Answer
$(-∞,\frac{-35}{6})$
Work Step by Step
$-3(2x-1) \lt -4[2+3(x+2)]$
Applying distributive property,
$-6x+3 \lt -4[2+3x+6]$
$-6x+3 \lt -4[8+3x]$
$-6x+3 \lt -32-12x$
Add $-3$ on both sides.
$-6x+3 -3 \lt -32-12x -3$
$-6x \lt -35-12x $
Add $12x$ on both sides.
$-6x+12x \lt -35-12x +12x$
$6x \lt -35$
Divide by 6 on both sides.
$x \lt \frac{-35}{6}$
In Interval notation : $(-∞,\frac{-35}{6})$