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

Giselle and Anish

Answer 1

To solve the inequality \( \frac{5}{6} x \leq -10 \), we can analyze the claims made by Juana, Anish, and Giselle.

1. Juana's claim: She says that the inequality symbol must be reversed because there is a negative sign in the inequality. This statement is incorrect. The inequality symbol needs to be reversed only when you multiply or divide both sides of the inequality by a negative number. In this case, we are not dividing by a negative number yet.

2. Anish's claim: He mentions the Multiplication Property of Inequality or Division Property of Inequality must be applied, which is somewhat accurate. We will divide both sides of the inequality by \( \frac{5}{6} \) to solve for \( x \). Since \( \frac{5}{6} \) is positive, the direction of the inequality does not change.

3. Giselle's claim: She says the inequality symbol must stay the same. This is correct at the stage of solving this particular inequality, as we will not change the symbol when dividing by a positive number.

Based on these evaluations:

• Anish is correct in recognizing that we will apply the division property (though his phrasing is a bit ambiguous).
• Giselle is correct in stating that the inequality symbol must stay the same during the division, assuming the division is by a positive number.

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

Giselle and Anish.