https://file.aiquickdraw.com/mathbot/file/1726495971739f9tobml8.jpg

The equation shown in the image is:

\[
|5 - b| = 12
\]

To solve this absolute value equation, we need to consider two cases based on the property of absolute values:

1. \( 5 - b = 12 \)
2. \( 5 - b = -12 \)

### Case 1:
\[
5 - b = 12
\]
Subtract 5 from both sides:
\[
-b = 12 - 5
\]
\[
-b = 7
\]
Multiply both sides by -1:
\[
b = -7
\]

### Case 2:
\[
5 - b = -12
\]
Subtract 5 from both sides:
\[
-b = -12 - 5
\]
\[
-b = -17
\]
Multiply both sides by -1:
\[
b = 17
\]

### Solution:
The two solutions are \( b = -7 \) and \( b = 17 \).

Would you like more details or have any questions?

Here are five related questions for further practice:
1. Solve \( |x + 4| = 9 \).
2. Solve \( |2 - t| = 5 \).
3. Solve \( |3p - 7| = 2 \).
4. Solve \( |k + 6| = 10 \).
5. Solve \( |x - 4| = 3 \).

**Tip:** Always remember that absolute value equations can have two possible solutions based on the definition \( |a| = b \) implies \( a = b \) or \( a = -b \).

Learn how to solve the absolute value equation |5 - b| = 12 step-by-step. This problem involves breaking down the absolute value into two cases and solving the corresponding linear equations. Suitable for students in Grades 7-9.

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