Question

Question 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 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 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.

Answer 1

The correct justification for the steps Mary Ann takes to solve the inequality \(-3x \geq 12\) is as follows:

Mary Ann divides both sides of the inequality by \(-3\) to get \(x\). However, when dividing by a negative number, the direction of the inequality sign must be reversed. Therefore, she correctly has:

\[ x \leq -4 \]

So the most accurate response would be:

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

This indicates the correct handling of the negative divisor and the necessary change in the inequality direction.