Final answer:
The inequality -2|x-9| > 6 has no solution because absolute values cannot be less than a negative number, and the simplification leads to |x-9| < -3, which is not possible.
Step-by-step explanation:
To solve the inequality -2|x-9| > 6, we first divide both sides by -2, remembering to reverse the inequality sign because we are dividing by a negative number. This simplifies the inequality to |x-9| < -3. However, since absolute values are always non-negative, there is no real number x that will satisfy this inequality. Therefore, the inequality has no solution. Absolute values cannot be less than a negative number.