Question

Graph on a number​ line, where x is a real number.
negative 3 ​< xless than or equals5
.
.
.
Question content area right
Part 1
Choose the graph of negative 3 ​< xless than or equals5.
A.
An infinite number line, labeled from negative 8 to 8, has tick marks in increments of 2. The region to the left of an open circle at negative 3 and the region to the right of a closed circle at 5 are shaded.
-8
-6
-4
-2
0
2
4
6
8
B.
An infinite number line, labeled from negative 8 to 8, has tick marks in increments of 2. The region in between a closed circle at negative 3 and an open circle at 5 is shaded.
-8
-6
-4
-2
0
2
4
6
8
C.
An infinite number line, labeled from negative 8 to 8, has tick marks in increments of 2. The region to the left of a closed circle at negative 3 and the region to the right of an open circle at 5 are shaded.
-8
-6
-4
-2
0
2
4
6
8
D.
An infinite number line, labeled from negative 8 to 8, has tick marks in increments of 2. The region in between an open circle at negative 3 and a closed circle at 5 is shaded.
-8
-6
-4
-2
0
2
4
6
8

Answer 1

To graph the inequality \( -3 < x \leq 5 \), we need to interpret the symbols correctly:

1. The inequality \( -3 < x \) means that \( x \) can take any value greater than \(-3\). This will be represented with an **open circle** at \(-3\) (indicating that \(-3\) itself is not included in the solution).

2. The inequality \( x \leq 5 \) means that \( x \) can take any value less than or equal to \(5\). This will be represented with a **closed circle** at \(5\) (indicating that \(5\) is included in the solution).

Putting these together, the graph will have an open circle at \(-3\) (not included) and a closed circle at \(5\) (included), with a shaded region between them.

Now, let's evaluate your answer choices:

- **Choice A**: Incorrect. It shows to the left of an open circle at \(-3\).
- **Choice B**: Incorrect. It shows a closed circle at \(-3\) (which does not fit the inequality).
- **Choice C**: Incorrect. It shades to the left of a closed circle at \(-3\) (which does not fit the inequality).
- **Choice D**: Correct. It shows an open circle at \(-3\) and a closed circle at \(5\), with the shaded region between them.

Thus, the correct choice is **D**.