Answer
$(\frac{9}{2}, ∞)$
Work Step by Step
$-2(4x+2) \gt -5[1+2(x-1)]$
Apply distributive property,
$-8x-4 \gt -5[1+2x-2]$
$-8x-4 \gt -5[2x-1]$
$-8x-4 \gt -10x+5$
Add $4 $ on both sides.
$-8x-4 +4\gt -10x+5+4$
$-8x \gt -10x+9$
Add $10x $ on both sides.
$-8x+10x \gt -10x+9+10x$
$2x \gt 9$
Divide by $2$ on both sides.
$x \gt \frac{9}{2}$
Interval Notation : $(\frac{9}{2}, ∞)$