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.

Based on these answers, which combination of people is correct?
(1 point)
Responses
Giselle and Juana
Giselle and Juana
Giselle and Anish
Giselle and Anish
Juana and Anish
Juana and Anish
Anish, Juana, and Giselle

1 answer

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

Let's use division or multiplication by a negative number, which is where confusion often arises.

To isolate \( x \), first multiply both sides by \( \frac{6}{5} \) (this is a positive number, so the inequality sign stays the same):

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

Calculating the right side:

\[ x \leq -12 \]

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

Juana's assertion: She believes the inequality sign must be reversed because there is a negative sign in the inequality. This is incorrect because we did not multiply or divide by a negative number here.
Anish's assertion: He says the Multiplication or Division Property of Inequality must be applied. This is correct because we did multiply by a positive number.
Giselle's assertion: She states that the inequality symbol must stay the same. This is correct, as we did not change the sign when multiplying by a positive number.

So, the correct combination of people who are correct in this situation is Giselle and Anish.