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

Juana and Anish
Juana and Anish

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

Giselle and Anish
Giselle and Anish

Giselle and Juana

Answer 1

To solve the inequality \( \frac{5}{6}x \leq -10 \), we can isolate \( x \) by following these steps:

1. Multiply both sides by \( \frac{6}{5} \) to eliminate the fraction. Since \( \frac{6}{5} \) is a positive number, the inequality symbol remains the same.

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

2. Calculate the right side:

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

So, the solution to the inequality is \( x \leq -12 \).

Now, let's analyze each person's statements:

• Juana: She believes the inequality symbol must be reversed because there is a negative sign in the inequality. This is incorrect; the symbol does not change because we haven't multiplied or divided by a negative number.

• Anish: He correctly states that the Multiplication Property of Inequality or Division Property of Inequality must be applied, and since we multiplied by a positive number, the inequality symbol stays the same. He is correct.

• Giselle: She says the inequality symbol must stay the same, which is also correct as we did not multiply or divide by a negative number.

Based on this analysis, the correct combination of people is:

Giselle and Anish.