To solve the inequality \(|m+2| + 7 \leq 16\), we can follow these steps:

1. **Isolate the absolute value expression:**
   \[
   |m + 2| + 7 \leq 16
   \]
   Subtract 7 from both sides:
   \[
   |m + 2| \leq 9
   \]

2. **Interpret the absolute value inequality:**
   The inequality \(|m + 2| \leq 9\) means that the expression inside the absolute value, \(m + 2\), is between \(-9\) and \(9\). This can be written as:
   \[
   -9 \leq m + 2 \leq 9
   \]

3. **Solve for \(m\):**
   To find \(m\), we subtract 2 from all parts of the inequality:
   \[
   -9 - 2 \leq m + 2 - 2 \leq 9 - 2
   \]
   Simplifying this, we get:
   \[
   -11 \leq m \leq 7
   \]

Therefore, the solution to the inequality is:

\[
-11 \leq m \leq 7
\]

This means that \(m\) can take any value between \(-11\) and \(7\), inclusive.

Would you like more details or have any questions?

### Related Questions:

1. How would the solution change if the inequality was \(|m+2| + 7 < 16\)?
2. What happens if the absolute value inequality was \(|m+2| - 7 \leq 16\)?
3. How do you solve inequalities involving absolute values with a variable on both sides?
4. Can you explain how to graph the solution \(-11 \leq m \leq 7\) on a number line?
5. What are the steps to solve \(|3m - 4| + 2 \leq 8\)?

### Tip:

When dealing with absolute value inequalities, remember that \(|x| \leq a\) can be rewritten as \(-a \leq x \leq a\), and \(|x| \geq a\) can be rewritten as \(x \leq -a\) or \(x \geq a\). This will help you handle and solve these types of inequalities systematically.

Learn how to solve the absolute value inequality |m+2| + 7 ≤ 16 step-by-step. Understand the concept of isolating variables, interpreting absolute value inequalities, and determining the solution set. Suitable for students in Grades 7-9.

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