To determine which inequality corresponds to the given graph on the number line, we need to analyze the characteristics of the graph provided:
- There's a closed point plotted at 5, which indicates that 5 is included in the solution.
- There is a leftward arrow indicating that all values less than or equal to 5 are part of the solution.
This suggests that the inequality should take the form of \( x \leq 5 \) or something equivalent that includes 5.
Now, let's evaluate each of the given inequalities:
-
\( 15x - 35 \leq 25 \)
Simplifying gives:
\( 15x \leq 60 \)
\( x \leq 4 \)
(This does not include 5.) -
\( \frac{1}{5}x - \frac{3}{5} < \frac{2}{5} \)
Simplifying yields:
\( \frac{1}{5}x < 1 \)
\( x < 5 \)
(This does not include 5, not suitable.) -
\( 35x + 25 \geq 325 \)
Simplifying gives:
\( 35x \geq 300 \)
\( x \geq \frac{300}{35} \approx 8.57 \)
(Not suitable, as it does not include values less than or equal to 5.) -
\( \frac{3}{5}x + \frac{2}{5} \geq 3\frac{2}{5} \)
Simplifying yields:
\( \frac{3}{5}x \geq \frac{15}{5} \implies x \geq 5 \)
(This does not include values below 5.) -
\( 37x + 17 \leq 167 \)
Simplifying gives:
\( 37x \leq 150 \)
\( x \leq \frac{150}{37} \approx 4.05 \)
(This does not include 5, not suitable.) -
\( 25x - 45 \geq 115 \)
Simplifying gives:
\( 25x \geq 160 \)
\( x \geq 6.4 \)
(Not suitable, as it does not include values less than or equal to 5.)
After considering each option, none of the inequalities presented corresponds directly to the graph described with values less than or equal to 5. However, if we're looking for the closest match that maintains the essence of how inequalities function, we realize that a complete '≤' (less than or equal to) inequality is not explicitly provided among the responses.
However, the inequality that indicates inclusion of 5 and extends leftward would typically represent something like \( x \leq 5 \) which is not correctly found in the options but overall indicates the expected behavior.
Since no inequality explicitly matches the graph description, it's possible there might be a confusion in the options presented or in the intended answer—we would look for flexibility in statements made by other inequalities but typically \( x \leq 5 \) would directly relate to extending from 5 leftward in the number line provided.
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