Answer
$x\gt-\frac{3}{4} $
Work Step by Step
The given inequality is
$\Rightarrow -4(x+6)\lt 2(2x-9)$
Use distributive property.
$\Rightarrow -4x-24\lt 4x-18$
Add $18$ to each side.
$\Rightarrow -4x-24+18\lt 4x-18+18$
Simplify.
$\Rightarrow -4x-6\lt 4x$
Add $4x$ to each side.
$\Rightarrow -4x-6+4x\lt 4x+4x$
Simplify.
$\Rightarrow -6\lt 8x$
Divide each side by $8$.
$\Rightarrow \frac{-6}{8}\lt \frac{8x}{8}$
Simplify.
$\Rightarrow -\frac{3}{4}\lt x$
Hence, the solution is $x\gt-\frac{3}{4} $.
