Use the image to answer the question.

Question

Which description is true about the graphed system of inequalities for x<−2 and x≥3
?

(1 point)
Responses

The system has infinite solutions.
The system has infinite solutions.

The system has two solutions.
The system has two solutions.

The system has no solutions.
The system has no solutions.

The system has one solution.
The system has one solution.

Answer 1

To analyze the system of inequalities \( x < -2 \) and \( x \geq 3 \):

• The inequality \( x < -2 \) includes all values to the left of -2 on the number line.
• The inequality \( x \geq 3 \) includes all values starting from 3 and moving to the right on the number line.

Since there is no overlap between the two inequalities (one is to the left of -2, and the other is to the right of 3), there are no values of \( x \) that satisfy both inequalities simultaneously.

Therefore, the correct description is:

The system has no solutions.