Question

Solve the inequality and graph the solution.
5(r+3)+9<4
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 \( 5(r + 3) + 9 < 4 \), we will start by simplifying the expression.

1. Distribute the \( 5 \):
\[
5r + 15 + 9 < 4
\]

2. Combine like terms:
\[
5r + 24 < 4
\]

3. Subtract \( 24 \) from both sides:
\[
5r < 4 - 24
\]
\[
5r < -20
\]

4. Divide both sides by \( 5 \):
\[
r < -4
\]

### Graphing the solution
The solution \( r < -4 \) means that \( r \) can take any value less than \(-4\).

- **Endpoint**: The endpoint is \(-4\).
- **Closed/Open**: Since the inequality is strict (\(<\)), we will use an open circle at \(-4\) to indicate that \(-4\) is not included in the solution.

### Graph
On a number line, we will:

1. Place an open circle at \(-4\).
2. Shade to the left of \(-4\) to indicate all numbers less than \(-4\).

#### Number Line Representation:
```
<---o========================>
-5 -4 -3 -2 -1 0
```

- The open circle at \(-4\) indicates that \(-4\) is not part of the solution, and the shaded area to the left represents all values less than \(-4\).