Answer
$ \frac{2}{3} < x < 2 $
Work Step by Step
1. Get rid of the absolute value. Since the absolute value must be less than 2, what is inside the absolute value brackets must be between -2 and 2.
So,
$|3x - 4| \lt 2$
$-2 \lt 3x -4 \lt 2$
2. Solve each side of the equation:
$-2 \lt 3x -4$
$2 \lt 3x$ (Add 4 to each side)
$\frac{2}{3} \lt x$ (divide each side by 3 to leave the x alone)
$3x -4 \lt 2$
$3x \lt 6$ (add 4 to each side)
$x \lt 2$ (divide each side by 3)
so:
$\frac{2}{3} \lt x \lt 2$
