Solve the inequality and graph the solution.

Question

c+2>
–
1
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 \( c + 2 > -1 \), we first isolate \( c \):

1. Subtract 2 from both sides: \[ c + 2 - 2 > -1 - 2 \] \[ c > -3 \]

This means that \( c \) can take any value greater than \(-3\).

Now, let's represent this on a number line:

1. Endpoints: The endpoint here is -3.
2. Open vs. Closed Endpoint: Since the inequality is \( c > -3 \) (not \( c \geq -3 \)), we will use an open circle at -3. This indicates that -3 is not included in the solution.
3. Deleting the Middle of the Segment, Ray, or Line: Since the solution is \( c > -3 \), we draw a ray starting from -3 (with an open circle) and extending to the right, indicating all values greater than -3.

Summary

• The solution to the inequality \( c + 2 > -1 \) is \( c > -3 \).
• On the number line:
  • Place an open circle at -3 to denote that it is not included.
  • Shade the line to the right of -3 to indicate all values greater than -3.

Graph

<---(---|------>
       -3

Where:

• The open parenthesis indicates -3 is not included.
• The arrow indicates the values greater than -3.