To solve the equation \( | -4b + 8 | = 44 \), we need to address the absolute value by considering two possible cases:

### Case 1: Positive scenario (without the absolute value)
\[
-4b + 8 = 44
\]
Solve for \( b \):
\[
-4b = 44 - 8
\]
\[
-4b = 36
\]
\[
b = \frac{36}{-4} = -9
\]

### Case 2: Negative scenario (opposite of what's inside the absolute value)
\[
-4b + 8 = -44
\]
Solve for \( b \):
\[
-4b = -44 - 8
\]
\[
-4b = -52
\]
\[
b = \frac{-52}{-4} = 13
\]

### Final solutions:
The two possible values for \( b \) are \( b = -9 \) and \( b = 13 \).

Would you like more details on any of the steps?

Here are some related questions for further practice:
1. Solve \( |2x - 3| = 11 \).
2. Solve \( |5x + 7| = 12 \).
3. Solve \( |3x - 9| = 18 \).
4. Solve \( |x + 4| = 20 \).
5. Solve \( |6x - 5| = 30 \).

**Tip:** When solving absolute value equations, always remember to consider both the positive and negative scenarios.

This guide explains how to solve the absolute value equation |−4b + 8| = 44. Follow a detailed step-by-step approach that explores both positive and negative scenarios, helping students grasp essential algebraic concepts. Ideal for Grades 8-10.

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