To solve the inequality \(-3 |a| - 5 \leq -17\), let's break it down step by step:

### Step 1: Isolate the term involving \(|a|\)

\[
-3 |a| - 5 \leq -17
\]
Add 5 to both sides:
\[
-3 |a| \leq -17 + 5
\]
\[
-3 |a| \leq -12
\]

### Step 2: Divide by -3

Since we're dividing by a negative number, we need to **reverse the inequality**:

\[
|a| \geq \frac{-12}{-3}
\]
\[
|a| \geq 4
\]

### Step 3: Solve for \(a\)

The absolute value inequality \(|a| \geq 4\) means that:
\[
a \geq 4 \quad \text{or} \quad a \leq -4
\]

### Final Answer:
\[
a \geq 4 \quad \text{or} \quad a \leq -4
\]

This is the solution to the inequality.

Would you like more details or have any questions?

Here are some related questions:
1. How do we handle absolute values in inequalities?
2. What happens when dividing inequalities by a negative number?
3. Can you provide more examples of inequalities involving absolute values?
4. How would the solution change if the inequality was strict (e.g., \(-3 |a| - 5 < -17\))?
5. How do we graph the solution on a number line?

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

Discover how to solve the inequality -3 |a| - 5 ≤ -17 step-by-step. Learn key concepts like handling absolute values, reversing inequalities when dividing by negative numbers, and solving for a variable. Ideal for students in Grades 8-10.

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