Juana, Anish, and Giselle are comparing their solutions to the inequality 5/6x ≤ −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.
Anish is correct. The Multiplication Property of Inequality or Division Property of Inequality states that if we multiply or divide both sides of an inequality by a negative number, we must reverse the inequality symbol. In this case, we can divide both sides of the inequality 5/6x ≤ -10 by 5/6, but since 5/6 is positive, the inequality symbol does not need to be reversed. Thus, Giselle's statement is incorrect.
To solve the inequality 5/6x ≤ -10, let's consider the statements made by Juana, Anish, and Giselle.
1. Juana says that the inequality symbol must be reversed because there is a negative sign in the inequality.
- However, Juana's statement is incorrect. When multiplying or dividing both sides of an inequality by a negative number, the inequality symbol needs to be reversed. But in this case, we are multiplying by 5/6, which is a positive number, and not dividing by a negative number. Therefore, the inequality symbol should not be reversed.
2. Anish says the Multiplication Property of Inequality or Division Property of Inequality must be applied.
- Anish's statement is partially correct. Indeed, we need to apply the Multiplication Property of Inequality to solve this inequality. According to this property, if we multiply or divide both sides of an inequality by a positive number, then the direction of the inequality remains the same. Since we have 5/6 multiplied by x, a positive number, the inequality symbol should stay the same.
3. Giselle says the inequality symbol must stay the same.
- Giselle's statement is correct. As explained above, when we multiply both sides of an inequality by a positive number, the inequality symbol remains the same.
In conclusion, Anish's and Giselle's statements are correct. The inequality symbol must stay the same when solving the inequality 5/6x ≤ -10.