Find the values of 1/x for `2lexle5`.

Explanation

To solve the problem of finding the values of \( \frac{1}{x} \) for \( 2 \leq x \leq 5 \), we can follow these steps:

### Step 1: Understand the given inequality
We are given that \( x \) lies between 2 and 5, inclusive. This means:
\[ 2 \leq x \leq 5 \]

### Step 2: Take the reciprocal of the inequality
When we take the reciprocal of an inequality, the direction of the inequality changes. Therefore, we need to find the reciprocal of the endpoints of the interval:
- The reciprocal of 2 is \( \frac{1}{2} \).
- The reciprocal of 5 is \( \frac{1}{5} \).

Thus, taking the reciprocal of the entire inequality gives us:
\[ \frac{1}{5} \leq \frac{1}{x} \leq \frac{1}{2} \]

### Step 3: Rearrange the inequality
Now we can rearrange the inequality:
\[ \frac{1}{5} \leq \frac{1}{x} \leq \frac{1}{2} \]

### Step 4: Write the final interval
From the rearranged inequality, we can conclude that:
\[ \frac{1}{x} \text{ belongs to the closed interval } \left[ \frac{1}{5}, \frac{1}{2} \right] \]

### Final Answer
Thus, the values of \( \frac{1}{x} \) for \( 2 \leq x \leq 5 \) are:
\[ \frac{1}{x} \in \left[ \frac{1}{5}, \frac{1}{2} \right] \]

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