To solve the inequality \( 7 > -x \geq -2 \), we can split it into two parts:
-
From \( 7 > -x \):
- This can be rewritten as \( -x < 7 \), which implies \( x > -7 \).
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From \( -x \geq -2 \):
- This can be rewritten as \( x \leq 2 \).
Now we combine these two results:
\[ -7 < x \leq 2 \]
This means that we are looking for all \( x \) values that are greater than \(-7\) and less than or equal to \( 2 \).
To graph this inequality:
- Draw a number line.
- Shade the region between \(-7\) (not included) and \(2\) (included).
- Put an open circle at \(-7\) and a closed circle at \(2\) to show that \(-7\) is not included and \(2\) is included.
Regarding your options (A, B, C, D), since I cannot see the actual graphs provided, look for the graph that accurately represents the specified interval \( (-7, 2] \), which shows:
- An open circle at \(-7\)
- A closed circle at \(2\)
- Shading between these two points.
Once you identify the correct graph, that will be the representation of your intersection \( -7 < x \leq 2 \).