https://file.aiquickdraw.com/mathbot/file/1725971665314m1n6w7ac.jpg

The equation in the image is:

\[
2|w + 5| - 37 = -7
\]

### Solution Steps:

1. **Isolate the absolute value term**:
   \[
   2|w + 5| - 37 = -7
   \]
   Add 37 to both sides:
   \[
   2|w + 5| = 30
   \]

2. **Solve for the absolute value**:
   Divide both sides by 2:
   \[
   |w + 5| = 15
   \]

3. **Solve the absolute value equation**:
   The equation \(|w + 5| = 15\) can be split into two cases:
   
   - Case 1: \( w + 5 = 15 \)
     \[
     w = 15 - 5 = 10
     \]
   
   - Case 2: \( w + 5 = -15 \)
     \[
     w = -15 - 5 = -20
     \]

### Final Solution:
The solutions to the equation are:
\[
w = 10 \quad \text{or} \quad w = -20
\]

Would you like more details or have any questions? Here are five related questions to explore:

1. How do we solve absolute value equations in general?
2. What is the geometric interpretation of absolute value?
3. What if the right-hand side of the equation was a negative number? Would it affect the solution?
4. How do you solve inequalities involving absolute values?
5. How do we graph equations with absolute values?

**Tip**: Always check the original equation after solving, to ensure that no extraneous solutions were introduced, especially in absolute value problems.

Learn how to solve the absolute value equation 2|w + 5| - 37 = -7 with a clear step-by-step breakdown. This problem involves isolating the absolute value, solving the cases, and arriving at the solutions w = 10 or w = -20. Suitable for students in Grades 8-10.

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