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

Juana and Anish
Juana and Anish

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

Giselle and Juana
Giselle and Juana

Giselle and Anish

Answer 1

To solve the inequality \( 56x \leq -10 \), let's first isolate \( x \) by dividing both sides by the coefficient of \( x \), which is 56.

When we divide both sides of the inequality by a positive number, the direction of the inequality does not change. Thus, we can divide both sides by 56 without reversing the inequality:

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

Since none of the participants' statements are correct about the necessity of reversing the inequality based on the presence of a negative sign (which relates to whether a negative number is multiplied or divided), let's summarize their positions:

- Juana incorrectly thinks the inequality must be reversed merely because there is a negative sign.
- Anish is correct in stating that the Division Property of Inequality applies, but he doesn't specify that the divisor is positive.
- Giselle is correct that the inequality symbol must stay the same because we are dividing by a positive number.

Thus, the only correct combination of people is **Giselle and Anish** since Anish is acknowledging the need for the Division Property, while Giselle is correct about the direction of the inequality not changing.

So the correct answer is:

**Giselle and Anish**.