Question

solve the absolute value inequality.
\\(|3x - 3| < 6\\)

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: Rewrite absolute value inequality

$-6 < 3x - 3 < 6$

Step2: Add 3 to all parts

$-6 + 3 < 3x - 3 + 3 < 6 + 3$
$\implies -3 < 3x < 9$

Step3: Divide all parts by 3

$\frac{-3}{3} < \frac{3x}{3} < \frac{9}{3}$
$\implies -1 < x < 3$

Answer:

A. The solution set in interval notation is $(-1, 3)$