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The equation to solve is:

\[
4 |x + 7| + 8 = 32
\]

### Step 1: Isolate the absolute value expression
Subtract 8 from both sides:

\[
4 |x + 7| = 32 - 8
\]

\[
4 |x + 7| = 24
\]

### Step 2: Divide both sides by 4

\[
|x + 7| = \frac{24}{4}
\]

\[
|x + 7| = 6
\]

### Step 3: Solve the absolute value equation
The equation \( |x + 7| = 6 \) leads to two cases:

1. \( x + 7 = 6 \)
2. \( x + 7 = -6 \)

#### Case 1:
\[
x + 7 = 6
\]
Subtract 7 from both sides:

\[
x = 6 - 7
\]

\[
x = -1
\]

#### Case 2:
\[
x + 7 = -6
\]
Subtract 7 from both sides:

\[
x = -6 - 7
\]

\[
x = -13
\]

### Step 4: Solution
The solutions are \( x = -1 \) and \( x = -13 \).

The correct answer is **A. \( x = -1 \) and \( x = -13 \)**.

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Would you like more details on any step? 

Here are 5 related questions for further practice:
1. Solve: \( 3 |x - 4| + 5 = 20 \).
2. Solve: \( 2 |x + 9| - 7 = 1 \).
3. How do you graph absolute value functions?
4. Solve: \( |2x + 3| = 7 \).
5. What are the steps to solve an inequality involving absolute value?

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

Learn how to solve the absolute value equation 4|x + 7| + 8 = 32 with a detailed step-by-step explanation. This algebraic problem involves isolating the absolute value expression and solving for both positive and negative cases. Suitable for students in Grades 8-10.

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