Answer
$-7\lt x\lt9$
Work Step by Step
The absolute value will keep the sign the same and the other side positive, and it will also flip the sign and make the other side negative. Solve for each inequality by dividing and multiplying both sides, and adding on both sides.
$|\frac{3(x-1)}{4}|\lt6$
$\frac{3(x-1)}{4}\lt6$
$x-1\lt8$
$x\lt9$
$\frac{3(x-1)}{4}\gt-6$
$x-1\gt-8$
$x\gt-7$
$-7\lt x\lt9$