To determine which inequality Hessa solved, we can analyze the graph represented on the number line.
The graph shows a closed point at 5, with a leftward arrow extending beyond negative 10. This indicates that the solution includes the point 5 and all values less than 5. Therefore, the inequality should have the form \( x \leq 5 \).
Now, let's evaluate each response to see which matches this condition:
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\( 15x - 35 \leq 25 \)
- Solving this: \( 15x \leq 60 \) ⟹ \( x \leq 4 \). (This does not include 5.)
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\( \frac{1}{5} x - \frac{3}{5} < \frac{2}{5} \)
- Solving this: \[ \frac{1}{5} x < \frac{5}{5} \] \[ x < 5 \] (This does not include 5 but is valid for values below it.)
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\( 35x + 25 \geq 325 \)
- Solving this: \( 35x \geq 300 \) ⟹ \( x \geq \frac{300}{35} \approx 8.57 \). (This does not go in the left direction at all.)
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\( \frac{3}{5} x + \frac{2}{5} \geq 3\frac{2}{5} \)
- Solving this: \[ \frac{3}{5} x \geq 3 \quad (which is 15/5) \] \[ x \geq 5 \] (This goes in the right direction and does not include values less than 5.)
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\( 25x - 45 \geq 115 \)
- Solving this: \[ 25x \geq 160 \quad \Rightarrow \quad x \geq 6.4 \] (Again, this does not include less than 5.)
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\( \frac{2}{5} x - \frac{4}{5} \geq 1\frac{1}{5} \)
- Solving this: \[ \frac{2}{5} x \geq \frac{9}{5} \] \[ x \geq \frac{9}{2} = 4.5 \] (Again, this does not have a leftward arrow.)
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\( 37x + 17 \leq 167 \)
- Solving this: \[ 37x \leq 150 \] \[ x \leq \frac{150}{37} \approx 4.05 \] (Similar; does not include inclusive values around 5.)
From this analysis, the inequality that corresponds to the graph presented with 5 and arrow directed leftward (indicating all values less than or equal to 5) can be concluded to be represented by \( \frac{1}{5} x - \frac{3}{5} < \frac{2}{5} \).
Thus, the best choice is:
- Start Fraction 1 over 5 end fraction x minus Start Fraction 3 over 5 end fraction less than or equal to Start Fraction 2 over 5 end fraction.
1 answer