Write a compound inequality that represents the following phrase. Graph the solutions.

Question

all real numbers that are between negative 4 and 2nothing
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Part 1
Write a compound inequality that represents the phrase. Choose the correct answer below.
A.
negative 4less than or equalsnless than2
B.
negative 4less thannless than2
C.
negative 4less than or equalsnless than or equals2
D.
negative 4less thannless than or equals2

Answer 1

To express the phrase "all real numbers that are between negative 4 and 2," we are looking for a compound inequality that includes the appropriate inequality signs.

Here’s the breakdown:

• "between negative 4 and 2" suggests that -4 is not included (which uses the < symbol) and 2 is not included either (again uses the < symbol).

Thus, the correct compound inequality would be:

B. \(-4 < n < 2\)

Graphing the Solutions:

To graph the inequality \(-4 < n < 2\):

1. Draw a number line.
2. Place an open circle at -4 (indicating that -4 is not included).
3. Place an open circle at 2 (indicating that 2 is not included).
4. Shade the region between -4 and 2 to indicate that all numbers in this range are solutions.

Here’s a description of how the graph would look:

• ----o====o----

• -4     2
  

Where:

• The "o" represents open circles at -4 and 2.
• The "=" sign represents the shaded region between these two values.

This visually signifies all numbers greater than -4 and less than 2.