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 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.
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.

Answer 1

The correct response is:

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

Justification:

When solving inequalities, if you divide or multiply both sides of the inequality by a negative number, you must reverse the inequality symbol.

In this case, Mary Ann starts with the inequality \( -3x \geq 12 \).

1. She divides both sides by \(-3\): \[ \frac{-3x}{-3} \leq \frac{12}{-3} \] This simplifies to: \[ x \leq -4 \]

Therefore, the final solution is \( x \leq -4 \), and the inequality symbol was correctly reversed when dividing by a negative number.