Question

Write a​ three-part inequality involving the variable x that describes the set of numbers graphed.
An infinite number line is labeled from negative 10 to 10 in increments of 1. The region between an open circle at negative 3 and a closed circle at 1 is shaded.
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
Question content area bottom
Part 1
Choose the correct inequality below.
A.negative 3 less than x less than 1
negative 3 less than x less than 1
B.negative 3 less than or equals x less than or equals 1
negative 3 less than or equals x less than or equals 1
C.negative 3 less than or equals x less than 1
negative 3 less than or equals x less than 1
D.negative 3 less than x less than or equals 1
negative 3 less than x less than or equals 1

Answer 1

To describe the set of numbers graphed, we can analyze the shaded region between the open circle at -3 and the closed circle at 1.

- The **open circle** at -3 means that -3 is **not included** in the interval, so we use the inequality \(x > -3\).
- The **closed circle** at 1 means that 1 is **included** in the interval, so we use the inequality \(x \leq 1\).

Putting these two parts together, we have:

\[
-3 < x \leq 1
\]

Based on your options, this corresponds to:

**D.** \( -3 < x \leq 1 \)