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

Answer 1

To solve the inequality \( 56x \leq -10 \), we can use the Division Property of Inequality, which states that if you divide (or multiply) both sides of an inequality by a positive number, the inequality symbol stays the same. However, if you divide (or multiply) both sides by a negative number, the inequality symbol must be reversed.

In the inequality \( 56x \leq -10 \):
1. We want to isolate \( x \) by dividing both sides by 56, which is a positive number. Therefore, the direction of the inequality does not change.

So, we divide both sides by 56:

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

This simplifies to:

\[
x \leq -\frac{5}{28}
\]

Now, let's evaluate the statements made by Juana, Anish, and Giselle:

- **Juana** is incorrect because the inequality symbol does not need to be reversed since we divided by a positive number.
- **Anish** is correct because he refers to using the Division Property of Inequality correctly, but the implication of needing to reverse the symbol is not applicable here.
- **Giselle** is correct because the inequality symbol must remain as \( \leq \).

Thus, the correct combination of people who are correct about the inequality is **Anish and Giselle**.