Question

Write a compound inequality that represents the following phrase. Graph the solutions.
all real numbers that are between negative 2 and 6
Question content area bottom
Part 1
Write a compound inequality that represents the phrase. Choose the correct answer below.
A.
negative 2less than or equalsnless than or equals6
B.
negative 2less thannless than6
C.
negative 2less than or equalsnless than6
D.
negative 2less thannless than or equals6

Answer 1

To represent the phrase "all real numbers that are between negative 2 and 6," we can set up the compound inequality. The phrase indicates that the numbers are greater than or equal to -2 and less than or equal to 6.

This corresponds to:

\[
-2 \leq n \leq 6
\]

Looking at the options you provided:

A. \(-2 \leq n \leq 6\) (This matches our inequality and is correct)

B. \(-2 < n < 6\) (This does not include -2 and 6, so it's incorrect)

C. \(-2 \leq n < 6\) (This includes -2 but not 6, so it's incorrect)

D. \(-2 < n \leq 6\) (This includes 6 but not -2, so it's incorrect)

The correct answer is:
**A. -2 ≤ n ≤ 6**

### Graphing the solution:

1. Draw a number line.
2. Shade the region between -2 and 6.
3. Include filled circles (or dots) at both -2 and 6 to indicate that these points are included in the solution.

Here is how you can visualize the graph:

```
<-------------------|-----------|------------------->
-2 6
● ●
```

In this representation, the filled circles (●) at -2 and 6 indicate that these values are included in the solution, consistent with the inequality.