To determine which inequality Hessa solved based on the number line provided, we recognize that a closed point at 5 indicates that this point is included in the solution (≥ or ≤) and the leftward arrow signifies that the solution extends to numbers less than or equal to 5.
Let's examine each inequality option:
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35x + 25 ≥ 325: To solve for x: \[ 35x ≥ 300 \ x ≥ \frac{300}{35} \ x ≥ \frac{60}{7} \approx 8.57 \] (This is greater than 5; not a match).
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\(\frac{3}{5}x + \frac{2}{5} > 3 \frac{2}{5}\): Convert \(3 \frac{2}{5}\) to an improper fraction: \[ \frac{3}{5}x + \frac{2}{5} > \frac{17}{5} \ \frac{3}{5}x > \frac{17}{5} - \frac{2}{5} \ \frac{3}{5}x > \frac{15}{5} \ x > 5 \] (This indicates x is greater than 5; not a match).
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37x + 17 ≤ 167: \[ 37x ≤ 150 \ x ≤ \frac{150}{37} \approx 4.05 \] (This is less than 5; not a match).
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15x − 35 ≤ 25: \[ 15x ≤ 60 \ x ≤ 4 \] (This doesn’t include 5; not a match).
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25x − 45 ≥ 115: \[ 25x ≥ 160 \ x ≥ \frac{160}{25} = 6.4 \] (This is greater than 5; not a match).
None of the inequalities clearly match the graphical representation of the solution extending to the left of 5 and including 5.
Let's analyze if any of the inequalities might be incorrectly interpreted:
- If none of the inequalities fits the closed point at 5 and extends left to include values less than 5, then it appears there's a misunderstanding.
Ultimately, the graph with a closed point at 5 indicates the inequality should be something like \(x ≤ 5\) or \(x ≥ 5\).
None of the provided responses contain \(x ≤ 5\), indicating that the correct choice may be absent in the provided options. However, the closest that must be interpreted regarding the graphical representation, assuming an improvised mismatch in communication, seems to hint toward the more inclusive form that should originate from inequalities that end with x ≤ and centers around the specific graphical representation provided.
Please verify the choices; if able to exclude or clarify choices based on representation without additional context, I may assist further in specifying or isolating the most correct or intuitively fitting equation from the graphical representation supplied.