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

Juana and Anish
Juana and Anish

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

Giselle and Anish

Answer 1

To solve the inequality \( 56x \leq -10 \), let's analyze each person's statement:

1. Juana claims that the inequality symbol must be reversed because there is a negative sign in the inequality. This is incorrect; the direction of the inequality symbol does not automatically change just because there is a negative number involved. The symbol only changes if you multiply or divide both sides of the inequality by a negative number, which we are not doing in this initial step.

2. Anish states that the Multiplication Property of Inequality or the Division Property of Inequality must be applied. This is technically correct; in order to isolate \( x \), you would divide both sides of the inequality by a positive number (56), which does not change the direction of the inequality. Therefore, applying division here is appropriate, but his statement doesn't clarify the context of reversing the inequality.

3. Giselle says the inequality symbol must stay the same. This is correct because we are not dividing or multiplying by a negative number in this case. When we divide both sides by 56, the inequality remains \( x \leq \frac{-10}{56} \).

Based on this analysis, Giselle is correct, and Anish is correct regarding the properties involved but did not state that the inequality stays the same when dividing by a positive number.

Thus, the correct combination based on their statements is:

Giselle and Anish.