Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 565 · 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.A father is 9 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
2. 2.The length of a rectangle is 12 cm more than its width. Its perimeter is 96 cm. What is its width (in cm)?
3. 3.Solve: m/4 + m/2 = 21. What is m?
4. 4.The sum of three consecutive whole numbers is 138. What is the smallest of them?
5. 5.The length of a rectangle is 15 cm more than its width. Its perimeter is 142 cm. What is its width (in cm)?
6. 6.The sum of two consecutive whole numbers is 119. What is the smallest of them?
7. 7.Solve: m/6 + m/4 = 25. What is m?
8. 8.Solve: 3(m − 1) = m + 23. What is m?
9. 9.Solve: 3(t − 1) = t + 7. What is t?
10. 10.The length of a rectangle is 7 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
11. 11.Solve: 5(m − 2) = 4m + 13. What is m?
12. 12.Solve: 9t + 5 = 8t + 18. What is t?
13. 13.Solve: y/5 + y/4 = 36. What is y?
14. 14.The sum of four consecutive whole numbers is 38. What is the smallest of them?
15. 15.The length of a rectangle is 7 cm more than its width. Its perimeter is 42 cm. What is its width (in cm)?
16. 16.The length of a rectangle is 9 cm more than its width. Its perimeter is 26 cm. What is its width (in cm)?
17. 17.The sum of two consecutive whole numbers is 19. What is the largest of them?
18. 18.Solve: y/4 + y/3 = 14. What is y?
19. 19.The sum of two consecutive whole numbers is 23. What is the largest of them?
20. 20.The sum of four consecutive whole numbers is 98. What is the largest of them?
21. 21.Solve: 8m + 9 = m + 107. What is m?
22. 22.The length of a rectangle is 2 cm more than its width. Its perimeter is 24 cm. What is its width (in cm)?
23. 23.A father is 11 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
24. 24.A father is 14 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
25. 25.Solve: x/3 + x/2 = 10. What is x?
26. 26.Solve: 3(t − 2) = t + 10. What is t?
27. 27.Solve: 4(t − 2) = t + 16. What is t?
28. 28.Solve: 5n + 7 = 4n + 21. What is n?
29. 29.The length of a rectangle is 6 cm more than its width. Its perimeter is 20 cm. What is its width (in cm)?
30. 30.The sum of four consecutive whole numbers is 114. What is the smallest of them?
31. 31.Solve: n/4 + n/2 = 3. What is n?
32. 32.A father is 45 years older than his son. In 4 years, the father will be four times as old as his son. How old is the son now?
33. 33.The sum of two consecutive whole numbers is 97. What is the largest of them?
34. 34.Solve: 6(p − 2) = p + 8. What is p?
35. 35.The sum of four consecutive whole numbers is 146. What is the smallest of them?
36. 36.The sum of two consecutive whole numbers is 87. What is the largest of them?
37. 37.Solve: 4p + 1 = p + 40. What is p?
38. 38.Solve: 3(x − 2) = x + 4. What is x?
39. 39.Solve: t/4 + t/5 = 54. What is t?
40. 40.A father is 17 years older than his son. In 6 years, the father will be twice as old as his son. How old is the son now?

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