The inequality you provided is:

\[
-8| -c | \geq -8
\]

Let's break it down and solve for \( c \).

### Step 1: Isolate the absolute value term
First, we divide both sides of the inequality by \(-8\). When dividing or multiplying an inequality by a negative number, we must **reverse the inequality sign**.

\[
| -c | \leq 1
\]

### Step 2: Simplify the absolute value
Since \( | -c | = | c | \), the inequality becomes:

\[
| c | \leq 1
\]

### Step 3: Solve for \( c \)
This absolute value inequality can be rewritten as:

\[
-1 \leq c \leq 1
\]

Thus, the solution is:

\[
c \in [-1, 1]
\]

### Conclusion:
The variable \( c \) is between \(-1\) and \(1\), inclusive.

Would you like more details or have any questions?

Here are 5 related questions to explore this further:
1. How do we solve absolute value inequalities in general?
2. What happens if the inequality sign had been \(>\) instead of \( \geq \)?
3. How do you solve a system of inequalities with absolute values?
4. Can absolute values have complex numbers inside them?
5. What are some real-world applications of absolute value inequalities?

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

Understand how to solve the absolute value inequality –8|–c| ≥ –8 with a detailed explanation. This guide covers key algebraic concepts such as inequalities and absolute values, emphasizing the proper handling of inequalities when multiplying or dividing by negative numbers. Suitable for students in Grades 8-10.

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