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.

Question

Based on these answers, which combination of people is correct?

(1 point)
Responses

Giselle and Juana
Giselle and Juana

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

Giselle and Anish
Giselle and Anish

Juana and Anish

Answer 1

To solve the inequality \( 56x \leq -10 \), we need to analyze the statements made by Juana, Anish, and Giselle.

1. Juana: She claims that the inequality symbol must be reversed because there is a negative sign in the inequality. This statement is incorrect. The inequality does not require reversing solely due to the presence of a negative number on the right side.

2. Anish: He mentions the Multiplication or Division Property of Inequality. When dividing or multiplying both sides of an inequality by a negative number, the inequality symbol must be reversed. However, in this case, we are dividing (or multiplying) \( 56x \) by a positive number (56) to isolate \( x \). So Anish's statement about needing to apply that property is not applicable here either.

3. Giselle: She says the inequality symbol must stay the same. This is correct at this stage of solving the inequality because we are dividing by a positive number.

Based on the analysis:

• Juana is incorrect.
• Anish is not correct in this context.
• Giselle is correct.

Therefore, the correct combination of people is:

Giselle and Anish.