Question

Solve the inequality and graph the solution.
17 < j + 19
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \(17 < j + 19\), we start by isolating \(j\).

1. Subtract 19 from both sides:
\[
17 - 19 < j
\]
This simplifies to:
\[
-2 < j
\]
or equivalently,
\[
j > -2
\]

The solution to the inequality is \(j > -2\).

### Graphing the solution:

1. **Endpoints**: The endpoint of interest is \(-2\).
2. **Open endpoint**: Since the inequality is strict (greater than, not greater than or equal to), we will use an open circle at \(-2\) to indicate that \(-2\) is not included in the solution.
3. **Ray**: The solution extends to the right (toward positive infinity) from \(-2\).

### Graph:
- Draw a number line.
- Place an open circle at \(-2\).
- Shade the region to the right of \(-2\) (indicating all values greater than \(-2\)).

Here's a textual representation of the graph:

```
<---o------------------->
-2
```

- The "o" at \(-2\) represents the open circle.
- The shaded arrow indicates that the values greater than \(-2\) are included in the solution.