We are given the compound inequality:

\[
-17 \leq u - 11 - 3u \leq -7
\]

Let's solve this step by step.

### Step 1: Simplify both sides of the inequality
First, combine like terms in the middle expression:

\[
u - 11 - 3u = -2u - 11
\]

So the inequality becomes:

\[
-17 \leq -2u - 11 \leq -7
\]

### Step 2: Solve the left inequality
Now solve the left part of the inequality:

\[
-17 \leq -2u - 11
\]

Add 11 to both sides:

\[
-17 + 11 \leq -2u
\]

\[
-6 \leq -2u
\]

Divide both sides by -2 (remember, dividing by a negative number reverses the inequality sign):

\[
3 \geq u \quad \text{or} \quad u \leq 3
\]

### Step 3: Solve the right inequality
Now solve the right part of the inequality:

\[
-2u - 11 \leq -7
\]

Add 11 to both sides:

\[
-2u \leq 4
\]

Divide by -2 (again, reverse the inequality sign):

\[
u \geq -2
\]

### Step 4: Combine the results
We now have:

\[
-2 \leq u \leq 3
\]

### Final Answer:
The solution to the compound inequality is:

\[
u \in [-2, 3]
\]

Would you like more details or have any questions?

Here are five related questions:
1. How do you solve compound inequalities involving fractions?
2. What happens if both inequalities are strict (e.g., \( < \) instead of \( \leq \))?
3. How do we graph the solution of compound inequalities on a number line?
4. What is the method to solve absolute value inequalities?
5. How do you deal with inequalities that require multiplying by negative numbers?

**Tip:** Always remember that multiplying or dividing by a negative number reverses the inequality sign.

Learn how to solve the compound inequality -17 ≤ u - 11 - 3u ≤ -7 with a detailed step-by-step solution. This problem covers essential algebraic concepts like simplifying and solving inequalities, reversing inequality signs, and more. Suitable for students in Grades 9-10.

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