Question

Solve for n and graph the solution.

n - 16 ≥ -6 or n + 6 ≤ 1

| | | | | | | |
-10 -5. 0 5 10 15 20 25

Answer 1

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:

1. An arrow pointing to the right starting at 10 (including 10).
2. 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 \( n \geq 10 \).