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)
Responses

Juana and Anish
Juana and Anish

Giselle and Anish
Giselle and Anish

Giselle and Juana
Giselle and Juana

Anish, Juana, and Giselle

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To solve the inequality \(56x \leq -10\), let's consider the implications of each person's reasoning:

1. **Juana's Reasoning**: Juana states that the inequality symbol must be reversed because there is a negative sign in the inequality. This is incorrect. The inequality symbol is not reversed just because there is a negative number on the right side.

2. **Anish's Reasoning**: Anish states that the Multiplication Property of Inequality or Division Property of Inequality must be applied. This is correct. To isolate \(x\), we would divide both sides of the inequality by 56, which is a positive number. When dividing by a positive number, the direction of the inequality symbol remains the same.

3. **Giselle's Reasoning**: Giselle says the inequality symbol must stay the same. This is also correct. Since we are dividing by a positive number (56 in this case), the direction of the inequality does not change.

Based on this analysis, Anish and Giselle are correct while Juana is not. The correct combination is **Giselle and Anish**.