Question

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

A. 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 .

B. 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 .

C. 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 .

D. Mary Ann adds −3 to both sides of the inequality and changes the inequality symbol to ≤ to get x≤9.

Answer 1

To solve the inequality \(-3x \geq 12\), Mary Ann needs to isolate \(x\). The correct steps involve dividing by a negative number, which requires a change in the inequality symbol.

Let's evaluate the options:

**A.** Mary Ann divides both sides of the inequality by −3 to get \(x \geq −4\).
- This statement is incorrect. Dividing by −3 should flip the inequality symbol.

**B.** Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get \(x ≤ −4\).
- This statement is correct! Dividing both sides by −3 gives \(x \leq -4\).

**C.** Mary Ann adds −3 to both sides of the inequality to get \(x \geq 9\).
- This statement is incorrect. Adding -3 does not isolate \(x\) properly and is not the appropriate operation.

**D.** Mary Ann adds −3 to both sides of the inequality and changes the inequality symbol to ≤ to get \(x ≤ 9\).
- This statement is incorrect. Adding -3 is not the correct step to solve the original inequality.

Therefore, the best response is:
**B.** Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get \(x ≤ −4\).