To solve the inequality \( \frac{5}{6}x \leq -10 \), we need to isolate \( x \). Here are the steps involved:
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Multiply both sides by the reciprocal of \( \frac{5}{6} \), which is \( \frac{6}{5} \). Since \( \frac{6}{5} \) is positive, the direction of the inequality remains the same:
\[ x \leq -10 \cdot \frac{6}{5} \]
Calculating \( -10 \cdot \frac{6}{5} \):
\[ -10 \cdot \frac{6}{5} = -12 \]
So, after multiplying, we have:
\[ x \leq -12 \]
Now, analyzing the statements from Juana, Anish, and Giselle:
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Juana thinks the inequality symbol must be reversed because there is a negative sign in the inequality. This is incorrect because the direction of the inequality only reverses when you multiply or divide by a negative number. Since we multiplied by a positive number (the reciprocal of \( \frac{5}{6} \)), the inequality remains the same.
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Anish correctly mentions that the Multiplication Property of Inequality or Division Property of Inequality must be applied. This is true because we used the multiplication property to solve for \( x \).
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Giselle says the inequality symbol must stay the same. This is correct as well, since we did not multiply or divide by a negative number.
Therefore, the correct combination of people is:
- Anish and Giselle are correct.
- Juana is incorrect.
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