Solve the inequations
`0lt(-x)/(3)lt1`.

Answer

To solve the inequation \( 0 < \frac{-x}{3} < 1 \), we will break it down into two parts and solve each part step by step.

### Step 1: Break down the compound inequality
We can separate the compound inequality into two parts:
1. \( 0 < \frac{-x}{3} \)
2. \( \frac{-x}{3} < 1 \)

### Step 2: Solve the first part \( 0 < \frac{-x}{3} \)
To solve this, we will multiply both sides by -3. Remember, when we multiply or divide by a negative number, we must reverse the inequality sign.

\[ 0 \cdot (-3) > \frac{-x}{3} \cdot (-3) \]
This simplifies to:
\[ 0 > x \]
or
\[ x < 0 \]

### Step 3: Solve the second part \( \frac{-x}{3} < 1 \)
Similarly, we will multiply both sides by -3 and reverse the inequality sign:

\[ \frac{-x}{3} \cdot (-3) > 1 \cdot (-3) \]
This simplifies to:
\[ x > -3 \]

### Step 4: Combine the results
Now we have two inequalities:
1. \( x < 0 \)
2. \( x > -3 \)

Combining these gives us:
\[ -3 < x < 0 \]

### Final Answer
Thus, the solution to the inequation \( 0 < \frac{-x}{3} < 1 \) is:
\[ x \in (-3, 0) \]