Question

N.5 Graph solutions to one-step inequalities
TMX
Solve the inequality and graph the solution.
2p≤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 \(2p \leq 6\), we first isolate \(p\) by dividing both sides of the inequality by 2:

\[
p \leq \frac{6}{2}
\]

This simplifies to:

\[
p \leq 3
\]

Now we have the inequality \(p \leq 3\).

### Graphing the Solution:
1. **Plot the endpoint**: Place a point at \(p = 3\).
2. **Type of endpoint**: Since the inequality is "less than or equal to" (\(\leq\)), we use a closed dot at \(3\) to indicate that \(3\) is included in the solution.
3. **Direction of the ray**: Since we are looking for values of \(p\) that are less than or equal to \(3\), draw a ray that extends to the left from the closed dot.

This is how the graph would look:

```
<---●========>
3
```

- The closed dot at \(3\) shows that \(3\) is part of the solution.
- The arrow extending to the left indicates all values less than \(3\) are included in the solution.

The solution set in interval notation is \((-\infty, 3]\).