https://file.aiquickdraw.com/mathbot/file/1725486505964orzz2vo2.jpg

The equation you provided from the image is:

\[
\frac{|5b - 7|}{10} = 5
\]

To solve for \( b \), follow these steps:

### Step 1: Isolate the absolute value expression.
Multiply both sides by 10 to get rid of the denominator:

\[
|5b - 7| = 50
\]

### Step 2: Set up the two cases for the absolute value.

Case 1: \( 5b - 7 = 50 \)

\[
5b = 50 + 7 \\
5b = 57 \\
b = \frac{57}{5} = 11.4
\]

Case 2: \( 5b - 7 = -50 \)

\[
5b = -50 + 7 \\
5b = -43 \\
b = \frac{-43}{5} = -8.6
\]

### Solution:
The solutions for \( b \) are \( b = 11.4 \) and \( b = -8.6 \).

Would you like more details on any of the steps? 

Here are some related questions:
1. How do you solve absolute value equations?
2. What happens if the absolute value equation has no solution?
3. Can you explain the geometric interpretation of absolute values?
4. How would the equation change if the right side was negative?
5. How does solving an inequality with absolute values differ from solving an equation?

**Tip:** Always remember that absolute value equations usually have two cases to consider because the absolute value can represent both positive and negative scenarios.

Learn how to solve the absolute value equation |5b - 7| / 10 = 5. This problem demonstrates the use of absolute value properties and linear equation techniques, suitable for Grades 9-10.

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