Juana, Anish, and Giselle are comparing their solutions to the inequality 56x≤−10

Question

. 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

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

Giselle and Anish
Giselle and Anish

Juana and Anish
Juana and Anish

Giselle and Juana

Answer 1

To solve the inequality \( 56x \leq -10 \), we need to isolate \( x \) by dividing both sides by 56. According to the rules of inequalities:

1. If you multiply or divide both sides of an inequality by a positive number, the direction of the inequality does not change.
2. If you multiply or divide both sides of an inequality by a negative number, the direction of the inequality does change.

In this case, since we are dividing both sides by a positive number (56), the inequality symbol does not change. So, we divide:

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

This simplifies to:

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

Now, analyzing the responses:

• Juana is incorrect because the inequality does not need to be reversed just because there is a negative sign in the original inequality.
• Anish is correct; he is referencing the properties of inequalities appropriately by indicating that division is being applied correctly while maintaining the same direction of the inequality since 56 is positive.
• Giselle is also correct as the inequality symbol should indeed stay the same.

Based on this assessment, the correct answer is:

Giselle and Anish.