve: n/3 + n/5 = 16. What is n?
24. 24.The length of a rectangle is 14 cm more than its width. Its perimeter is 68 cm. What is its width (in cm)?
25. 25.A father is 12 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
26. 26.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?
27. 27.Solve: 6n + 2 = 2n + 22. What is n?
28. 28.The sum of four consecutive whole numbers is 226. What is the smallest of them?
29. 29.Solve: 3(y − 4) = 2y + 2. What is y?
30. 30.The length of a rectangle is 5 cm more than its width. Its perimeter is 30 cm. What is its width (in cm)?
31. 31.Solve: 7p + 20 = 6p + 33. What is p?
32. 32.Solve: p/3 + p/4 = 35. What is p?
33. 33.Solve: 6m + 14 = 4m + 38. What is m?
34. 34.Solve: 8p + 19 = 3p + 49. What is p?
35. 35.The sum of four consecutive whole numbers is 82. What is the largest of them?
36. 36.Solve: 4(x − 5) = 3x + 9. What is x?
37. 37.The length of a rectangle is 2 cm more than its width. Its perimeter is 32 cm. What is its width (in cm)?
38. 38.The length of a rectangle is 3 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
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: 7x + 2 = 6x + 16. What is x?

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