Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 156 · 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: 4(p − 3) = p + 27. What is p?
2. 2.The length of a rectangle is 5 cm more than its width. Its perimeter is 114 cm. What is its width (in cm)?
3. 3.The sum of three consecutive whole numbers is 69. What is the largest of them?
4. 4.Solve: x/2 + x/3 = 35. What is x?
5. 5.A father is 51 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?
6. 6.Solve: 3(y − 4) = 2y + 5. What is y?
7. 7.Solve: 4n + 1 = n + 10. What is n?
8. 8.A father is 11 years older than his son. In 1 year, the father will be twice as old as his son. How old is the son now?
9. 9.The sum of four consecutive whole numbers is 114. What is the smallest of them?
10. 10.Solve: 5(n − 2) = 2n + 23. What is n?
11. 11.Solve: 7m + 10 = m + 40. What is m?
12. 12.Solve: 5(n − 1) = n + 39. What is n?
13. 13.The length of a rectangle is 13 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
14. 14.The sum of four consecutive whole numbers is 50. What is the largest of them?
15. 15.Solve: 4p + 8 = 2p + 14. What is p?
16. 16.Solve: y/3 + y/4 = 56. What is y?
17. 17.The sum of three consecutive whole numbers is 144. What is the smallest of them?
18. 18.The sum of two consecutive whole numbers is 13. What is the largest of them?
19. 19.Solve: 6(m − 3) = 4m + 8. What is m?
20. 20.The length of a rectangle is 9 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
21. 21.The length of a rectangle is 2 cm more than its width. Its perimeter is 12 cm. What is its width (in cm)?
22. 22.Solve: 5x + 2 = 3x + 30. What is x?
23. 23.Solve: y/6 + y/3 = 6. What is y?
24. 24.Solve: m/3 + m/5 = 8. What is m?
25. 25.A father is 28 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?
26. 26.A father is 7 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
27. 27.The sum of two consecutive whole numbers is 25. What is the smallest of them?
28. 28.A father is 13 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
29. 29.The sum of four consecutive whole numbers is 246. What is the smallest of them?
30. 30.A father is 30 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?
31. 31.Solve: 3y + 3 = y + 27. What is y?
32. 32.Solve: n/3 + n/5 = 40. What is n?
33. 33.Solve: 3(p − 1) = p + 15. What is p?
34. 34.The length of a rectangle is 10 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
35. 35.The sum of three consecutive whole numbers is 147. What is the smallest of them?
36. 36.The length of a rectangle is 13 cm more than its width. Its perimeter is 38 cm. What is its width (in cm)?
37. 37.The sum of two consecutive whole numbers is 37. What is the smallest of them?
38. 38.Solve: 4m + 5 = 2m + 21. What is m?
39. 39.The length of a rectangle is 4 cm more than its width. Its perimeter is 128 cm. What is its width (in cm)?
40. 40.Solve: t/5 + t/2 = 21. What is t?

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