Question

Question

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.

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

Giselle and Anish
Giselle and Anish

Anish, Juana, and Giselle

Answer 1

To solve the inequality \( 56x \leq -10 \), we follow these steps:

1. Dividing by a positive number: The first step is to isolate \( x \) by dividing both sides of the inequality by \( 56 \). Since \( 56 \) is a positive number, the direction of the inequality remains the same.

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

2. Simplifying: This can be simplified to:

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

Now, let's evaluate the statements from Juana, Anish, and Giselle:

• Juana's statement: Incorrect. She is wrong because the inequality symbol does not need to be reversed when dividing by a positive number. The presence of the negative sign on the right side of the inequality does not affect the inequality symbol.

• Anish's statement: Correct. He is correct in saying that the Multiplication or Division Property of Inequality applies here, but it's specifically that since we are dividing by a positive number, the inequality does not flip.

• Giselle's statement: Correct. She is correct that the inequality symbol must stay the same when dividing by a positive number.

Thus, the correct combination of people is:

Giselle and Anish.