To solve the inequality \( n - 16 \geq -6 \) or \( n + 6 \leq 1 \), we need to solve each individual inequality separately.
Step 1: Solve the first inequality
We start with:
\[ n - 16 \geq -6 \]
Add 16 to both sides:
\[ n \geq -6 + 16 \] \[ n \geq 10 \]
Step 2: Solve the second inequality
Now, we solve:
\[ n + 6 \leq 1 \]
Subtract 6 from both sides:
\[ n \leq 1 - 6 \] \[ n \leq -5 \]
Step 3: Combine the results
The solutions can be summarized as:
- \( n \geq 10 \)
- \( n \leq -5 \)
Since this is an "or" inequality, the solution set includes values from both ranges.
Step 4: Graph the solution
On the number line, the solution can be represented as:
- An arrow pointing to the right starting at 10 (including 10).
- An arrow pointing to the left starting at -5 (including -5).
The graph would look like this:
| | | | | | | |
-10 -5. 0 5 10 15 20 25
<-- [----> [---->
Summary of the solution:
- The solution set is \( n \leq -5 \) or \( n \geq 10 \).