Juana, Anish, and Giselle are comparing their solutions to the inequality 56x≤−10

Question

5
6
𝑥
≤
−
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

Giselle and Juana
Giselle and Juana

Anish, Juana, and Giselle

Answer 1

To analyze the inequality \( 56x \leq -10 \), we need to consider how to solve it.

1. You can divide both sides of the inequality by a positive number (in this case, 56). The Multiplication and Division Properties of Inequalities state that if you divide (or multiply) both sides of an inequality by a negative number, you must reverse the inequality symbol.

So, let's apply what Anish said: we'll divide both sides by 56 (which is positive):

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

This simplifies to:

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

Since 56 is positive, the inequality symbol does not change.

Juana's claim that the inequality symbol must be reversed because of the negative sign is incorrect. The negative sign in front of 10 does not affect how the inequality symbol is used during division by a positive number.

Giselle's claim that the inequality symbol must stay the same is correct.

Anish’s claim about the need to apply the Division Property of Inequality is also correct, as we did divide by a positive number.

Therefore, the correct combination is:

Giselle and Anish.