Question

Solve the inequality and graph the solution.
w+2
2
>
–
1
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:

\[
\frac{w + 2}{2} > -1
\]

we first eliminate the fraction by multiplying both sides by 2 (since 2 is positive, the direction of the inequality remains the same):

\[
w + 2 > -2
\]

Next, we isolate \(w\) by subtracting 2 from both sides:

\[
w > -4
\]

### Graphing the Solution:

1. The endpoint of the inequality is \(w = -4\).
2. Since the inequality is strict (greater than, not greater than or equal to), we will use an open circle at \(-4\).
3. The solution includes all values to the right of \(-4\).

### Graph Representation:

- Draw a number line.
- Place an open circle at \(-4\) to indicate that \(-4\) is not included in the solution.
- Shade the area to the right of \(-4\) to indicate that all values greater than \(-4\) are part of the solution.

\[
\text{Number Line Representation:}
\]

```
<---|----|----|----|----|----|----|----|---->
-5 -4 -3 -2 -1 0 1 2
(-------------------------->
```

Here, the parentheses \( ( \) indicates that the endpoint \(-4\) is not included in the solution set. The shaded line indicates all numbers greater than \(-4\).