Question

Solve the inequality and graph the solution.
3(q+27)>63
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 \(3(q + 27) > 63\), follow these steps:

1. Start by distributing the \(3\):
\[
3q + 81 > 63
\]

2. Next, subtract \(81\) from both sides:
\[
3q > 63 - 81
\]
\[
3q > -18
\]

3. Finally, divide both sides by \(3\):
\[
q > -6
\]

The solution to the inequality is \(q > -6\).

### Endpoint Selection
- The endpoint here is \(-6\).
- Since \(q > -6\) does not include \(-6\), we will represent it as an open endpoint.

### Graphing the Solution
1. Plot the point \(-6\) on the number line with an open circle (since \(-6\) is not included).
2. Shade the area to the right of \(-6\) to represent all values greater than \(-6\).

Here's a rough sketch of what the number line looks like:

```
<---|----|----|----|----|----|----|----|----|----|--->
-8 -7 -6 -5 -4 -3 -2 -1 0
( )
```

In this graph:
- The open circle at \(-6\) indicates that \(-6\) is not part of the solution.
- The shading to the right illustrates that all values greater than \(-6\) are included in the solution.