To solve the inequality \( \frac{5}{6}x \leq -10 \), we need to isolate \( x \).
According to the rules of inequalities:
- When you multiply or divide both sides of an inequality by a positive number, the inequality symbol stays the same.
- When you multiply or divide by a negative number, the inequality symbol is reversed.
In this case, we will divide both sides by \( \frac{5}{6} \), which is a positive number. Therefore, the inequality symbol remains unchanged:
\[ x \leq -10 \div \frac{5}{6} \]
Now, solving \( -10 \div \frac{5}{6} \) is equivalent to multiplying by the reciprocal:
\[ -10 \times \frac{6}{5} = -12 \]
Thus, the correct statement is \( x \leq -12 \).
Now, evaluating the claims:
- Juana is incorrect; the inequality does not need to be reversed because the number we're dividing by is positive.
- Anish is correct; we must apply the multiplication or division property of inequality, but he needs to clarify that it involves a positive number.
- Giselle is also correct; the inequality symbol must stay the same since we were dividing by a positive number.
Therefore, the correct combination of people who are correct is:
Giselle and Anish.