Let's solve the inequality step by step:

We are given:

\[
| -3u | - 9 \geq -6
\]

### Step 1: Isolate the absolute value expression.
Add 9 to both sides to get:

\[
| -3u | \geq -6 + 9
\]

\[
| -3u | \geq 3
\]

### Step 2: Solve the absolute value inequality.
For any absolute value inequality \( |x| \geq a \), where \( a \geq 0 \), the solution is:

\[
x \leq -a \quad \text{or} \quad x \geq a
\]

Applying this to \( | -3u | \geq 3 \), we have:

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

### Step 3: Solve each inequality.

- For \( -3u \leq -3 \):

  Divide both sides by -3 (remember to flip the inequality sign when dividing by a negative number):

  \[
  u \geq 1
  \]

- For \( -3u \geq 3 \):

  Divide both sides by -3 (again, flip the inequality sign):

  \[
  u \leq -1
  \]

### Step 4: Combine the solutions.

The solution is:

\[
u \geq 1 \quad \text{or} \quad u \leq -1
\]

Thus, the final solution in interval notation is:

\[
(-\infty, -1] \cup [1, \infty)
\]

Let me know if you'd like more details or have any questions.

Here are 5 related questions:
1. How do you solve absolute value equations with two sides?
2. Can you solve \( |x + 2| \geq 5 \)?
3. What happens if the inequality is \( |x| < a \) instead?
4. What does it mean to flip the inequality when dividing by a negative number?
5. How do you solve compound inequalities?

**Tip:** When dealing with absolute value inequalities, always isolate the absolute value expression before solving.

Explore how to solve the absolute value inequality |–3u|–9 ≥ –6 using algebraic techniques. This step-by-step solution isolates the absolute value expression and applies properties of inequalities, ideal for students in Grades 8-10. Key concepts include absolute value inequalities and handling negative values in inequalities.

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