Question

N.5 Graph solutions to one-step inequalities
TMX
Solve the inequality and graph the solution.
n+1≥6
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

Answer 1

To solve the inequality \( n + 1 \geq 6 \), we need to isolate \( n \).

1. **Subtract 1 from both sides:**
\[
n + 1 - 1 \geq 6 - 1
\]
\[
n \geq 5
\]

The solution to the inequality is \( n \geq 5 \).

### Graphing the Solution:

1. **Plot the endpoint**: Mark the point \( 5 \) on the number line.
2. **Select the type of endpoint**: Since the inequality is "greater than or equal to" (\(\geq\)), we will use a **closed dot** on the point \( 5 \) to indicate that \( 5 \) is included in the solution.
3. **Draw the ray**: From the point \( 5 \), draw a ray that extends to the right, indicating all numbers greater than \( 5 \).

The graph of the inequality \( n \geq 5 \) looks like this:

```
<---|---|---|---|---|---|---|---|---|--->
3 4 • 6 7 8
n
```

The closed dot on \( 5 \) indicates it is part of the solution, and the arrow extends to the right, indicating that there are infinitely many solutions greater than \( 5 \).