The equation given is:

\[
|b - 9| = 20
\]

To solve this, we break it into two cases because the absolute value of a number can be either positive or negative.

### Case 1:
\[
b - 9 = 20
\]
Solving for \(b\):
\[
b = 20 + 9 = 29
\]

### Case 2:
\[
b - 9 = -20
\]
Solving for \(b\):
\[
b = -20 + 9 = -11
\]

Thus, the solutions are:
\[
b = 29 \quad \text{or} \quad b = -11
\]

Would you like further explanation or more details?

Here are some related questions:
1. What is the concept behind absolute values?
2. How do you handle absolute value inequalities?
3. What happens if \( |b - 9| = 0 \)?
4. Can absolute values ever result in negative solutions?
5. How do absolute values apply to real-world problems?

**Tip:** Always split absolute value equations into two cases: one for the positive and one for the negative scenario!

Learn how to solve the absolute value equation |b - 9| = 20 by splitting it into two cases. This problem covers key algebraic concepts and the absolute value theorem. Suitable for students in Grades 6-8, this guide includes a detailed, step-by-step solution.

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