Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 264 · 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 34 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
2. 2.Solve: 9x + 6 = 7x + 24. What is x?
3. 3.The length of a rectangle is 4 cm more than its width. Its perimeter is 104 cm. What is its width (in cm)?
4. 4.The length of a rectangle is 4 cm more than its width. Its perimeter is 108 cm. What is its width (in cm)?
5. 5.Solve: 7p + 4 = 4p + 40. What is p?
6. 6.Solve: 3(y − 1) = 2y + 1. What is y?
7. 7.Solve: p/6 + p/3 = 15. What is p?
8. 8.The length of a rectangle is 9 cm more than its width. Its perimeter is 134 cm. What is its width (in cm)?
9. 9.Solve: 3x + 16 = 2x + 29. What is x?
10. 10.Solve: 3t + 9 = t + 29. What is t?
11. 11.The length of a rectangle is 4 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
12. 12.Solve: 4(m − 1) = m + 23. What is m?
13. 13.Solve: 6(x − 1) = 5x + 6. What is x?
14. 14.Solve: 5(n − 3) = n + 13. What is n?
15. 15.Solve: m/6 + m/2 = 24. What is m?
16. 16.The length of a rectangle is 8 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
17. 17.Solve: m/4 + m/5 = 27. What is m?
18. 18.The length of a rectangle is 2 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
19. 19.Solve: 3(t − 5) = t + 3. What is t?
20. 20.Solve: 8p + 2 = 5p + 5. What is p?
21. 21.The length of a rectangle is 9 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
22. 22.A father is 30 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?
23. 23.A father is 16 years older than his son. In 6 years, the father will be three times as old as his son. How old is the son now?
24. 24.Solve: p/5 + p/6 = 22. What is p?
25. 25.The length of a rectangle is 3 cm more than its width. Its perimeter is 122 cm. What is its width (in cm)?
26. 26.The length of a rectangle is 6 cm more than its width. Its perimeter is 132 cm. What is its width (in cm)?
27. 27.A father is 11 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?
28. 28.A father is 10 years older than his son. In 8 years, the father will be twice as old as his son. How old is the son now?
29. 29.A father is 36 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?
30. 30.Solve: y/4 + y/6 = 30. What is y?
31. 31.Solve: 6(p − 2) = 3p + 21. What is p?
32. 32.Solve: y/4 + y/6 = 10. What is y?
33. 33.The sum of four consecutive whole numbers is 78. What is the largest of them?
34. 34.Solve: 8m + 18 = 2m + 84. What is m?
35. 35.Solve: y/2 + y/4 = 18. What is y?
36. 36.Solve: 3t + 3 = 2t + 8. What is t?
37. 37.The length of a rectangle is 2 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
38. 38.Solve: n/6 + n/5 = 22. What is n?
39. 39.A father is 18 years older than his son. In 2 years, the father will be three times as old as his son. How old is the son now?
40. 40.A father is 33 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?

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