Question

Graph the compound inequality.
x>0 and x<1
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.

Answer 1

To graph the compound inequality \( x > 0 \) and \( x < 1 \), follow these steps:

1. **Identify the endpoints**: The endpoints in this case are \( x = 0 \) and \( x = 1 \).

2. **Determine the type of endpoints**:
- For \( x > 0 \), the endpoint at \( x = 0 \) is *open* (not included).
- For \( x < 1 \), the endpoint at \( x = 1 \) is *open* (not included).

3. **Graph the inequality**:
- Draw a number line.
- Place an open circle at \( x = 0 \) to indicate that 0 is not included.
- Place another open circle at \( x = 1 \) to indicate that 1 is not included.
- Shade the region between 0 and 1, indicating all values of \( x \) that are greater than 0 and less than 1.

The final graph will show an open circle at both \( 0 \) and \( 1 \) with a shaded line between them, representing the solution set for \( 0 < x < 1 \).

### Visual Representation

```
---(0)=================(1)---
```

Where:
- `(0)` and `(1)` are open circles (indicating exclusion of endpoints).
- The line between the two open circles represents all numbers in the interval \( (0, 1) \).