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.

Question

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 Juana
Giselle and Juana

Giselle and Anish

Answer 1

To solve the inequality \( \frac{5}{6}x \leq -10 \), let's analyze the statements made by Juana, Anish, and Giselle:

1. Juana's Statement: She believes the inequality symbol must be reversed because there is a negative sign in the inequality. This is incorrect. The inequality symbol only needs to be reversed when multiplying or dividing both sides by a negative number, which is not applicable until we solve for \(x\).

2. Anish's Statement: He mentions applying the Multiplication Property of Inequality or Division Property of Inequality, which is appropriate. We need to isolate \(x\) by multiplying or dividing both sides of the inequality. In this case, we will multiply both sides by \( \frac{6}{5} \), which is a positive number, therefore the direction of the inequality will remain the same.

3. Giselle's Statement: She claims the inequality symbol must stay the same. This is correct as long as we multiply or divide by a positive number.

To solve the inequality:

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

Multiply both sides by \( \frac{6}{5} \):

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

Calculating the right side:

\[ x \leq -12 \]

Since Anish correctly pointed out that we must apply the multiplication or division property of inequality, and Giselle correctly stated that the inequality stays the same:

• Anish and Giselle are correct.

Thus, the correct answer is:

Giselle and Anish.