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To solve the given absolute value inequality, let's start by analyzing the problem provided:

### Problem
The inequality is:

\[
-8 |x - 1| \geq -48
\]

### Step 1: Simplify the Inequality

First, divide both sides by -8. Remember, when dividing by a negative number, the inequality sign flips:

\[
|x - 1| \leq 6
\]

### Step 2: Rewrite Without Absolute Value Bars

To solve the absolute value inequality \(|x - 1| \leq 6\), we can rewrite it as two inequalities:

\[
-6 \leq x - 1 \leq 6
\]

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

Now, solve for \(x\) by adding 1 to all parts of the inequality:

\[
-6 + 1 \leq x - 1 + 1 \leq 6 + 1
\]

\[
-5 \leq x \leq 7
\]

### Step 4: Select the Correct Choice

The correct answer matches option **B: \(x - 1 \leq 6\) or \(x - 1 \geq -6\).**

### Step 5: Express the Solution in Interval Notation

The solution in interval notation is:

\[
[-5, 7]
\]

### Answer

- **Choice for rewriting without absolute value bars:** B.
- **Solution set in interval notation:** \([-5, 7]\)

Would you like further details or explanations? Here are some related questions you might consider:

1. What are the rules for solving absolute value inequalities?
2. How does dividing by a negative number affect an inequality?
3. Can you solve an inequality that involves an absolute value expression?
4. What are some common mistakes when solving absolute value inequalities?
5. How can you verify that your solution to an inequality is correct?

**Tip:** Remember to always check the direction of the inequality sign when dividing or multiplying by a negative number.

Solve the absolute value inequality: -8|x - 1| ≥ -48.

Learn how to solve the absolute value inequality -8|x - 1| ≥ -48 using algebraic methods. This step-by-step solution involves dividing by a negative number, flipping the inequality sign, and solving for x. Suitable for Grades 8-10 students.

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