Mary Ann solves the inequality −3x≥12 . Justify the steps Mary Ann takes to find the solution set.(1 point)

Question

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 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 .

Answer 1

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

1. Divide by -3: To isolate \(x\), she needs to divide both sides of the inequality by \(-3\). However, it's crucial to remember that when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality symbol must be reversed.

2. Change the inequality symbol: After dividing both sides by \(-3\), the inequality \(-3x \geq 12\) becomes \(x \leq -4\).

So the correct response is:

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 to get x less-than-or-equal-to negative 4.