To solve the inequality \( s/4 \leq -2 \), we will first isolate \( s \).
- Multiply both sides of the inequality by 4 to eliminate the fraction:
\[ s \leq -2 \times 4 \]
\[ s \leq -8 \]
Now, we can interpret the solution \( s \leq -8 \). This indicates that \( s \) can take any value less than or equal to -8.
Graphing the Solution
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Plot the endpoint: The endpoint is -8. Since the inequality is less than or equal to (≤), we will use a closed dot (●) to indicate that -8 is included in the solution.
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Select the middle of the segment to delete: We are considering all values less than -8, which means we will shade to the left of -8 on the number line.
Final Graph Representation
- Place a closed dot at -8.
- Shade the region to the left of -8 (indicating all numbers less than -8).
The resultant number line will visually represent the inequality with the included point at -8 and the shaded area extending to the left.
This is the final solution and graphical representation for the inequality \( s/4 \leq -2 \) (or \( s \leq -8 \)).