Solve the inequality and graph the solution.

Question

c
3
<2
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \( c < 2 \), we need to determine the values of \( c \) that are less than 2.

Step 1: Identify the solution

The inequality indicates that \( c \) can take any value that is less than 2.

Step 2: Graph the solution

1. Endpoint: The endpoint here is \( c = 2 \).
2. Type of endpoint: Since the inequality is \( < \) (which does not include 2), the endpoint at 2 will be open (not included in the solution).
3. Graphing:
   • Draw a number line.
   • Place an open circle at 2 to indicate that 2 is not included in the solution.
   • Shade to the left of the circle to indicate all values less than 2 are included in the solution.

Resulting Graph

Here is a representation of the final graph:

<----o=======================> 
     0  1  2  3

Where:

• The "o" at 2 is an open circle, indicating that \( c \) does not include 2.
• The shading to the left indicates all values less than 2 are part of the solution.

Summary

The solution to the inequality \( c < 2 \) is all real numbers less than 2, represented graphically with an open circle at 2 and shading to the left on a number line.