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

Juana and Anish
Juana and Anish

Giselle and Juana
Giselle and Juana

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

Giselle and Anish

Answer 1

To solve the inequality \( 56x \leq -10 \), we must remember the properties of inequalities, particularly when dividing or multiplying by negative numbers:

1. Juana's Claim: Juana believes the inequality symbol should be reversed because there is a negative sign in the inequality. However, in this inequality, the sign of \( 56 \) is not negative. She is incorrect in assuming the symbol must be reversed simply due to a negative number on the right side.

2. Anish's Claim: Anish states that the Multiplication Property or the Division Property of Inequality must be applied. This is also correct; to isolate \( x \), you can divide both sides of the inequality by 56, which is positive, and the direction of the inequality does not change. Therefore, Anish is correct.

3. Giselle's Claim: Giselle states that the inequality symbol must stay the same, which is true in this case since we’re dividing by a positive number (56). Therefore, she is also correct.

Based on the analysis:

• Anish and Giselle are correct in their statements.
• Juana is incorrect.

Thus, the correct combination of people is Giselle and Anish.