Let's start solving the given problem step by step:
1. We have the compound inequality 1/4 < 2x - 7/2 < 5.
2. The goal is to isolate x in the middle of the inequality. Firstly, let's make 2x the subject of the inequality. We can do this by adding 7/2 to all parts of the inequality. We get 1/4 + 7/2 < 2x < 5 + 7/2.
3. Simplify the fractions on both sides: 15/4 < 2x < 17/2
4. The next step is to get x alone. We can achieve this by dividing all parts of the inequality by 2: 15/8 < x < 17/4
Therefore, the solution to the compound inequality 1/4 < 2x - 7/2 < 5 is 15/8 < x < 17/4. This means x can be any number between 15/8 and 17/4.