Determine the smallest integer $x$ that satisfies the given inequality.

$3^{\sqrt{2 x}} > 32$
$x >$

$x^{\sqrt{3}} > 140$
$x >$

$8.7^{\sqrt{3 x}} > 31$
$x >$

$x^{\sqrt{\frac{3}{3}}} > 31$
$x >$