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The problem asks to solve for \( b \) in the absolute value equation:

\[
\left| \frac{b}{12} \right| = 8
\]

### Step-by-step solution:

1. Start by understanding that the absolute value of an expression is always non-negative. The equation \( \left| \frac{b}{12} \right| = 8 \) means that \( \frac{b}{12} \) can either be 8 or -8.

2. Split the equation into two cases:
   - Case 1: \( \frac{b}{12} = 8 \)
   - Case 2: \( \frac{b}{12} = -8 \)

3. Solve each case:
   - For Case 1:
     \[
     \frac{b}{12} = 8 \implies b = 8 \times 12 = 96
     \]
   - For Case 2:
     \[
     \frac{b}{12} = -8 \implies b = -8 \times 12 = -96
     \]

### Final Answer:
The solutions for \( b \) are \( b = 96 \) and \( b = -96 \).

Would you like further clarification or more details?

Here are 5 related questions to practice:

1. How do you solve an absolute value equation involving a fraction?
2. What is the general approach to solving equations with absolute values?
3. How do you handle absolute value inequalities?
4. What are the properties of absolute value functions?
5. How do you graph absolute value equations?

**Tip:** When solving absolute value equations, always check for two possible cases: the positive and negative scenarios!

Solve for all values of b in simplest form: |b/12| = 8

Learn how to solve the absolute value equation |b/12| = 8 with a detailed step-by-step solution. This problem involves understanding absolute value properties and basic algebra. Suitable for students in Grades 7-9.

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