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Let's solve the compound inequality step by step:

The inequality is given as:

\[
4 \geq \frac{3u - 7}{2} \geq -5
\]

### Step 1: Solve the left part of the inequality
\[
4 \geq \frac{3u - 7}{2}
\]

Multiply both sides by 2 to eliminate the denominator:
\[
8 \geq 3u - 7
\]

Now, add 7 to both sides:
\[
15 \geq 3u
\]

Finally, divide by 3:
\[
5 \geq u
\]

This simplifies to:
\[
u \leq 5
\]

### Step 2: Solve the right part of the inequality
\[
\frac{3u - 7}{2} \geq -5
\]

Multiply both sides by 2:
\[
3u - 7 \geq -10
\]

Now, add 7 to both sides:
\[
3u \geq -3
\]

Finally, divide by 3:
\[
u \geq -1
\]

### Step 3: Combine the inequalities
We have:
\[
-1 \leq u \leq 5
\]

### Step 4: Graph the solution
On the number line, plot the endpoints -1 and 5. Since the inequality includes the equality (≤), both endpoints will be closed circles.

The solution is the segment between -1 and 5, inclusive.

Do you have any questions or would you like more details on this?

Here are 5 related questions:
1. How do you solve compound inequalities involving absolute values?
2. What are the differences between open and closed circles on a graph?
3. How do you handle inequalities when multiplying or dividing by negative numbers?
4. Can compound inequalities have more than two parts?
5. How do you check if your solution to an inequality is correct?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing by a negative number!

Solve for u and graph the solution: 4 ≥ (3u - 7)/2 ≥ -5

Step-by-step solution for solving the compound inequality 4 ≥ (3u - 7)/2 ≥ -5. Learn how to isolate variables, solve inequalities, and graph the solution on a number line. Suitable for students in Grades 7-9.

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