Mary Ann solves the inequality −3x≥12 . Justify the steps Mary Ann takes to find the solution set.(1 point) Responses Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x≤−4. Mary Ann divides both sides of the inequality by negative 3 and changes the inequality symbol to less-than-or-equal-to to get x less-than-or-equal-to negative 4 . Mary Ann divides both sides of the inequality by −3 to get x≥−4. Mary Ann divides both sides of the inequality by negative 3 to get x greater-than-or-equal-to negative 4 . Mary Ann adds −3 to both sides of the inequality to get x≥9. Mary Ann adds negative 3 to both sides of the inequality to get x greater-than-or-equal-to 9 . Mary Ann adds −3 to both sides of the inequality and changes the inequality symbol to ≤ to get x≤9. Mary Ann adds negative 3 to both sides of the inequality and changes the inequality symbol to less-than-or-equal-to to get x less-than-or-equal-to 9 .

Answer 1

The correct response regarding Mary Ann's solution to the inequality \(-3x \geq 12\) is:

Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get \(x \leq -4\).

This is justified because when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality symbol must be reversed.

Here’s a breakdown of the steps:

1. Start with the inequality: \(-3x \geq 12\).
2. Divide both sides by \(-3\). Remember to reverse the inequality sign: \[ x \leq \frac{12}{-3} \]
3. This simplifies to: \[ x \leq -4 \]

Thus, the solution set is \(x \leq -4\).