Mary Ann solves the inequality −3x≥12 . Justify the steps Mary Ann takes to find the solution set.(1 point) Responses 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 . 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 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 divides both sides of the inequality by −3 to get x≥−4.

Answer 1

To solve the inequality \(-3x \geq 12\), Mary Ann should follow these steps correctly:

1. Divide both sides by \(-3\): When dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

   \[ -3x \geq 12 \] Dividing both sides by \(-3\) gives: \[ x \leq -4 \]

2. Change the inequality symbol: Because we divided by a negative number, the inequality symbol changes from \(\geq\) to \(\leq\).

Thus, the correct response is:

Mary Ann divides both sides of the inequality by negative 3 and changes the inequality symbol to less-than-or-equal-to to get \(x \leq -4\).