Question

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

Answer 1

To solve the inequality \( 56x \leq -10 \), we need to isolate \( x \).

1. **Dividing by a positive number:** The first step would be to divide both sides of the inequality by 56, which is positive. According to the rules of inequalities, when dividing by a positive number, the direction of the inequality remains the same.

So, we divide as follows:

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

2. **Result simplification:** This simplifies to:

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

Now, let's review what the three individuals said:

- **Juana:** She believes that the inequality symbol must be reversed because there is a negative sign. This is incorrect as we only reverse the inequality when we divide or multiply by a negative number. Since we divided by 56, which is positive, the symbol does not change.

- **Anish:** He talks about the Multiplication Property of Inequality or Division Property of Inequality. This is relevant since we did divide the inequality, and he is correct in that respect.

- **Giselle:** She states that the inequality symbol must stay the same, which is also correct, as we saw above; the symbol does not change when dividing by a positive number.

Based on this analysis:

- **Correct individuals: Anish and Giselle**.

So the correct combination of people is **Giselle and Anish**.