## Calculus (3rd Edition)

$\frac{2}{3} < x < 2$
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: $\frac{2}{3} \lt x \lt 2$