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:
- The endpoint of the inequality is \(w = -4\).
- Since the inequality is strict (greater than, not greater than or equal to), we will use an open circle at \(-4\).
- 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 \(-4\).