Question

solve the absolute value inequality
\\(|3x - 6| > 12\\)

select the correct choice below and, if necessary, fill in the answer box to complete your choice

\\(\bigcirc\\) a. the solution set in interval notation is \\(\square\\)
(simplify your answer )
\\(\bigcirc\\) b. the solution set is \\(\varnothing\\).

Explanation:

Step1: Split absolute value inequality

For $|3x-6|>12$, this translates to two inequalities:
$3x - 6 > 12$ or $3x - 6 < -12$

Step2: Solve first inequality

Isolate $x$ by adding 6, then divide by 3.
$3x > 12 + 6$
$3x > 18$
$x > \frac{18}{3}$
$x > 6$

Step3: Solve second inequality

Isolate $x$ by adding 6, then divide by 3.
$3x < -12 + 6$
$3x < -6$
$x < \frac{-6}{3}$
$x < -2$

Step4: Write in interval notation

Combine the two solution sets.
$(-\infty, -2) \cup (6, \infty)$

Answer:

A. The solution set in interval notation is $(-\infty, -2) \cup (6, \infty)$