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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

Let's start by analyzing the inequality \( 56x \leq -10 \).

1. **Dividing by a Positive Number**: The first step is to isolate \( x \) by dividing both sides of the inequality by \( 56 \) (which is positive). According to the properties of inequalities, if we divide or multiply by a positive number, the direction of the inequality remains the same.

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

2. **Negative Sign**: The presence of a negative sign in \( -10 \) does not affect the direction of the inequality when we are dividing by the positive number \( 56 \).

Now, let's evaluate each person's claims:

- **Juana**: Says the inequality symbol must be reversed because there is a negative sign in the inequality. **This is incorrect** because the negative sign in the number does not affect the inequality's direction when dividing by a positive number.

- **Anish**: States that the Multiplication Property of Inequality or Division Property of Inequality must be applied. **This is correct** because we need to apply these properties to solve the inequality.

- **Giselle**: Claims that the inequality symbol must stay the same. **This is also correct** because the inequality will not change its direction when divided by the positive number \( 56 \).

Based on the analysis:
- Anish and Giselle are correct.
- Juana is incorrect.

Therefore, the correct answer is **Giselle and Anish**.