Final answer:
The solution to the inequality -4|3x| > -12 is the set x , which does not match any of the provided options A-D. There may be an error in the question or options.
Step-by-step explanation:
To solve the inequality -4|3x| > -12, we can start by dividing both sides of the inequality by -4. Remember that dividing by a negative number reverses the inequality sign. So, after dividing, we get |3x| < 3. Now, we can remove the absolute value by setting up two separate inequalities: 3x < 3 and -3x < 3.
For 3x < 3, we divide both sides by 3 to get x < 1. For -3x < 3, we again divide both sides by -3 (remembering to reverse the inequality sign), which gives us x > -1.
Therefore, the solution in set builder notation is x . However, this solution is not represented in any of the provided options A through D. If this is an error in the question, the correct set builder notation is still as provided. If the options are correct, then there may be a mistake in copying the original inequality or in the provided options.