To solve the inequality:

\[
|x+6| - 4 < 5
\]

### Step 1: Isolate the absolute value expression
First, add \(4\) to both sides:

\[
|x+6| < 9
\]

### Step 2: Set up two cases for the absolute value
The expression \(|x+6| < 9\) means that the expression inside the absolute value is between \(-9\) and \(9\):

\[
-9 < x + 6 < 9
\]

### Step 3: Solve for \(x\)
Now subtract \(6\) from all three parts of the inequality:

\[
-9 - 6 < x < 9 - 6
\]
\[
-15 < x < 3
\]

### Solution:
The solution to the inequality is:

\[
x \in (-15, 3)
\]

This means \(x\) lies between \(-15\) and \(3\), but does not include these endpoints.

Would you like further details, or have any questions?

Here are 5 related questions for you:
1. How do you solve inequalities involving absolute value with greater than instead of less than?
2. What changes if the inequality was \(|x+6| - 4 \leq 5\)?
3. How can we graph the solution set of this inequality?
4. Can you explain the difference between a strict inequality and a non-strict inequality?
5. What happens if the absolute value inequality results in a negative number?

**Tip:** Always isolate the absolute value expression first before handling inequalities.

Learn how to solve the absolute value inequality |x+6|-4<5 with a clear, step-by-step approach. This problem involves isolating the absolute value expression and solving inequalities, suitable for students in Grades 8-10.

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