Question

Solve the inequality and graph the solution.
w+10
4
≥3
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

\[
\frac{w + 10}{4} \geq 3,
\]

we will first eliminate the fraction by multiplying both sides by 4:

\[
w + 10 \geq 12.
\]

Next, we will isolate \(w\) by subtracting 10 from both sides:

\[
w \geq 12 - 10,
\]
which simplifies to

\[
w \geq 2.
\]

### Graphing the Solution

The solution \(w \geq 2\) indicates that \(w\) can take any value greater than or equal to 2.

1. **Plotting the Endpoint**: You would put a solid point (closed dot) at 2 because the inequality includes equality (\(\geq\)).
2. **Shade the Region**: Shade everything to the right of 2 to indicate that all values greater than 2 are included in the solution.

If we were to select a point to change from closed to open, we could decide to illustrate this by demonstrating what the solution would look like for a strict inequality (if the inequality were just \(w > 2\)). However, since we are dealing with \(w \geq 2\), we'll keep the endpoint closed.

3. **Delete the Middle of the Segment, Ray, or Line**: In this case, there is no segment or line to delete, as the solution simply extends to the right.

Here is a representation of the graph:

\[
\text{---(●)------->}
\]
- The closed dot at \(2\) indicates that \(w\) can equal \(2\).
- The arrow extending to the right shows that all values greater than \(2\) are included.

Thus, the final answer and graph represents the solution \(w \geq 2\).