Answer
$x\gt\frac{8}{3}$
Work Step by Step
$\frac{1}{4}(x+4)\lt\frac{1}{5}(2x+3)$
$\frac{x}{4}+1\lt\frac{2x}{5}+\frac{3}{5}$
$\frac{x}{4}-\frac{2x}{5}+1-1\lt\frac{2x}{5}-\frac{2x}{5}+\frac{3}{5}-1$
$-\frac{3x}{20}\lt-\frac{2}{5}$
$x\gt\frac{8}{3}$