Solve the inequality and graph the solution.

Question

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

1. Subtract 2 from both sides:

\[ c + 2 - 2 > 1 - 2 \]

This simplifies to:

\[ c > -1 \]

Graphing the Solution

The solution \( c > -1 \) is represented on a number line. Here’s how we can graph this solution:

1. Endpoints: The endpoint is -1.
2. Closed/Open Endpoint: Since the inequality is strictly greater than (>), we use an open circle at -1 to indicate that -1 is not included in the solution set.
3. Direction: Shade to the right of -1 to indicate all values greater than -1.

Visual Representation

Number Line:
<---|----|------|------|----|----|--->
    -3   -2    -1     0    1    2
                  (------->)

• The open circle at -1 indicates it's not included in the solution.
• The shaded area to the right of -1 indicates all values \( c > -1 \).

Summary of Steps

• Isolate \(c\).
• Identify the type of endpoint (open).
• Shade the appropriate direction on the graph.