Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 859 · 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: 5y + 10 = 4y + 18. What is y?
2. 2.Solve: 8m + 19 = 2m + 67. What is m?
3. 3.Solve: 7m + 12 = m + 18. What is m?
4. 4.The length of a rectangle is 8 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
5. 5.The sum of two consecutive whole numbers is 103. What is the largest of them?
6. 6.The sum of two consecutive whole numbers is 69. What is the smallest of them?
7. 7.A father is 18 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
8. 8.Solve: 6y + 17 = 2y + 33. What is y?
9. 9.Solve: 4m + 15 = 3m + 28. What is m?
10. 10.Solve: x/6 + x/4 = 5. What is x?
11. 11.The sum of two consecutive whole numbers is 75. What is the smallest of them?
12. 12.The sum of four consecutive whole numbers is 130. What is the smallest of them?
13. 13.The length of a rectangle is 2 cm more than its width. Its perimeter is 100 cm. What is its width (in cm)?
14. 14.Solve: n/2 + n/3 = 10. What is n?
15. 15.Solve: 4n + 2 = n + 5. What is n?
16. 16.Solve: 5p + 17 = p + 61. What is p?
17. 17.Solve: 6(p − 4) = p + 56. What is p?
18. 18.Solve: 4(n − 1) = n + 32. What is n?
19. 19.A father is 54 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?
20. 20.A father is 28 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?
21. 21.The length of a rectangle is 11 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
22. 22.Solve: p/4 + p/2 = 3. What is p?
23. 23.Solve: n/4 + n/6 = 40. What is n?
24. 24.The length of a rectangle is 3 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
25. 25.Solve: 4(y − 4) = 3y + 3. What is y?
26. 26.Solve: y/6 + y/2 = 8. What is y?
27. 27.The sum of three consecutive whole numbers is 129. What is the smallest of them?
28. 28.The sum of four consecutive whole numbers is 142. What is the smallest of them?
29. 29.Solve: 4(y − 4) = 3y + 1. What is y?
30. 30.A father is 8 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: 3m + 11 = 2m + 13. What is m?
32. 32.Solve: 3(m − 3) = m + 5. What is m?
33. 33.The sum of two consecutive whole numbers is 43. What is the largest of them?
34. 34.A father is 24 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?
35. 35.The sum of three consecutive whole numbers is 144. What is the smallest of them?
36. 36.The sum of three consecutive whole numbers is 174. What is the smallest of them?
37. 37.The length of a rectangle is 5 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
38. 38.The length of a rectangle is 15 cm more than its width. Its perimeter is 90 cm. What is its width (in cm)?
39. 39.The length of a rectangle is 9 cm more than its width. Its perimeter is 138 cm. What is its width (in cm)?
40. 40.Solve: p/3 + p/2 = 20. What is p?

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