Juana, Anish, and Giselle are comparing their solutions to the inequality \frac{5}{6}x\le -10. Juana says that the inequality symbol must be reversed because there is a negative sign in the inequality. Anish says the Multiplication Property of Inequality or Division Property of Inequality must be applied. Gisele says the inequality symbol must stay the same.

Question

based on these answers, which combination of people is correct

Answer 1

To solve the inequality \(\frac{5}{6}x \le -10\), we can 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 will not change.

1. Juana is incorrect; the inequality symbol does not need to be reversed just because there’s a negative on the right side.

2. Anish is correct; the Multiplication Property of Inequality should be applied here. We can multiply both sides by \(\frac{6}{5}\) without reversing the inequality symbol.

3. Giselle is incorrect; the inequality symbol does not stay the same because the inequality itself needs to be solved by multiplying both sides by a positive number.

So, the combination of people that is correct is Anish.