Question

Write a compound inequality that represents the following phrase. Graph the solutions.
all real numbers that are between negative 7 and 4
Question content area bottom
Part 1
Write a compound inequality that represents the phrase. Choose the correct answer below.
A.
negative 7less than or equalsnless than or equals4
B.
negative 7less thannless than or equals4
C.
negative 7less than or equalsnless than4
D.
negative 7less thannless than4

Answer 1

The phrase "all real numbers that are between negative 7 and 4" can be represented by the compound inequality:

\[
-7 < n < 4
\]

This means \( n \) is greater than negative 7 but less than 4.

Now, let's analyze the answer choices:

A. \(-7 \leq n \leq 4\) (includes -7 and 4)
B. \(-7 < n \leq 4\) (includes 4 but not -7)
C. \(-7 \leq n < 4\) (includes -7 but not 4)
D. \(-7 < n < 4\) (excludes both -7 and 4)

Since the phrase mentions "between" (exclusively), the correct answer is **D. -7 < n < 4**.

### Graphing the Solutions:

To graph the inequality \(-7 < n < 4\):

1. Draw a number line.
2. Place open circles (to indicate that -7 and 4 are not included) at -7 and 4.
3. Shade the region between -7 and 4 to indicate that all numbers in this interval are solutions.

Here's a simple representation of the graph:

```
|----|----|----|----|----|----|----|----|
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5
(--------------------------------)
```

The parentheses indicate that -7 and 4 are not included in the solution.