The solution set of $$|3 - 4x| \geq 9$$​ is:

Correct option is A

Given:
​$$|3 - 4x| \geq 9 \\$$​​
Concept used :
Inequality of the form $$|A| \geq B \text{ implies } A \leq -B \text{ or } A \geq B \\$$​​

Solution:
​$$|3 - 4x| \geq 9 \Rightarrow \\3 - 4x \geq 9 \quad \text{or} \quad 3 - 4x \leq -9 \\$$​​
Case 1: $$\quad 3 - 4x \geq 9 \Rightarrow -4x \geq 6 \Rightarrow x \leq -\frac{3}{2} \\$$​​
Case 2: $$\quad 3 - 4x \leq -9 \Rightarrow -4x \leq -12 \Rightarrow x \geq 3 \\$$​​
So the solution set is: $$\quad x \in (-\infty, -\frac{3}{2}] \cup [3, \infty) \\$$​​
Correct answer is (a).