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 Anish
Giselle and Anish

Juana and Anish
Juana and Anish

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

Giselle and Juana

Answer 1

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

When dividing both sides of an inequality by a positive number (in this case, 56), the direction of the inequality symbol does NOT change. So we have:

\[ x \leq \frac{-10}{56} \]

This simplifies to:

\[ x \leq -\frac{5}{28} \]

Let's analyze the statements made by Juana, Anish, and Giselle:

1. Juana: She believes the inequality symbol must be reversed because there is a negative sign in the inequality. This is incorrect. The inequality doesn't reverse just because there is a negative number; it only reverses when you multiply or divide by a negative number.

2. Anish: He mentions the Multiplication Property of Inequality or Division Property of Inequality must be applied. This is correct but he needs to specify that we are dividing by a positive number (56) in this case, which does not change the direction of the inequality.

3. Giselle: She says the inequality symbol must stay the same. This is also correct because we are dividing by a positive number.

So, Anish and Giselle are correct in their reasoning. Thus, the correct combination is:

Giselle and Anish.