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

Question

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 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 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

Answer 1

The correct response that justifies the steps Mary Ann takes to solve 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≤−4.

This is because when dividing or multiplying both sides of an inequality by a negative number, we must reverse the inequality sign.

To break it down:

1. Start with the original inequality: \(-3x \geq 12\).
2. Divide both sides by \(-3\): \[ \frac{-3x}{-3} \quad \text{and} \quad \frac{12}{-3} \] This gives \(x \leq -4\).

So Mary Ann correctly identifies that by dividing by a negative number, she must flip the inequality sign, leading to the solution \(x \leq -4\).