Question

Solve the inequality and graph the solution.
p/2+5>4

Answer 1

To solve the inequality \( \frac{p}{2} + 5 > 4 \), follow these steps:

1. **Subtract 5 from both sides**:
\[
\frac{p}{2} > 4 - 5
\]
\[
\frac{p}{2} > -1
\]

2. **Multiply both sides by 2** (note that multiplying or dividing by a positive number does not change the inequality):
\[
p > -2
\]

The solution to the inequality is \( p > -2 \).

### Graphing the solution:

To graph \( p > -2 \):

- Draw a number line.
- Mark the point at -2.
- Since it's a strict inequality (greater than, not greater than or equal to), draw an open circle at -2 to indicate that -2 is not included in the solution.
- Shade to the right of -2 to show all numbers greater than -2.

Here’s a simple representation of the graph:

```
<---o========================>
-2
```

In this graph:
- The open circle (o) at -2 indicates that -2 is not part of the solution.
- The shaded line to the right indicates all values greater than -2 are included in the solution.