Answer
$(-7,9)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | \frac{3x-3}{4}\right |\lt6$
Rewrite the inequality without absolute value bars.
$\Rightarrow -6\lt \frac{3x-3}{4}\lt6$
Solve compound inequality.
Multiply all three parts by $4$.
$\Rightarrow -6(4)\lt \frac{3x-3}{4}(4)\lt6(4)$
Simplify.
$\Rightarrow -24\lt 3x-3\lt24$
Add $3$ to all three parts.
$\Rightarrow -24+3\lt 3x-3+3\lt24+3$
Simplify.
$\Rightarrow -21\lt 3x\lt27$
Divide by $3$ to all three parts.
$\Rightarrow \frac{-21}{3}\lt \frac{3x}{3}\lt\frac{27}{3}$
Simplify.
$\Rightarrow -7\lt x\lt9$
The solution set $(-7,9)$.
