Question

Juana, Anish, and Giselle are comparing their solutions to the inequality 5/6x≤−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

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

Giselle and Anish
Giselle and Anish

Juana and Anish

Answer 1

To solve the inequality \( \frac{5}{6} x \leq -10 \), we need to isolate \( x \).

First, we can multiply both sides of the inequality by \( \frac{6}{5} \) in order to eliminate the fraction. However, we must be careful:

1. **Multiplication by a Positive Number**: Since \( \frac{6}{5} \) is positive, the inequality symbol will not change.
2. **Applying the Multiplication**: We multiply both sides:
\[
x \leq -10 \cdot \frac{6}{5}
\]
\[
x \leq -12
\]

Now, let's analyze the statements of Juana, Anish, and Giselle:

- **Juana**: She incorrectly states that the inequality symbol must be reversed because there is a negative sign in the inequality. This is not true; we only reverse the inequality when we multiply or divide by a negative number.

- **Anish**: He correctly states that we must apply the Multiplication Property of Inequality (by multiplying both sides by \(\frac{6}{5}\)). So he is correct.

- **Giselle**: She says the inequality symbol must stay the same, which is correct only under the premise that we are multiplying by a positive number. Since we did not multiply or divide by any negative number, this statement is accurate.

Therefore, the correct combination of people is:

**Giselle and Anish**.