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

Giselle and Anish
Giselle and Anish

Giselle and Juana
Giselle and Juana

Juana and Anish
Juana and Anish

Anish, Juana, and Giselle

Answer 1

To solve the inequality \( 56x \leq -10 \), we can divide both sides by 56. Since 56 is a positive number, the inequality symbol remains the same.

Here’s the process:

1. Start with the original inequality: \[ 56x \leq -10 \]

2. Divide both sides by 56: \[ x \leq \frac{-10}{56} \]

3. Simplifying \(-10/56\) gives \(-5/28\): \[ x \leq -\frac{5}{28} \]

Based on this reasoning:

• Juana is incorrect because the inequality symbol does not reverse due to a negative number on the right side; it only reverses when you multiply or divide by a negative number.
• Anish is correct about needing to apply the Division Property of Inequality. However, he does not address the correct application related to the sign of the number, which is important.
• Giselle is correct because the inequality symbol remains the same when dividing by a positive number.

Therefore, the correct combination of people is Giselle and Anish because Anish is thinking about applying division correctly, and Giselle is correctly affirming that the inequality symbol stays the same.

Thus, the answer is: Giselle and Anish.