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Graph on a number​ line, where x is a real number.

negative 3 ​< xless than or equals5
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.
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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

1 answer

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.