We need to solve the equation:

\[
5|x + 6| + 8 = -6|x + 6| + 8
\]

### Step 1: Simplify the equation
First, subtract 8 from both sides:

\[
5|x + 6| = -6|x + 6|
\]

### Step 2: Combine like terms
Now, add \(6|x + 6|\) to both sides to move the absolute value terms to one side:

\[
5|x + 6| + 6|x + 6| = 0
\]

This simplifies to:

\[
11|x + 6| = 0
\]

### Step 3: Solve for the absolute value
For the equation \(11|x + 6| = 0\), divide both sides by 11:

\[
|x + 6| = 0
\]

### Step 4: Solve the absolute value equation
Since the absolute value of any number is zero only if the number itself is zero, we have:

\[
x + 6 = 0
\]

Thus:

\[
x = -6
\]

### Final Answer:
The solution to the equation is \(x = -6\).

---

Would you like a more detailed explanation of the process? Let me know if you have any questions!

### Related Questions:
1. What is the effect of absolute value on the solution of equations?
2. How would the solution change if the equation were \(5|x + 6| + 8 = 6|x + 6| + 8\)?
3. What happens if you have a negative coefficient outside of the absolute value?
4. How do you solve equations that involve multiple absolute values?
5. How can you check if a solution satisfies the original equation?

**Tip:** Always isolate the absolute value first before solving, as it simplifies the process.

Learn how to solve the absolute value equation 5|x + 6| + 8 = -6|x + 6| + 8 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving absolute value equations and isolating the absolute value expression. Suitable for students in Grades 8-10.

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