9x - 14 < 5x + 2 < 3x + 12

This inequality is actually two inequalities. Let's solve them separately:

1. 9x - 14 < 5x + 2

First, subtract 5x from both sides to get: 4x - 14 < 2

Then, add 14 to both sides to get: 4x < 16

Finally, divide both sides by 4 to get: x < 4

2. 5x + 2 < 3x + 12

First, subtract 3x from both sides to get: 2x + 2 < 12

Then, subtract 2 from both sides to get: 2x < 10

Finally, divide both sides by 2 to get: x < 5

So, the solution to the inequality 9x - 14 < 5x + 2 < 3x + 12 is x < 4 and x < 5. Since x must satisfy both conditions, the final solution is x < 4.