Juana, Anish, and Giselle are comparing their solutions to the inequality 56x≤−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. Giselle says the inequality symbol must stay the same. Based on these answers, which combination of people is correct? (1 point)

Question

GPT-4o mini · Answer

To solve the inequality $ 56x \leq -10 $, we can divide both sides by 56, assuming it's positive, without reversing the inequality sign. 1. **Juana's claim** that the inequality symbol must be reversed because of a negative sign is incorrect for this particular operation (dividing by a positive number). The sign only needs to be reversed when you divide or multiply by a negative number. 2. **Anish's claim** that either the multiplication property or division property of inequality needs to be applied is correct. We should divide by 56 to isolate $ x $: $$ x \leq \frac{-10}{56} = -\frac{5}{28} $$ 3. **Giselle's claim** that the inequality symbol must stay the same is correct in this context because we are dividing by a positive number. So, **Anish** and **Giselle** are correct. The combination of people that is correct is Anish and Giselle.