Question

uana, 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

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

Giselle and Anish
Giselle and Anish

Giselle and Juana
Giselle and Juana

Juana and Anish
Juana and Anish

Answer 1

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

According to the rules of inequalities:

1. When you multiply or divide both sides of an inequality by a **positive number**, the inequality symbol stays the same.
2. When you multiply or divide by a **negative number**, the inequality symbol is reversed.

In this case, we will divide both sides by \( \frac{5}{6} \), which is a positive number. Therefore, the inequality symbol remains unchanged:

\[
x \leq -10 \div \frac{5}{6}
\]

Now, solving \( -10 \div \frac{5}{6} \) is equivalent to multiplying by the reciprocal:

\[
-10 \times \frac{6}{5} = -12
\]

Thus, the correct statement is \( x \leq -12 \).

Now, evaluating the claims:

- **Juana** is incorrect; the inequality does not need to be reversed because the number we're dividing by is positive.
- **Anish** is correct; we must apply the multiplication or division property of inequality, but he needs to clarify that it involves a positive number.
- **Giselle** is also correct; the inequality symbol must stay the same since we were dividing by a positive number.

Therefore, the correct combination of people who are correct is:

**Giselle and Anish.**