Solve the inequality and graph the solution.

Question

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2≤w+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 \( -2 \leq w + 2 \), we can isolate \( w \) by following these steps:

1. Start by subtracting 2 from both sides: \[ -2 - 2 \leq w \] \[ -4 \leq w \] or, equivalently, \[ w \geq -4 \]

Thus, the solution to the inequality is \( w \geq -4 \).

Graphing the Solution

1. Endpoints: The endpoint of the interval is \( -4 \).
2. Closed or Open Endpoint: Since the inequality is \( \geq \), the endpoint \( -4 \) will be closed (included in the solution).
3. Plotting the Graph:
   • Place a closed circle at \( -4 \).
   • Draw a ray extending to the right (the positive direction) indicating that any value greater than or equal to \( -4 \) is included in the solution.

Final Graph Representation:

The graph will look like this:

\[ \text{Closed circle at } -4 ; ; ; \text{--------->} \text{(ray extending right)} \]

Summary of Steps:

• The solution is \( w \geq -4 \).
• Closed circle at \( -4 \) indicates it is included.
• Ray extends to the right, indicating all values greater than \( -4 \) are part of the solution.