` -15 lt (3(x - 2))/(5) le 0`

Explanation

To solve the inequality \(-15 < \frac{3(x - 2)}{5} \leq 0\), we will break it down into two parts and solve each part step by step.

### Step 1: Rewrite the Inequality
The given inequality is:
\[ -15 < \frac{3(x - 2)}{5} \leq 0 \]

### Step 2: Solve the Left Part of the Inequality
First, let's solve the left part:
\[ -15 < \frac{3(x - 2)}{5} \]
To eliminate the fraction, multiply both sides by 5:
\[ -15 \times 5 < 3(x - 2) \]
This simplifies to:
\[ -75 < 3(x - 2) \]
Next, divide both sides by 3:
\[ -25 < x - 2 \]
Now, add 2 to both sides:
\[ -25 + 2 < x \]
This simplifies to:
\[ -23 < x \quad \text{or} \quad x > -23 \]

### Step 3: Solve the Right Part of the Inequality
Now, let's solve the right part:
\[ \frac{3(x - 2)}{5} \leq 0 \]
Again, multiply both sides by 5:
\[ 3(x - 2) \leq 0 \]
Now, divide both sides by 3:
\[ x - 2 \leq 0 \]
Add 2 to both sides:
\[ x \leq 2 \]

### Step 4: Combine the Results
Now we have two inequalities:
1. \(x > -23\)
2. \(x \leq 2\)

Combining these gives us:
\[ -23 < x \leq 2 \]

### Step 5: Write the Final Solution
In interval notation, the solution can be expressed as:
\[ (-23, 2] \]