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.
- Plotting the Endpoint: You would put a solid point (closed dot) at 2 because the inequality includes equality (\(\geq\)).
- 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.
- 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 \(w \geq 2\).