Question

Solve the compound inequality. Graph the solutions.
1 < 2p - 3 < 13

Answer 1

To solve the compound inequality, we will solve the individual inequalities and then combine the solutions.

1 < 2p - 3:
Adding 3 to both sides, we get:
1 + 3 < 2p - 3 + 3
4 < 2p
Dividing both sides by 2, we get:
4/2 < 2p/2
2 < p

2p - 3 < 13:
Adding 3 to both sides, we get:
2p - 3 + 3 < 13 + 3
2p < 16
Dividing both sides by 2, we get:
2p/2 < 16/2
p < 8

The solution for the compound inequality is 2 < p < 8.

To graph the solutions on a number line, we will plot a closed circle at 2 and an open circle at 8, and shade the region between them.

The graph is as follows:

```
-∞ ┌─────┲━━━━━o─────o━━━━━┱─────┐ ∞
2 8
```