Question
Solving Linear Inequalities Quick Check
3 of 53 of 5 Items
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
Anish, Juana, and Giselle
Anish, Juana, and Giselle
Giselle and Anish
Giselle and Anish
Juana and Anish
Juana and Anish
Giselle and Juana
3 of 53 of 5 Items
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
Anish, Juana, and Giselle
Anish, Juana, and Giselle
Giselle and Anish
Giselle and Anish
Juana and Anish
Juana and Anish
Giselle and Juana
Answers
GPT-4o mini
To solve the inequality \( 56x \leq -10 \), we need to isolate \( x \) by dividing both sides of the inequality by 56.
The important point here is that when dividing or multiplying both sides of an inequality by a positive number, the inequality symbol remains the same. Since 56 is positive, the symbol does not reverse.
1. **Juana** is incorrect because the inequality symbol does not need to be reversed simply because there is a negative sign on the right side.
2. **Anish** is correct that we can apply the Multiplication or Division Property of Inequality to solve it, as we are dividing both sides by a positive number.
3. **Giselle** is also correct because the inequality symbol does stay the same when dividing by a positive number.
So the correct combination of people who are correct is **Anish and Giselle**.
However, since this specific combination is not listed in your responses, the best option that fits is **Giselle and Anish**.
The important point here is that when dividing or multiplying both sides of an inequality by a positive number, the inequality symbol remains the same. Since 56 is positive, the symbol does not reverse.
1. **Juana** is incorrect because the inequality symbol does not need to be reversed simply because there is a negative sign on the right side.
2. **Anish** is correct that we can apply the Multiplication or Division Property of Inequality to solve it, as we are dividing both sides by a positive number.
3. **Giselle** is also correct because the inequality symbol does stay the same when dividing by a positive number.
So the correct combination of people who are correct is **Anish and Giselle**.
However, since this specific combination is not listed in your responses, the best option that fits is **Giselle and Anish**.