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 5 and a closed circle at 3 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 5 less than or equals x less than 3
negative 5 less than or equals x less than 3
B.negative 5 less than x less than 3
negative 5 less than x less than 3
C.negative 5 less than or equals x less than or equals 3
negative 5 less than or equals x less than or equals 3
D.negative 5 less than x less than or equals 3
negative 5 less than x less than or equals 3

Answer 1

To describe the shaded region on the number line with an open circle at -5 and a closed circle at 3, we can determine the correct inequality:

- The open circle at -5 means that -5 is not included, so we use \( > \) (greater than) for -5.
- The closed circle at 3 means that 3 is included, so we use \( \leq \) (less than or equal to) for 3.

This gives us the inequality:

\(-5 < x \leq 3\)

Now, looking at the options provided:

- **A.** \(-5 \leq x < 3\) (not correct because -5 is not included)
- **B.** \(-5 < x < 3\) (not correct because 3 is not included)
- **C.** \(-5 \leq x \leq 3\) (not correct because -5 is not included)
- **D.** \(-5 < x \leq 3\) (this is correct)

The correct answer is: **D. \(-5 < x \leq 3\)**.