Solve `-5lt=(5-3x)/2lt=8.`

Explanation

To solve the inequality \(-5 \leq \frac{5 - 3x}{2} \leq 8\), we will follow these steps:

### Step 1: Write the inequality
We start with the inequality:
\[ -5 \leq \frac{5 - 3x}{2} \leq 8 \]

### Step 2: Eliminate the fraction
To eliminate the fraction, we multiply the entire inequality by 2:
\[ 2 \cdot -5 \leq 2 \cdot \frac{5 - 3x}{2} \leq 2 \cdot 8 \]
This simplifies to:
\[ -10 \leq 5 - 3x \leq 16 \]

### Step 3: Isolate the term involving \(x\)
Next, we will isolate the term involving \(x\). We can do this by subtracting 5 from all parts of the inequality:
\[ -10 - 5 \leq -3x \leq 16 - 5 \]
This simplifies to:
\[ -15 \leq -3x \leq 11 \]

### Step 4: Multiply by -1
Now, we will multiply the entire inequality by -1. Remember that when we multiply or divide an inequality by a negative number, we must reverse the inequality signs:
\[ 15 \geq 3x \geq -11 \]
This can also be written as:
\[ -11 \leq 3x \leq 15 \]

### Step 5: Divide by 3
Finally, we divide the entire inequality by 3 to solve for \(x\):
\[ \frac{-11}{3} \leq x \leq 5 \]

### Final Answer
Thus, the solution to the inequality is:
\[ x \in \left[-\frac{11}{3}, 5\right] \]

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