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

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

Juana and Anish
Juana and Anish

Giselle and Anish
Giselle and Anish

Giselle and Juana

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To solve the inequality \( 56x \leq -10 \), we need to isolate \( x \). We can do this by dividing both sides of the inequality by 56. Importantly, since we are dividing by a positive number (56), the direction of the inequality will remain the same.

The steps are as follows:

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

This simplifies to:
\[
x \leq -\frac{5}{28}
\]

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

- Juana says the inequality symbol must be reversed because there is a negative sign. This is incorrect because the sign is reversed only if we divide or multiply by a negative number.

- Anish mentions that the Multiplication or Division Property of Inequality must be applied, which is correct, but it’s important to note that we will not change the direction of the inequality in this case since we are dividing by a positive number.

- Giselle states the inequality symbol must stay the same. This is correct, as the symbol does remain the same when dividing by 56.

Thus, the correct combination of people is **Anish and Giselle**. Anish correctly identifies the use of the properties of inequalities, and Giselle correctly states that the inequality symbol stays the same.

So, the final answer is:
**Giselle and Anish**.