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.

Question

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

Giselle and Anish
Giselle and Anish

Anish, Juana, and Giselle

Answer 1

To solve the inequality \( 56x \leq -10 \), we should first divide both sides by 56 to isolate \( x \):

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

When we perform division by a positive number (56 in this case), the direction of the inequality does not change. Therefore, the inequality sign remains as \( \leq \).

Now, let's evaluate what each person said:

• Juana: Incorrect. She believes the inequality symbol must be reversed because there's a negative sign. This is not true; the direction of the inequality only changes if you multiply or divide both sides by a negative number.

• Anish: Correct. He refers to the Multiplication and Division Property of Inequalities, emphasizing that we can apply division without changing the inequality sign when dividing by a positive number.

• Giselle: Correct. She correctly states that the inequality symbol must stay the same when dividing by a positive number.

Based on this analysis, the correct combination of people is:

Giselle and Anish.