Question

Juana, Anish, and Giselle are comparing their solutions to the inequality 56x≤−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

Answer 1

To solve the inequality \( 56x \leq -10 \), we need to isolate \( x \) by dividing both sides of the inequality by 56.

When we divide both sides of an inequality by a positive number, the inequality symbol remains the same. Thus, the correct step is:

\[
x \leq \frac{-10}{56}
\]

Now let's analyze each person's statements:

- **Juana** claims that the inequality symbol must be reversed because there is a negative sign in the inequality. This is incorrect because we only reverse the inequality symbol when we divide or multiply both sides by a negative number, which is not the case here (56 is positive).

- **Anish** states that the Multiplication or Division Property of Inequality must be applied, which is true here since we are dividing both sides of the inequality by a positive number (56).

- **Giselle** says that the inequality symbol must stay the same, which is also correct since we are not multiplying or dividing by a negative number.

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

**Giselle and Anish**.