To determine which inequality corresponds to the given graph, we need to analyze the endpoints and the direction of the shading.
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Identifying the graph:
- The graph appears to shade a range to the left of a certain point. The filled dot indicates that the endpoint is included in the solution (a closed interval).
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Finding the critical point:
- The filled dot is at -3, so the inequality likely involves values less than or equal to -3.
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Checking the options:
- We will evaluate each inequality to see which one translates to "x is less than or equal to -3":
- \(x + 3.5 \geq -5.5\)
- Rearranging gives \(x \geq -9\) (not a match).
- \( -5.5x + 2.5 \geq 4.5\)
- Rearranging gives \( -5.5x \geq 2\) or \( x \leq -\frac{2}{5.5} \approx -0.36\) (not a match).
- \(x + 3.5 \geq 1.5\)
- Rearranging gives \(x \geq -2\) (not a match).
- \(x - 3.5 \geq 1.5\)
- Rearranging gives \(x \geq 5\) (not a match).
None of the equations provided directly translates to the interval that includes values less than -3.
We must conclude that none of the inequalities provided directly fit the shading indicated in the graph.
From the way the inequalities are structured, it seems that there may have been a transcription error or misalignment with the graph as detailed descriptions should yield that one option should lead to \(x \leq -3\) based on the filled dot.
If the graph visual confirms \(x \leq -3\), then you would typically check inequalities that express it explicitly such as \(x - 3 \leq 0\) or similar until the inequality can represent the provided conditions accurately. Since none match all expected conditions based on standard inequality translation, an additional review of the context from where the problem was derived or further options may be warranted.