Question

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

Giselle and Anish
Giselle and Anish

Anish, Juana, and Giselle
Anish, Juana, and Giselle

Giselle and Juana
Giselle and Juana

Juana and Anish

Answer 1

To solve the inequality \( 56x \leq -10 \), we need to isolate \( x \). This requires us to divide both sides by 56.

Here are the analyses of each person's statement:

- **Juana** says that the inequality symbol must be reversed because there is a negative sign in the inequality. This is incorrect. The inequality sign is reversed only when we multiply or divide by a negative number, not just because there is a negative sign present. In this case, we are dividing by a positive number (56), so the inequality sign does not change.

- **Anish** correctly states that the Multiplication or Division Property of Inequality must be applied. In this case, we will use the Division Property of Inequality to divide both sides by 56, and the inequality symbol will remain the same.

- **Giselle** says the inequality symbol must stay the same. This is indeed correct because we are dividing by a positive number.

Therefore, the correct combination of people who are correct is:

**Anish and Giselle.**

Since this option isn't provided, you can conclude that the most accurate choice based on the provided responses is **Giselle and Anish.**