To determine which inequality corresponds to the graphical representation described, we note that the number line has a closed point at 5 and a leftward arrow extending beyond negative 10.
This indicates that the solution set includes 5 and all numbers less than 5, which corresponds to a "less than or equal to" situation for values extending indefinitely left on the number line.
Next, let's analyze each of the provided inequalities:
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\(15x - 35 \leq 25\)
- Solving: \(15x \leq 60 \) gives \(x \leq 4\). This does not match.
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\(\frac{1}{5}x - \frac{3}{5} < \frac{2}{5}\)
- Solving: \(\frac{1}{5}x < 1\) gives \(x < 5\). This is not a closed point at 5, so this does not match.
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\(35x + 25 \geq 325\)
- This simplifies to \(35x \geq 300\) or \(x \geq \frac{300}{35} \approx 8.57\). This does not match.
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\(\frac{3}{5}x + \frac{2}{5} \geq 3\frac{2}{5}\)
- Solving gives \(\frac{3}{5}x \geq 3\) or \(x \geq 5\). This does not match.
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\(25x - 45 \geq 115\)
- This simplifies to \(25x \geq 160\) or \(x \geq 6.4\). This does not match.
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\(\frac{2}{5}x - \frac{4}{5} \geq 1\frac{1}{5}\)
- Solving gives \(\frac{2}{5}x \geq 2\) or \(x \geq 5\). This does not match.
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\(37x + 17 \leq 167\)
- This simplifies to \(37x \leq 150\) or \(x \leq 5.4\). This allows for \(5\) as an endpoint included, but a solid line to the left does not match.
Since none of these options completely satisfied the graphical description of a closed endpoint at 5 with a continuous line extending indefinitely left, it seems there might be no exact match among the answers.
However, the most closely related inequalities appear to be those resembling \(x \leq 5\) or \(x \text{less than or equal to} 5\).
If I must choose among the given options, I would conclude none perfectly match but none of the inequalities provided match the attributes completely described. Would you like more elaboration on any specific part or a broader explanation?