Write a​ three-part inequality involving the variable x that describes the set of numbers graphed.

Question

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