`- 3 le 4 - (7x)/(2) le 10`

Explanation

To solve the inequality \(-3 \leq 4 - \frac{7x}{2} \leq 10\), we will break it down into two separate inequalities and solve them step by step.

### Step 1: Break down the compound inequality
We have:
\[ -3 \leq 4 - \frac{7x}{2} \quad \text{and} \quad 4 - \frac{7x}{2} \leq 10 \]

### Step 2: Solve the first inequality
Starting with the first part:
\[ -3 \leq 4 - \frac{7x}{2} \]
Subtract 4 from both sides:
\[ -3 - 4 \leq -\frac{7x}{2} \]
This simplifies to:
\[ -7 \leq -\frac{7x}{2} \]
Now, multiply both sides by -1 (remember to reverse the inequality sign):
\[ 7 \geq \frac{7x}{2} \]
Next, multiply both sides by 2:
\[ 14 \geq 7x \]
Now, divide both sides by 7:
\[ 2 \geq x \quad \text{or} \quad x \leq 2 \]

### Step 3: Solve the second inequality
Now, we solve the second part:
\[ 4 - \frac{7x}{2} \leq 10 \]
Subtract 4 from both sides:
\[ -\frac{7x}{2} \leq 10 - 4 \]
This simplifies to:
\[ -\frac{7x}{2} \leq 6 \]
Multiply both sides by -1 (remember to reverse the inequality sign):
\[ \frac{7x}{2} \geq -6 \]
Multiply both sides by 2:
\[ 7x \geq -12 \]
Now, divide both sides by 7:
\[ x \geq -\frac{12}{7} \]

### Step 4: Combine the results
From the two inequalities, we have:
1. \(x \leq 2\)
2. \(x \geq -\frac{12}{7}\)

Combining these results, we get:
\[ -\frac{12}{7} \leq x \leq 2 \]

### Final Answer
Thus, the solution to the inequality \(-3 \leq 4 - \frac{7x}{2} \leq 10\) is:
\[ x \in \left[-\frac{12}{7}, 2\right] \]