Question

Solve the inequality and graph the solution.
18≥2(q+17)
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 \( 18 \geq 2(q + 17) \), we start by simplifying it step by step.

1. **Distribute** the 2 on the right side:
\[
18 \geq 2q + 34
\]

2. **Subtract 34** from both sides:
\[
18 - 34 \geq 2q
\]
\[
-16 \geq 2q
\]

3. **Divide by 2** (remember that dividing by a positive number does not change the inequality sign):
\[
-8 \geq q
\]

This can be rewritten as:
\[
q \leq -8
\]

### Graphing the Solution

The solution \( q \leq -8 \) means that \( q \) can take any value less than or equal to \(-8\).

- **Endpoint**: The endpoint is \(-8\).
- Since we have \( q \leq -8\), this endpoint will be closed (indicating that \(-8\) is included in the solution).
- **Direction**: The solution will be towards the left, meaning all values less than -8.

### Final Representation
On a number line:
- A closed dot (●) is placed at \(-8\) to indicate that \(-8\) is included.
- A line extends to the left from \(-8\) to indicate all values less than \(-8\).

### Annotation
- **Endpoint**: -8 (closed dot)
- **Ray direction**: Leftward, indicating all values less than -8.

Here is how you would describe it on the graph:

- Place a closed dot at \(-8\).
- Draw an arrow pointing left from \(-8\) to indicate that values are included all the way to negative infinity.

### Example of Graph Representation
```
<-----●=========>
-8
```

This visual means the solution set includes \(-8\) and all numbers to the left of it.