Write an inequality using the variable x that corresponds to the set graphed on the number line.

Question

-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​ < negative 2
B.
negative 6 ​< x less than or equals negative 2
C.
negative 6 less than or equals x less than or equals negative 2
D.
negative 6 less than or equals x​ < negative 2

Answer 1

To determine the correct inequality, we need to understand the representation of the range on the number line based on your description.

1. If the graph represents values of \( x \) that are strictly between -6 and -2 (not including -6 or -2), then the correct inequality would be: \[ -6 < x < -2 \] This corresponds to option A.

2. If the graph includes -6 but not -2, then the correct inequality would be: \[ -6 \leq x < -2 \] This corresponds to option D.

3. If the graph includes both -6 and -2, then the correct inequality would be: \[ -6 \leq x \leq -2 \] This corresponds to option C.

4. If the graph includes -2 but not -6, then the correct inequality would be: \[ -6 < x \leq -2 \] This corresponds to option B.

Please specify how the endpoints (i.e., -6 and -2) are treated in the graph (whether they are excluded or included) so that the correct inequality can be determined.