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)

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 \( \frac{6}{5} \) to eliminate the fraction, while keeping in mind that when we multiply or divide both sides of an inequality by a positive number, the direction of the inequality symbol remains the same.

So, \[ x \leq -10 \times \frac{6}{5} \] Calculating the right side, we get: \[ x \leq -12 \]

Now, examining each person's claim:

• Juana is incorrect. The inequality symbol is not reversed just because there is a negative sign; it only needs to be reversed if you multiply or divide by a negative number.

• Anish is correct. The division or multiplication properties can apply here, and we multiplied by a positive number \( \frac{6}{5} \), so the inequality remains unchanged.

• Giselle is also correct in saying the inequality symbol must stay the same since we multiplied by a positive number.

Therefore, the correct combination of people is Anish and Giselle.