Find the values of `1/x` for `-5lexle-1`.

Explanation

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

### Step 1: Understand the given inequality
We are given that \( x \) lies in the interval \( [-5, -1] \). This means \( x \) can take any value between -5 and -1, inclusive.

### Step 2: Take the reciprocal of the inequality
When we take the reciprocal of a negative number, the inequality sign reverses. Therefore, we need to consider the reciprocal of the endpoints of the interval:

- The reciprocal of -5 is \( \frac{1}{-5} = -\frac{1}{5} \)
- The reciprocal of -1 is \( \frac{1}{-1} = -1 \)

### Step 3: Reverse the inequality
Since we are taking the reciprocal of the entire inequality \( -5 \leq x \leq -1 \), we reverse the inequality signs:

\[ -1 \leq \frac{1}{x} \leq -\frac{1}{5} \]

### Step 4: Write the final interval
This means that the values of \( \frac{1}{x} \) lie in the interval:

\[ [-1, -\frac{1}{5}] \]

### Conclusion
Thus, the values of \( \frac{1}{x} \) for \( -5 \leq x \leq -1 \) are in the interval \( [-1, -\frac{1}{5}] \).

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