To determine which inequality Hessa solved, we can solve each of the inequalities given in the choices and figure out the respective solutions. Here's how we can solve each of them step-by-step.
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For the first inequality:
\[ \frac{3}{5}x + \frac{2}{5} \geq \frac{3}{2} \]
Multiplying through by 5 to clear the fractions:
\[ 3x + 2 \geq 15 \] \[ 3x \geq 13 \] \[ x \geq \frac{13}{3} \]
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For the second inequality:
\[ \frac{1}{5}x - \frac{3}{5} \leq \frac{2}{5} \]
Multiplying through by 5 to clear the fractions:
\[ x - 3 \leq 2 \] \[ x \leq 5 \]
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For the third inequality:
\[ \frac{2}{5}x - \frac{4}{5} \geq \frac{1}{5} \]
Multiplying through by 5 to clear the fractions:
\[ 2x - 4 \geq 1 \] \[ 2x \geq 5 \] \[ x \geq \frac{5}{2} \]
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For the fourth inequality:
\[ \frac{3}{7}x + \frac{1}{7} \leq \frac{16}{7} \]
Multiplying through by 7 to clear the fractions:
\[ 3x + 1 \leq 16 \] \[ 3x \leq 15 \] \[ x \leq 5 \]
Now that we've solved all the inequalities, the solutions are as follows:
- \( x \geq \frac{13}{3} \)
- \( x \leq 5 \)
- \( x \geq \frac{5}{2} \)
- \( x \leq 5 \)
Without any information on which graph corresponds to which solution, it is impossible to select an answer confidently. But you can match each solution to the graph that Hessa drew to find the correct inequality.
Determine which of the inequalities correlates with the graph, especially looking for values such as \( x \leq 5 \) or \( x \geq \frac{13}{3} \). Based on this analysis, you can identify the correct option. If Hessa's graph shows shading towards \( 5 \), then option 2 or 4 may be correct. If the graph has a closed circle at or beyond \( \frac{13}{3} \), then option 1 is correct.
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