Graph.

7 ​>minusxgreater than or equalsminus2
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Question content area right
Part 1
Which of the following is the graph of the​ intersection?
A.
-15
-10
-5
0
5
10
15
B.
-15
-10
-5
0
5
10
15
C.
-15
-10
-5
0
5
10
15
D.
-15
-10
-5
0
5
10
15

1 answer

To solve the inequality \( 7 > -x \geq -2 \), we can split it into two parts:

  1. From \( 7 > -x \):

    • This can be rewritten as \( -x < 7 \), which implies \( x > -7 \).
  2. 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 \( -7 < x \leq 2 \).