Question

Question content area top
Part 1
Write an inequality using the variable x that corresponds to the set graphed on the number line.
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Question content area bottom
Part 1
A.
negative 6 ​< x less than or equals negative 2
B.
negative 6 less than or equals x​ < negative 2
C.
negative 6 ​< x​ < negative 2
D.
negative 6 less than or equals x less than or equals negative 2

Answer 1

To determine the correct inequality that corresponds to the set graphed on the number line, we need to consider the endpoints and whether they are included in the interval.

1. If the interval includes the endpoints (closed circle), we use "less than or equal to" (≤).
2. If the interval does not include the endpoints (open circle), we use "less than" (<).

Now, let’s review the options:

A. \(-6 < x \le -2\) means \(x\) is greater than \(-6\) but less than or equal to \(-2\).
B. \(-6 \le x < -2\) means \(x\) is greater than or equal to \(-6\) but less than \(-2\).
C. \(-6 < x < -2\) means \(x\) is greater than \(-6\) and less than \(-2\).
D. \(-6 \le x \le -2\) means \(x\) is greater than or equal to \(-6\) and less than or equal to \(-2\).

You would select the appropriate statement based on whether the endpoints \(-6\) and \(-2\) are included (closed circle) or not (open circle).

If the graph shows:
- an open circle at \(-6\) (not included)
- a closed circle at \(-2\) (included)

Then the correct inequality would be:

**A. \(-6 < x \le -2\)**

If both endpoints are included, then the correct choice would instead be:

**D. \(-6 \le x \le -2\)**

Please confirm the nature of the circles in the graph to select the right answer based on your observation.